From 3b8e93e0193fae823ac89fc6838b17739703054e Mon Sep 17 00:00:00 2001
From: Peyton <peytonstrahan@outlook.com>
Date: Thu, 12 Oct 2023 16:26:13 -0500
Subject: [PATCH 1/7] did 1-2 + 4

---
 src/recursion.js | 47 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 47 insertions(+)

diff --git a/src/recursion.js b/src/recursion.js
index 691d0ac99..5639c3353 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -5,11 +5,35 @@
 // Example:  5! = 5 x 4 x 3 x 2 x 1 = 120
 // factorial(5);  // 120
 var factorial = function(n) {
+  let nEx = n;//Creates a variable equal to the input variable
+  if(n < 0){//returns null if the input number is negative
+    return null;
+  }
+  if (n === 0){//checks if n is 0 and ends the function if it is
+    return 1;
+  }
+  else{
+    n = n - 1;//decreases the original variable by 1
+  }
+
+  return nEx * factorial(n);//recalls the function in a way that multiplies nEx by itself until n reaches 0
 };
 
 // 2. Compute the sum of an array of integers.
 // Example:  sum([1, 2, 3, 4, 5, 6]);  // 21
 var sum = function(array) {
+  let ara = [...array];//creates a new array with the contents of the input array
+  if(ara.length === 1){//returns the sum when the length of ara is condensed down to 1, ending the function
+    return ara[0];
+  }
+  if(ara.length < 1){//returns 0 when given an empty array
+    return 0;
+  }
+  if(ara.length > 1){//adds the front 2 numbers of an array, sets the result to the array's second number, and deletes the first number in the array
+    ara[1] = ara[0] + ara[1];
+    ara.shift();
+  }
+  return sum(ara);//recalls function to repeat the process
 };
 
 // 3. Sum all numbers in an array containing nested arrays.
@@ -19,12 +43,35 @@ var arraySum = function(array) {
 
 // 4. Check if a number is even.
 var isEven = function(n) {
+  if(n === 0){//returns true if the number is even (meaning the number has no remainder when divided by 2) and ends the function
+    return true;
+  }
+  else if (n === -1 || n === 1){//returns false if the number is odd (meaning the number has a remainder of -1 or 1 when divided by 2) and ends the function
+    return false;
+  }
+  if(n > 0){//decreases the number by 2 when it is greater than 0 and not 1
+    return isEven(n - 2);
+  }
+  else if (n < 0){//increases the number by 2 when it is lesser than 0 and not 1
+    return isEven(n + 2);
+  }
 };
 
 // 5. Sum all integers below a given integer.
 // sumBelow(10); // 45
 // sumBelow(7); // 21
 var sumBelow = function(n) {
+  let nEx = n;//Creates a variable equal to the input variable
+  if(n < 0){//returns null if the input number is negative
+    n = n + 1;
+  }
+  else{
+    n = n - 1;//decreases the original variable by 1
+  }
+  if (n === 0){//checks if n is 0 and ends the function if it is
+    return 1;
+  }
+  return nEx + sumBelow(n);//recalls the function in a way that adds nEx by itself until n reaches 0
 };
 
 // 6. Get the integers in range (x, y).

From 2c448d493973afa2684d8e5ae8e40be9fc4e95f5 Mon Sep 17 00:00:00 2001
From: SpecTrail <elijahiwatson2003@gmail.com>
Date: Fri, 13 Oct 2023 16:29:03 -0500
Subject: [PATCH 2/7]  Completed SumBelow & IntegerRange

---
 .vscode/settings.json |   3 +
 src/recursion.js      | 139 ++++++++++++++++++++++++++----------------
 2 files changed, 88 insertions(+), 54 deletions(-)
 create mode 100644 .vscode/settings.json

diff --git a/.vscode/settings.json b/.vscode/settings.json
new file mode 100644
index 000000000..aef844305
--- /dev/null
+++ b/.vscode/settings.json
@@ -0,0 +1,3 @@
+{
+  "liveServer.settings.port": 5501
+}
\ No newline at end of file
diff --git a/src/recursion.js b/src/recursion.js
index 5639c3353..323ec267b 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -4,15 +4,15 @@
 // denoted by n!, is the product of all positive integers less than or equal to n.
 // Example:  5! = 5 x 4 x 3 x 2 x 1 = 120
 // factorial(5);  // 120
-var factorial = function(n) {
+var factorial = function (n) {
   let nEx = n;//Creates a variable equal to the input variable
-  if(n < 0){//returns null if the input number is negative
+  if (n < 0) {//returns null if the input number is negative
     return null;
   }
-  if (n === 0){//checks if n is 0 and ends the function if it is
+  if (n === 0) {//checks if n is 0 and ends the function if it is
     return 1;
   }
-  else{
+  else {
     n = n - 1;//decreases the original variable by 1
   }
 
@@ -21,15 +21,15 @@ var factorial = function(n) {
 
 // 2. Compute the sum of an array of integers.
 // Example:  sum([1, 2, 3, 4, 5, 6]);  // 21
-var sum = function(array) {
+var sum = function (array) {
   let ara = [...array];//creates a new array with the contents of the input array
-  if(ara.length === 1){//returns the sum when the length of ara is condensed down to 1, ending the function
+  if (ara.length === 1) {//returns the sum when the length of ara is condensed down to 1, ending the function
     return ara[0];
   }
-  if(ara.length < 1){//returns 0 when given an empty array
+  if (ara.length < 1) {//returns 0 when given an empty array
     return 0;
   }
-  if(ara.length > 1){//adds the front 2 numbers of an array, sets the result to the array's second number, and deletes the first number in the array
+  if (ara.length > 1) {//adds the front 2 numbers of an array, sets the result to the array's second number, and deletes the first number in the array
     ara[1] = ara[0] + ara[1];
     ara.shift();
   }
@@ -38,21 +38,21 @@ var sum = function(array) {
 
 // 3. Sum all numbers in an array containing nested arrays.
 // Example: arraySum([1,[2,3],[[4]],5]); // 15
-var arraySum = function(array) {
+var arraySum = function (array) {
 };
 
 // 4. Check if a number is even.
-var isEven = function(n) {
-  if(n === 0){//returns true if the number is even (meaning the number has no remainder when divided by 2) and ends the function
+var isEven = function (n) {
+  if (n === 0) {//returns true if the number is even (meaning the number has no remainder when divided by 2) and ends the function
     return true;
   }
-  else if (n === -1 || n === 1){//returns false if the number is odd (meaning the number has a remainder of -1 or 1 when divided by 2) and ends the function
+  else if (n === -1 || n === 1) {//returns false if the number is odd (meaning the number has a remainder of -1 or 1 when divided by 2) and ends the function
     return false;
   }
-  if(n > 0){//decreases the number by 2 when it is greater than 0 and not 1
+  if (n > 0) {//decreases the number by 2 when it is greater than 0 and not 1
     return isEven(n - 2);
   }
-  else if (n < 0){//increases the number by 2 when it is lesser than 0 and not 1
+  else if (n < 0) {//increases the number by 2 when it is lesser than 0 and not 1
     return isEven(n + 2);
   }
 };
@@ -60,23 +60,41 @@ var isEven = function(n) {
 // 5. Sum all integers below a given integer.
 // sumBelow(10); // 45
 // sumBelow(7); // 21
-var sumBelow = function(n) {
-  let nEx = n;//Creates a variable equal to the input variable
-  if(n < 0){//returns null if the input number is negative
+var sumBelow = function (n) {
+  if (n === 0) {//checks if n is 0 and ends the function if it is
+    return 0;
+  }
+
+  if (n < 0) {//returns null if the input number is negative
     n = n + 1;
   }
-  else{
+  else {
     n = n - 1;//decreases the original variable by 1
   }
-  if (n === 0){//checks if n is 0 and ends the function if it is
-    return 1;
-  }
+
+  let nEx = n;//Creates a variable equal to the input variable
   return nEx + sumBelow(n);//recalls the function in a way that adds nEx by itself until n reaches 0
 };
 
 // 6. Get the integers in range (x, y).
 // Example:  range(2, 9);  // [3, 4, 5, 6, 7, 8]
-var range = function(x, y) {
+var range = function (x, y, arr = []) {
+
+  if (x === y) {
+    arr.pop()
+    console.log(arr)
+    return arr
+  }
+  if (x > y) {
+    x = x - 1
+    arr.push(x)
+  }
+  if (x < y) {
+    x = x + 1
+    arr.push(x)
+  }
+
+  return range(x, y, arr)
 };
 
 // 7. Compute the exponent of a number.
@@ -84,22 +102,35 @@ var range = function(x, y) {
 // 8^2 = 8 x 8 = 64.  Here, 8 is the base and 2 is the exponent.
 // Example:  exponent(4,3);  // 64
 // https://www.khanacademy.org/computing/computer-science/algorithms/recursive-algorithms/a/computing-powers-of-a-number
-var exponent = function(base, exp) {
-};
+var exponent = function (base, exp) {
+  if (exp === 0) {
+    return 1
+  }
+  if (exp === 1) {
+    return base
+  }
+  
+  if (exp > 0) {
+    return base * exponent(base, exp)
+  } else { 
+
+  }
+}
+
 
 // 8. Determine if a number is a power of two.
 // powerOfTwo(1); // true
 // powerOfTwo(16); // true
 // powerOfTwo(10); // false
-var powerOfTwo = function(n) {
+var powerOfTwo = function (n) {
 };
 
 // 9. Write a function that accepts a string a reverses it.
-var reverse = function(string) {
+var reverse = function (string) {
 };
 
 // 10. Write a function that determines if a string is a palindrome.
-var palindrome = function(string) {
+var palindrome = function (string) {
 };
 
 // 11. Write a function that returns the remainder of x divided by y without using the
@@ -107,18 +138,18 @@ var palindrome = function(string) {
 // modulo(5,2) // 1
 // modulo(17,5) // 2
 // modulo(22,6) // 4
-var modulo = function(x, y) {
+var modulo = function (x, y) {
 };
 
 // 12. Write a function that multiplies two numbers without using the * operator  or
 // JavaScript's Math object.
 // ATTENTION DO NOT LEAVE COMMENTS IN THIS FUNCTION. The test is looking for any ('/').
-var multiply = function(x, y) {
+var multiply = function (x, y) {
 };
 
 // 13. Write a function that divides two numbers without using the / operator  or
 // JavaScript's Math object.
-var divide = function(x, y) {
+var divide = function (x, y) {
 };
 
 // 14. Find the greatest common divisor (gcd) of two positive numbers.  The GCD of two
@@ -126,7 +157,7 @@ var divide = function(x, y) {
 // Example:  gcd(4,36);  // 4
 // http://www.cse.wustl.edu/~kjg/cse131/Notes/Recursion/recursion.html
 // https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/the-euclidean-algorithm
-var gcd = function(x, y) {
+var gcd = function (x, y) {
 };
 
 // 15. Write a function that compares each character of two strings and returns true if
@@ -134,12 +165,12 @@ var gcd = function(x, y) {
 // compareStr('house', 'houses') // false
 // compareStr('', '') // true
 // compareStr('tomato', 'tomato') // true
-var compareStr = function(str1, str2) {
+var compareStr = function (str1, str2) {
 };
 
 // 16. Write a function that accepts a string and creates an array where each letter
 // occupies an index of the array.
-var createArray = function(str){
+var createArray = function (str) {
 };
 
 // 17. Reverse the order of an array
@@ -149,37 +180,37 @@ var reverseArr = function (array) {
 // 18. Create a new array with a given value and length.
 // buildList(0,5) // [0,0,0,0,0]
 // buildList(7,3) // [7,7,7]
-var buildList = function(value, length) {
+var buildList = function (value, length) {
 };
 
 // 19. Count the occurence of a value inside a list.
 // countOccurrence([2,7,4,4,1,4], 4) // 3
 // countOccurrence([2,'banana',4,4,1,'banana'], 'banana') // 2
-var countOccurrence = function(array, value) {
+var countOccurrence = function (array, value) {
 };
 
 // 20. Write a recursive version of map.
 // rMap([1,2,3], timesTwo); // [2,4,6]
-var rMap = function(array, callback) {
+var rMap = function (array, callback) {
 };
 
 // 21. Write a function that counts the number of times a key occurs in an object.
 // var testobj = {'e': {'x':'y'}, 't':{'r': {'e':'r'}, 'p': {'y':'r'}},'y':'e'};
 // countKeysInObj(testobj, 'r') // 1
 // countKeysInObj(testobj, 'e') // 2
-var countKeysInObj = function(obj, key) {
+var countKeysInObj = function (obj, key) {
 };
 
 // 22. Write a function that counts the number of times a value occurs in an object.
 // var testobj = {'e': {'x':'y'}, 't':{'r': {'e':'r'}, 'p': {'y':'r'}},'y':'e'};
 // countValuesInObj(testobj, 'r') // 2
 // countValuesInObj(testobj, 'e') // 1
-var countValuesInObj = function(obj, value) {
+var countValuesInObj = function (obj, value) {
 };
 
 // 23. Find all keys in an object (and nested objects) by a provided name and rename
 // them to a provided new name while preserving the value stored at that key.
-var replaceKeysInObj = function(obj, key, newKey) {
+var replaceKeysInObj = function (obj, key, newKey) {
 };
 
 // 24. Get the first n Fibonacci numbers.  In the Fibonacci Sequence, each subsequent
@@ -187,7 +218,7 @@ var replaceKeysInObj = function(obj, key, newKey) {
 // Example:  0, 1, 1, 2, 3, 5, 8, 13, 21, 34.....
 // fibonacci(5);  // [0, 1, 1, 2, 3, 5]
 // Note:  The 0 is not counted.
-var fibonacci = function(n) {
+var fibonacci = function (n) {
 };
 
 // 25. Return the Fibonacci number located at index n of the Fibonacci sequence.
@@ -195,18 +226,18 @@ var fibonacci = function(n) {
 // nthFibo(5); // 5
 // nthFibo(7); // 13
 // nthFibo(3); // 2
-var nthFibo = function(n) {
+var nthFibo = function (n) {
 };
 
 // 26. Given an array of words, return a new array containing each word capitalized.
 // var words = ['i', 'am', 'learning', 'recursion'];
 // capitalizedWords(words); // ['I', 'AM', 'LEARNING', 'RECURSION']
-var capitalizeWords = function(input) {
+var capitalizeWords = function (input) {
 };
 
 // 27. Given an array of strings, capitalize the first letter of each index.
 // capitalizeFirst(['car', 'poop', 'banana']); // ['Car', 'Poop', 'Banana']
-var capitalizeFirst = function(array) {
+var capitalizeFirst = function (array) {
 };
 
 // 28. Return the sum of all even numbers in an object containing nested objects.
@@ -218,17 +249,17 @@ var capitalizeFirst = function(array) {
 //   e: {e: {e: 2}, ee: 'car'}
 // };
 // nestedEvenSum(obj1); // 10
-var nestedEvenSum = function(obj) {
+var nestedEvenSum = function (obj) {
 };
 
 // 29. Flatten an array containing nested arrays.
 // Example: flatten([1,[2],[3,[[4]]],5]); // [1,2,3,4,5]
-var flatten = function(arrays) {
+var flatten = function (arrays) {
 };
 
 // 30. Given a string, return an object containing tallies of each letter.
 // letterTally('potato'); // {'p':1, 'o':2, 't':2, 'a':1}
-var letterTally = function(str, obj) {
+var letterTally = function (str, obj) {
 };
 
 // 31. Eliminate consecutive duplicates in a list.  If the list contains repeated
@@ -236,51 +267,51 @@ var letterTally = function(str, obj) {
 // elements should not be changed.
 // Example: compress([1, 2, 2, 3, 4, 4, 5, 5, 5]) // [1, 2, 3, 4, 5]
 // Example: compress([1, 2, 2, 3, 4, 4, 2, 5, 5, 5, 4, 4]) // [1, 2, 3, 4, 2, 5, 4]
-var compress = function(list) {
+var compress = function (list) {
 };
 
 // 32. Augment every element in a list with a new value where each element is an array
 // itself.
 // Example: augmentElements([[],[3],[7]], 5); // [[5],[3,5],[7,5]]
-var augmentElements = function(array, aug) {
+var augmentElements = function (array, aug) {
 };
 
 // 33. Reduce a series of zeroes to a single 0.
 // minimizeZeroes([2,0,0,0,1,4]) // [2,0,1,4]
 // minimizeZeroes([2,0,0,0,1,0,0,4]) // [2,0,1,0,4]
-var minimizeZeroes = function(array) {
+var minimizeZeroes = function (array) {
 };
 
 // 34. Alternate the numbers in an array between positive and negative regardless of
 // their original sign.  The first number in the index always needs to be positive.
 // alternateSign([2,7,8,3,1,4]) // [2,-7,8,-3,1,-4]
 // alternateSign([-2,-7,8,3,-1,4]) // [2,-7,8,-3,1,-4]
-var alternateSign = function(array) {
+var alternateSign = function (array) {
 };
 
 // 35. Given a string, return a string with digits converted to their word equivalent.
 // Assume all numbers are single digits (less than 10).
 // numToText("I have 5 dogs and 6 ponies"); // "I have five dogs and six ponies"
-var numToText = function(str) {
+var numToText = function (str) {
 };
 
 // *** EXTRA CREDIT ***
 
 // 36. Return the number of times a tag occurs in the DOM.
-var tagCount = function(tag, node) {
+var tagCount = function (tag, node) {
 };
 
 // 37. Write a function for binary search.
 // Sample array:  [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
 // console.log(binarySearch(5)) will return '5'
 
-var binarySearch = function(array, target, min, max) {
+var binarySearch = function (array, target, min, max) {
 };
 
 // 38. Write a merge sort function.
 // Sample array:  [34,7,23,32,5,62]
 // Sample output: [5,7,23,32,34,62]
-var mergeSort = function(array) {
+var mergeSort = function (array) {
 };
 
 

From ca674622a6a9ce9ed7efa99e471178ec65167e1b Mon Sep 17 00:00:00 2001
From: Peyton <peytonstrahan@outlook.com>
Date: Mon, 16 Oct 2023 16:27:54 -0500
Subject: [PATCH 3/7] got up to 10

---
 src/recursion.js | 76 +++++++++++++++++++++++++++++++++++++++++++-----
 1 file changed, 69 insertions(+), 7 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index 323ec267b..8bc13c19f 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -82,7 +82,7 @@ var range = function (x, y, arr = []) {
 
   if (x === y) {
     arr.pop()
-    console.log(arr)
+    //console.log(arr)
     return arr
   }
   if (x > y) {
@@ -111,9 +111,10 @@ var exponent = function (base, exp) {
   }
   
   if (exp > 0) {
-    return base * exponent(base, exp)
+    return base * exponent(base, exp - 1)
   } else { 
-
+    let bain = base / exponent(base, exp + 1)
+    return 1 / bain;
   }
 }
 
@@ -122,16 +123,58 @@ var exponent = function (base, exp) {
 // powerOfTwo(1); // true
 // powerOfTwo(16); // true
 // powerOfTwo(10); // false
-var powerOfTwo = function (n) {
+var powerOfTwo = function (n, x = n, y = 2) {
+  //console.log("n: " + n + " x: " + x + " y: " + y)
+  if(n === 1){
+    return true;
+  }
+  if (y === n) {
+    return true;
+  }
+  else if (x === 0){
+    return false;
+  }
+  if (x > 0) {
+    y = y * 2
+    x--
+  } 
+  return powerOfTwo(n, x, y);
 };
 
 // 9. Write a function that accepts a string a reverses it.
-var reverse = function (string) {
+var reverse = function (string, x = string.length, gnirts = "") {
+  //console.log(gnirts);
+  if (x === 0){
+    //console.log(gnirts);
+    return gnirts;
+  }
+  if (x > 0){
+    x--;
+    gnirts = gnirts + string[x];
+  }
+  return reverse(string, x, gnirts);
 };
 
 // 10. Write a function that determines if a string is a palindrome.
-var palindrome = function (string) {
+var palindrome = function (string, x = string.replace(/\s/g, "").length, gnirts = "") {
+  //console.log(gnirts);
+  //console.log(string.toLowerCase());
+  gnirts = gnirts.replace(/\s/g, "").toLowerCase();
+  string = string.replace(/\s/g, "").toLowerCase();
+  //console.log(gnirts);
+
+  if (x === 0){
+    //console.log(gnirts);
+    //console.log(string);
+    return gnirts === string;
+  }
+  if (x > 0){
+    x--;
+    gnirts = gnirts + string[x];
+  }
+  return palindrome(string, x, gnirts);
 };
+//console.log(palindrome('Rotor'));
 
 // 11. Write a function that returns the remainder of x divided by y without using the
 // modulo (%) operator.
@@ -144,7 +187,26 @@ var modulo = function (x, y) {
 // 12. Write a function that multiplies two numbers without using the * operator  or
 // JavaScript's Math object.
 // ATTENTION DO NOT LEAVE COMMENTS IN THIS FUNCTION. The test is looking for any ('/').
-var multiply = function (x, y) {
+var multiply = function (x, y, holder1 = x, holder2 = y) {
+  if (x === 1){
+    return y;
+  }
+  if (y === 0 || x === 0){
+    return 0;
+  }
+  if (y === 1){
+    return x;
+  }
+  x = x + holder1
+  y--
+  let answer = multiply(x, y, holder1, holder2);
+  if ((holder1 < 0 && holder2 > 0) || (holder2 < 0 && holder1 > 0)){
+    console.log(answer)
+  answer = (answer - answer) - answer
+  return answer
+  } else {
+    return answer;
+  }
 };
 
 // 13. Write a function that divides two numbers without using the / operator  or

From c0d99555af24b81e9b9012fdecc8e1786d0f74e7 Mon Sep 17 00:00:00 2001
From: SpecTrail <elijahiwatson2003@gmail.com>
Date: Tue, 17 Oct 2023 16:31:04 -0500
Subject: [PATCH 4/7]  working on multiply

---
 src/recursion.js | 36 ++++++++++++++++++++----------------
 1 file changed, 20 insertions(+), 16 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index 8bc13c19f..9396b1823 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -109,10 +109,10 @@ var exponent = function (base, exp) {
   if (exp === 1) {
     return base
   }
-  
+
   if (exp > 0) {
     return base * exponent(base, exp - 1)
-  } else { 
+  } else {
     let bain = base / exponent(base, exp + 1)
     return 1 / bain;
   }
@@ -125,30 +125,30 @@ var exponent = function (base, exp) {
 // powerOfTwo(10); // false
 var powerOfTwo = function (n, x = n, y = 2) {
   //console.log("n: " + n + " x: " + x + " y: " + y)
-  if(n === 1){
+  if (n === 1) {
     return true;
   }
   if (y === n) {
     return true;
   }
-  else if (x === 0){
+  else if (x === 0) {
     return false;
   }
   if (x > 0) {
     y = y * 2
     x--
-  } 
+  }
   return powerOfTwo(n, x, y);
 };
 
 // 9. Write a function that accepts a string a reverses it.
 var reverse = function (string, x = string.length, gnirts = "") {
   //console.log(gnirts);
-  if (x === 0){
+  if (x === 0) {
     //console.log(gnirts);
     return gnirts;
   }
-  if (x > 0){
+  if (x > 0) {
     x--;
     gnirts = gnirts + string[x];
   }
@@ -163,12 +163,12 @@ var palindrome = function (string, x = string.replace(/\s/g, "").length, gnirts
   string = string.replace(/\s/g, "").toLowerCase();
   //console.log(gnirts);
 
-  if (x === 0){
+  if (x === 0) {
     //console.log(gnirts);
     //console.log(string);
     return gnirts === string;
   }
-  if (x > 0){
+  if (x > 0) {
     x--;
     gnirts = gnirts + string[x];
   }
@@ -188,22 +188,26 @@ var modulo = function (x, y) {
 // JavaScript's Math object.
 // ATTENTION DO NOT LEAVE COMMENTS IN THIS FUNCTION. The test is looking for any ('/').
 var multiply = function (x, y, holder1 = x, holder2 = y) {
-  if (x === 1){
+
+  if (x === 1) {
     return y;
   }
-  if (y === 0 || x === 0){
+  if (y === 0 || x === 0) {
     return 0;
   }
-  if (y === 1){
+  if (y === 1) {
     return x;
   }
   x = x + holder1
   y--
+  
   let answer = multiply(x, y, holder1, holder2);
-  if ((holder1 < 0 && holder2 > 0) || (holder2 < 0 && holder1 > 0)){
-    console.log(answer)
-  answer = (answer - answer) - answer
-  return answer
+
+  if (holder2 < 0 && holder1 > 0) {
+
+    answer = (answer - answer) - answer
+    return answer
+
   } else {
     return answer;
   }

From 51474ae0b8c380f29ad642bac88051dea90a2208 Mon Sep 17 00:00:00 2001
From: Peyton <peytonstrahan@outlook.com>
Date: Wed, 18 Oct 2023 16:26:25 -0500
Subject: [PATCH 5/7] Just 2 problems left

---
 src/recursion.js | 177 ++++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 151 insertions(+), 26 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index 9396b1823..0b6b175a4 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -189,28 +189,34 @@ var modulo = function (x, y) {
 // ATTENTION DO NOT LEAVE COMMENTS IN THIS FUNCTION. The test is looking for any ('/').
 var multiply = function (x, y, holder1 = x, holder2 = y) {
 
-  if (x === 1) {
+  if (x === 1 || x === -1) {
     return y;
   }
   if (y === 0 || x === 0) {
     return 0;
   }
-  if (y === 1) {
-    return x;
+  if (y === 1 || y === -1) {
+    if (holder2 < 0 && holder1 > 0) {
+      console.log("fdivfjnsh poo")
+      x = (x - x) - x
+      return x
+  
+    } else if (holder2 > 0 && holder1 < 0 || holder2 > 0 && holder1 > 0){
+      return x;
+    } else if (holder2 < 0 && holder1 < 0){
+      x = (x - x) - x
+      return x
+    }
   }
   x = x + holder1
-  y--
+  if(y < 0){
+    y++
+  }else if(y > 0){
+    y--
+  }
   
   let answer = multiply(x, y, holder1, holder2);
-
-  if (holder2 < 0 && holder1 > 0) {
-
-    answer = (answer - answer) - answer
-    return answer
-
-  } else {
-    return answer;
-  }
+  return answer;
 };
 
 // 13. Write a function that divides two numbers without using the / operator  or
@@ -231,33 +237,89 @@ var gcd = function (x, y) {
 // compareStr('house', 'houses') // false
 // compareStr('', '') // true
 // compareStr('tomato', 'tomato') // true
-var compareStr = function (str1, str2) {
+var compareStr = function (str1, str2, i = 0) {
+  // if(str1.length !== str2.length){
+  //   return false
+  // }
+  if (str1[i] === str2[i]){
+    i++
+    if(str1.length >= str2.length){
+      if(i >= str1.length){
+        return true;
+      }
+    }
+
+    if(str1.length < str2.length){
+      if(i >= str2.length){
+        return true;
+      }
+    }
+    return compareStr(str1, str2, i)
+  }else{
+    return false
+  }
 };
 
 // 16. Write a function that accepts a string and creates an array where each letter
 // occupies an index of the array.
-var createArray = function (str) {
+var createArray = function (str, newArr = [], i = 0) {
+  newArr.push(str[i]);
+  if (str[i] === str[str.length - 1]){
+    return newArr;
+  }
+  i++
+  return createArray(str, newArr, i);
 };
 
 // 17. Reverse the order of an array
-var reverseArr = function (array) {
+var reverseArr = function (array, x = array.length, yarra = []) {
+  //console.log(gnirts);
+  if (x === 0) {
+    //console.log(gnirts);
+    return yarra;
+  }
+  if (x > 0) {
+    x--;
+    yarra.push(array[x]);
+  }
+  return reverseArr(array, x, yarra);
 };
 
 // 18. Create a new array with a given value and length.
 // buildList(0,5) // [0,0,0,0,0]
 // buildList(7,3) // [7,7,7]
-var buildList = function (value, length) {
+var buildList = function (value, length, newArr = []) {
+  if(length === 0){
+    return newArr;
+  }
+  newArr.push(value);
+  length--
+  return buildList(value, length, newArr);
 };
 
 // 19. Count the occurence of a value inside a list.
 // countOccurrence([2,7,4,4,1,4], 4) // 3
 // countOccurrence([2,'banana',4,4,1,'banana'], 'banana') // 2
-var countOccurrence = function (array, value) {
+var countOccurrence = function (array, value, i = 0, count = 0) {
+  if(array[i] === value){
+    count++
+  }
+  if(i === array.length - 1){
+    return count;
+  }
+  i++
+  return countOccurrence(array, value, i, count)
 };
 
 // 20. Write a recursive version of map.
 // rMap([1,2,3], timesTwo); // [2,4,6]
-var rMap = function (array, callback) {
+var rMap = function (array, callback, i = 0, newArr = []) {
+  newArr.push(callback(array[i]))
+  if(i === array.length - 1){
+    return newArr;
+  }
+  i++
+  return rMap(array, callback, i, newArr)
 };
 
 // 21. Write a function that counts the number of times a key occurs in an object.
@@ -292,18 +354,41 @@ var fibonacci = function (n) {
 // nthFibo(5); // 5
 // nthFibo(7); // 13
 // nthFibo(3); // 2
-var nthFibo = function (n) {
+var nthFibo = function (n, newArr = [0,1], i = 1) {
+  if(n < 0){
+    return null;
+  }
+  newArr.push(newArr[newArr.length - 1] + newArr[newArr.length - 2])
+  i++
+if(i >= n){
+  return newArr[n];
+}
+return nthFibo(n, newArr, i)
 };
 
 // 26. Given an array of words, return a new array containing each word capitalized.
 // var words = ['i', 'am', 'learning', 'recursion'];
 // capitalizedWords(words); // ['I', 'AM', 'LEARNING', 'RECURSION']
-var capitalizeWords = function (input) {
+var capitalizeWords = function (input, i = 0) {
+  if(i === input.length){
+    return input
+  }
+  input[i] = input[i].toUpperCase();
+  i++
+  return capitalizeWords(input, i)
 };
 
 // 27. Given an array of strings, capitalize the first letter of each index.
 // capitalizeFirst(['car', 'poop', 'banana']); // ['Car', 'Poop', 'Banana']
-var capitalizeFirst = function (array) {
+var capitalizeFirst = function (array, i = 0) {
+  if(i === array.length){
+    return array
+  }
+  let word = array[i];
+  console.log(word)
+  array[i] = word[0].toUpperCase() + word.substring(1);
+  i++
+  return capitalizeFirst(array, i)
 };
 
 // 28. Return the sum of all even numbers in an object containing nested objects.
@@ -325,7 +410,17 @@ var flatten = function (arrays) {
 
 // 30. Given a string, return an object containing tallies of each letter.
 // letterTally('potato'); // {'p':1, 'o':2, 't':2, 'a':1}
-var letterTally = function (str, obj) {
+var letterTally = function (str, obj = {}, i = 0) {
+  if(i === str.length){
+    return obj;
+  }
+  if(!obj[str[i]]){
+    obj[str[i]] = 1
+  } else{
+    obj[str[i]]++
+  }
+  i++
+  return letterTally(str, obj, i)
 };
 
 // 31. Eliminate consecutive duplicates in a list.  If the list contains repeated
@@ -333,7 +428,22 @@ var letterTally = function (str, obj) {
 // elements should not be changed.
 // Example: compress([1, 2, 2, 3, 4, 4, 5, 5, 5]) // [1, 2, 3, 4, 5]
 // Example: compress([1, 2, 2, 3, 4, 4, 2, 5, 5, 5, 4, 4]) // [1, 2, 3, 4, 2, 5, 4]
-var compress = function (list) {
+var compress = function (list, i = 0, obj = {}) {
+  if(i === list.length){
+    return list
+  }
+  if(!obj[list[i]]){
+    obj[list[i]] = 1
+    i++
+  } else if(list[i] !== list[i - 1]){
+    obj[list[i]]++
+    i++
+  }
+  else{
+    obj[list[i]]++
+    list.splice(i,1);
+  }
+  return compress(list, i, obj)
 };
 
 // 32. Augment every element in a list with a new value where each element is an array
@@ -345,14 +455,29 @@ var augmentElements = function (array, aug) {
 // 33. Reduce a series of zeroes to a single 0.
 // minimizeZeroes([2,0,0,0,1,4]) // [2,0,1,4]
 // minimizeZeroes([2,0,0,0,1,0,0,4]) // [2,0,1,0,4]
-var minimizeZeroes = function (array) {
+var minimizeZeroes = function (array, i = 0, obj = {}) {
+  if(i === array.length){
+    return array
+  }
+  if(!obj[array[i]] && array[i] === 0){
+    obj[array[i]] = 1
+    i++
+  }
+  else if(array[i] === 0 && array[i-1] === 0){
+    obj[array[i]]++
+    array.splice(i,1);
+  } else{
+    i++
+  }
+  return minimizeZeroes(array, i, obj)
 };
 
 // 34. Alternate the numbers in an array between positive and negative regardless of
 // their original sign.  The first number in the index always needs to be positive.
 // alternateSign([2,7,8,3,1,4]) // [2,-7,8,-3,1,-4]
 // alternateSign([-2,-7,8,3,-1,4]) // [2,-7,8,-3,1,-4]
-var alternateSign = function (array) {
+var alternateSign = function (array, i = 0) {
+  return alternateSign(array, i)
 };
 
 // 35. Given a string, return a string with digits converted to their word equivalent.

From 40bff3c5f04cd503d503a582eb697eb1203563d5 Mon Sep 17 00:00:00 2001
From: SpecTrail <elijahiwatson2003@gmail.com>
Date: Thu, 19 Oct 2023 16:10:43 -0500
Subject: [PATCH 6/7]  completed recursion-prompts

---
 src/recursion.js | 112 ++++++++++++++++++++++++++++++-----------------
 1 file changed, 71 insertions(+), 41 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index 0b6b175a4..4aaba25e0 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -197,24 +197,24 @@ var multiply = function (x, y, holder1 = x, holder2 = y) {
   }
   if (y === 1 || y === -1) {
     if (holder2 < 0 && holder1 > 0) {
-      console.log("fdivfjnsh poo")
+
       x = (x - x) - x
       return x
-  
-    } else if (holder2 > 0 && holder1 < 0 || holder2 > 0 && holder1 > 0){
+
+    } else if (holder2 > 0 && holder1 < 0 || holder2 > 0 && holder1 > 0) {
       return x;
-    } else if (holder2 < 0 && holder1 < 0){
+    } else if (holder2 < 0 && holder1 < 0) {
       x = (x - x) - x
       return x
     }
   }
   x = x + holder1
-  if(y < 0){
+  if (y < 0) {
     y++
-  }else if(y > 0){
+  } else if (y > 0) {
     y--
   }
-  
+
   let answer = multiply(x, y, holder1, holder2);
   return answer;
 };
@@ -241,21 +241,21 @@ var compareStr = function (str1, str2, i = 0) {
   // if(str1.length !== str2.length){
   //   return false
   // }
-  if (str1[i] === str2[i]){
+  if (str1[i] === str2[i]) {
     i++
-    if(str1.length >= str2.length){
-      if(i >= str1.length){
+    if (str1.length >= str2.length) {
+      if (i >= str1.length) {
         return true;
       }
     }
 
-    if(str1.length < str2.length){
-      if(i >= str2.length){
+    if (str1.length < str2.length) {
+      if (i >= str2.length) {
         return true;
       }
     }
     return compareStr(str1, str2, i)
-  }else{
+  } else {
     return false
   }
 };
@@ -264,7 +264,7 @@ var compareStr = function (str1, str2, i = 0) {
 // occupies an index of the array.
 var createArray = function (str, newArr = [], i = 0) {
   newArr.push(str[i]);
-  if (str[i] === str[str.length - 1]){
+  if (str[i] === str[str.length - 1]) {
     return newArr;
   }
   i++
@@ -289,7 +289,7 @@ var reverseArr = function (array, x = array.length, yarra = []) {
 // buildList(0,5) // [0,0,0,0,0]
 // buildList(7,3) // [7,7,7]
 var buildList = function (value, length, newArr = []) {
-  if(length === 0){
+  if (length === 0) {
     return newArr;
   }
   newArr.push(value);
@@ -301,10 +301,10 @@ var buildList = function (value, length, newArr = []) {
 // countOccurrence([2,7,4,4,1,4], 4) // 3
 // countOccurrence([2,'banana',4,4,1,'banana'], 'banana') // 2
 var countOccurrence = function (array, value, i = 0, count = 0) {
-  if(array[i] === value){
+  if (array[i] === value) {
     count++
   }
-  if(i === array.length - 1){
+  if (i === array.length - 1) {
     return count;
   }
   i++
@@ -315,7 +315,7 @@ var countOccurrence = function (array, value, i = 0, count = 0) {
 // rMap([1,2,3], timesTwo); // [2,4,6]
 var rMap = function (array, callback, i = 0, newArr = []) {
   newArr.push(callback(array[i]))
-  if(i === array.length - 1){
+  if (i === array.length - 1) {
     return newArr;
   }
   i++
@@ -354,23 +354,23 @@ var fibonacci = function (n) {
 // nthFibo(5); // 5
 // nthFibo(7); // 13
 // nthFibo(3); // 2
-var nthFibo = function (n, newArr = [0,1], i = 1) {
-  if(n < 0){
+var nthFibo = function (n, newArr = [0, 1], i = 1) {
+  if (n < 0) {
     return null;
   }
   newArr.push(newArr[newArr.length - 1] + newArr[newArr.length - 2])
   i++
-if(i >= n){
-  return newArr[n];
-}
-return nthFibo(n, newArr, i)
+  if (i >= n) {
+    return newArr[n];
+  }
+  return nthFibo(n, newArr, i)
 };
 
 // 26. Given an array of words, return a new array containing each word capitalized.
 // var words = ['i', 'am', 'learning', 'recursion'];
 // capitalizedWords(words); // ['I', 'AM', 'LEARNING', 'RECURSION']
 var capitalizeWords = function (input, i = 0) {
-  if(i === input.length){
+  if (i === input.length) {
     return input
   }
   input[i] = input[i].toUpperCase();
@@ -381,11 +381,11 @@ var capitalizeWords = function (input, i = 0) {
 // 27. Given an array of strings, capitalize the first letter of each index.
 // capitalizeFirst(['car', 'poop', 'banana']); // ['Car', 'Poop', 'Banana']
 var capitalizeFirst = function (array, i = 0) {
-  if(i === array.length){
+  if (i === array.length) {
     return array
   }
   let word = array[i];
-  console.log(word)
+
   array[i] = word[0].toUpperCase() + word.substring(1);
   i++
   return capitalizeFirst(array, i)
@@ -411,12 +411,12 @@ var flatten = function (arrays) {
 // 30. Given a string, return an object containing tallies of each letter.
 // letterTally('potato'); // {'p':1, 'o':2, 't':2, 'a':1}
 var letterTally = function (str, obj = {}, i = 0) {
-  if(i === str.length){
+  if (i === str.length) {
     return obj;
   }
-  if(!obj[str[i]]){
+  if (!obj[str[i]]) {
     obj[str[i]] = 1
-  } else{
+  } else {
     obj[str[i]]++
   }
   i++
@@ -429,19 +429,19 @@ var letterTally = function (str, obj = {}, i = 0) {
 // Example: compress([1, 2, 2, 3, 4, 4, 5, 5, 5]) // [1, 2, 3, 4, 5]
 // Example: compress([1, 2, 2, 3, 4, 4, 2, 5, 5, 5, 4, 4]) // [1, 2, 3, 4, 2, 5, 4]
 var compress = function (list, i = 0, obj = {}) {
-  if(i === list.length){
+  if (i === list.length) {
     return list
   }
-  if(!obj[list[i]]){
+  if (!obj[list[i]]) {
     obj[list[i]] = 1
     i++
-  } else if(list[i] !== list[i - 1]){
+  } else if (list[i] !== list[i - 1]) {
     obj[list[i]]++
     i++
   }
-  else{
+  else {
     obj[list[i]]++
-    list.splice(i,1);
+    list.splice(i, 1);
   }
   return compress(list, i, obj)
 };
@@ -456,17 +456,17 @@ var augmentElements = function (array, aug) {
 // minimizeZeroes([2,0,0,0,1,4]) // [2,0,1,4]
 // minimizeZeroes([2,0,0,0,1,0,0,4]) // [2,0,1,0,4]
 var minimizeZeroes = function (array, i = 0, obj = {}) {
-  if(i === array.length){
+  if (i === array.length) {
     return array
   }
-  if(!obj[array[i]] && array[i] === 0){
+  if (!obj[array[i]] && array[i] === 0) {
     obj[array[i]] = 1
     i++
   }
-  else if(array[i] === 0 && array[i-1] === 0){
+  else if (array[i] === 0 && array[i - 1] === 0) {
     obj[array[i]]++
-    array.splice(i,1);
-  } else{
+    array.splice(i, 1);
+  } else {
     i++
   }
   return minimizeZeroes(array, i, obj)
@@ -477,13 +477,43 @@ var minimizeZeroes = function (array, i = 0, obj = {}) {
 // alternateSign([2,7,8,3,1,4]) // [2,-7,8,-3,1,-4]
 // alternateSign([-2,-7,8,3,-1,4]) // [2,-7,8,-3,1,-4]
 var alternateSign = function (array, i = 0) {
+  if (i === array.length) {
+    return array
+  }
+
+  if (i === 0 && array[i] < 0) {
+    array[i] = array[i] * -1
+  } else if (array[i - 1] < 0 && array[i] < 0) {
+    array[i] = array[i] * -1
+  } else if (array[i - 1] > 0 && array[i] > 0) {
+    array[i] = array[i] * -1
+  }
+  i++
   return alternateSign(array, i)
 };
 
 // 35. Given a string, return a string with digits converted to their word equivalent.
 // Assume all numbers are single digits (less than 10).
 // numToText("I have 5 dogs and 6 ponies"); // "I have five dogs and six ponies"
-var numToText = function (str) {
+var numToText = function (str, i = 0) {
+  if (i === str.length) {
+    return str
+  }
+  str = str.replace(1, 'one')
+  str = str.replace(2, 'two')
+  str = str.replace(3, 'three')
+  str = str.replace(4, 'four')
+  str = str.replace(5, 'five')
+  str = str.replace(6, 'six')
+  str = str.replace(7, 'seven')
+  str = str.replace(8, 'eight')
+  str = str.replace(9, 'nine')
+  str = str.replace(0, 'zero')
+
+  if (i < str.length) {
+    i++
+    return numToText(str, i)
+  }
 };
 
 // *** EXTRA CREDIT ***

From 822801f8f69c77f6d9ba8a9ff8b8f9b701275dc2 Mon Sep 17 00:00:00 2001
From: Peyton <peytonstrahan@outlook.com>
Date: Fri, 20 Oct 2023 15:13:48 -0500
Subject: [PATCH 7/7] added comments

---
 src/recursion.js | 183 ++++++++++++++++++++++++-----------------------
 1 file changed, 92 insertions(+), 91 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index 4aaba25e0..458376a22 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -80,21 +80,21 @@ var sumBelow = function (n) {
 // Example:  range(2, 9);  // [3, 4, 5, 6, 7, 8]
 var range = function (x, y, arr = []) {
 
-  if (x === y) {
+  if (x === y) { //when x becomes equal to y, the end of the array is chopped off and the function ends
     arr.pop()
     //console.log(arr)
     return arr
   }
-  if (x > y) {
+  if (x > y) { //decreases x and pushes its value into the new array until x equals y
     x = x - 1
     arr.push(x)
   }
-  if (x < y) {
+  if (x < y) { //increases x and pushes its value into the new array until x equals y
     x = x + 1
     arr.push(x)
   }
 
-  return range(x, y, arr)
+  return range(x, y, arr) //recalls function
 };
 
 // 7. Compute the exponent of a number.
@@ -103,18 +103,18 @@ var range = function (x, y, arr = []) {
 // Example:  exponent(4,3);  // 64
 // https://www.khanacademy.org/computing/computer-science/algorithms/recursive-algorithms/a/computing-powers-of-a-number
 var exponent = function (base, exp) {
-  if (exp === 0) {
+  if (exp === 0) { //returns 1 when given an exponent of 0 (ends function)
     return 1
   }
-  if (exp === 1) {
+  if (exp === 1) { //returns base to the recall function in order to create and return the multiplied number (ends function)
     return base
   }
 
-  if (exp > 0) {
+  if (exp > 0) { //recalls function when the exponent is above 0 and not 1, resulting in the base number getting repeatedly multiplied by itself
     return base * exponent(base, exp - 1)
-  } else {
+  } else {//recalls function when the exponent is under 0, resulting in the base number getting repeatedly divided by itself
     let bain = base / exponent(base, exp + 1)
-    return 1 / bain;
+    return 1 / bain; //returns 1 divided by the new number to get the correct result
   }
 }
 
@@ -125,34 +125,34 @@ var exponent = function (base, exp) {
 // powerOfTwo(10); // false
 var powerOfTwo = function (n, x = n, y = 2) {
   //console.log("n: " + n + " x: " + x + " y: " + y)
-  if (n === 1) {
+  if (n === 1) {//returns true if the input is one (a power of two that's less than two)
     return true;
   }
-  if (y === n) {
+  if (y === n) {//returns true if the input is a power of two
     return true;
   }
-  else if (x === 0) {
+  else if (x === 0) {//returns false and ends the function if the input ends up not being a power of two
     return false;
   }
-  if (x > 0) {
+  if (x > 0) { //multiplies y by 2 over and over again until it equals the input or the x counter reaches 0
     y = y * 2
     x--
   }
-  return powerOfTwo(n, x, y);
+  return powerOfTwo(n, x, y);//recalls the function
 };
 
 // 9. Write a function that accepts a string a reverses it.
 var reverse = function (string, x = string.length, gnirts = "") {
   //console.log(gnirts);
-  if (x === 0) {
+  if (x === 0) {//returns the new string and ends the function when x reaches 0
     //console.log(gnirts);
     return gnirts;
   }
-  if (x > 0) {
+  if (x > 0) {//decreases x by 1 and adds the character at position x in the input string to the new string (resulting in the characters being added to the new string in reverse order)
     x--;
     gnirts = gnirts + string[x];
   }
-  return reverse(string, x, gnirts);
+  return reverse(string, x, gnirts);//recalls function
 };
 
 // 10. Write a function that determines if a string is a palindrome.
@@ -160,19 +160,19 @@ var palindrome = function (string, x = string.replace(/\s/g, "").length, gnirts
   //console.log(gnirts);
   //console.log(string.toLowerCase());
   gnirts = gnirts.replace(/\s/g, "").toLowerCase();
-  string = string.replace(/\s/g, "").toLowerCase();
+  string = string.replace(/\s/g, "").toLowerCase();//These two lines of code gets rid of all of the spaces and un-capitalizes any capital letters in both the input and new strings
   //console.log(gnirts);
 
-  if (x === 0) {
+  if (x === 0) {//returns an expression resolving to either true or false (based on whether or not the new backwards string equals the input string) after x reaches 0
     //console.log(gnirts);
     //console.log(string);
     return gnirts === string;
   }
-  if (x > 0) {
+  if (x > 0) {//decreases x by 1 and adds the character at position x in the input string to the new string (resulting in the characters being added to the new string in reverse order)
     x--;
     gnirts = gnirts + string[x];
   }
-  return palindrome(string, x, gnirts);
+  return palindrome(string, x, gnirts);//recalls function
 };
 //console.log(palindrome('Rotor'));
 
@@ -187,6 +187,7 @@ var modulo = function (x, y) {
 // 12. Write a function that multiplies two numbers without using the * operator  or
 // JavaScript's Math object.
 // ATTENTION DO NOT LEAVE COMMENTS IN THIS FUNCTION. The test is looking for any ('/').
+//This function adds x to itself over and over again to replicate multiplication
 var multiply = function (x, y, holder1 = x, holder2 = y) {
 
   if (x === 1 || x === -1) {
@@ -241,21 +242,21 @@ var compareStr = function (str1, str2, i = 0) {
   // if(str1.length !== str2.length){
   //   return false
   // }
-  if (str1[i] === str2[i]) {
+  if (str1[i] === str2[i]) {//checks if the current character in both strings are identical and moves on to the next one if they are
     i++
-    if (str1.length >= str2.length) {
+    if (str1.length >= str2.length) {//returns true and ends the function when the length of the longer input string becomes less than or equal to the i counter
       if (i >= str1.length) {
         return true;
       }
     }
 
-    if (str1.length < str2.length) {
+    if (str1.length < str2.length) {//returns true and ends the function when the length of the longer input string becomes less than or equal to the i counter
       if (i >= str2.length) {
         return true;
       }
     }
-    return compareStr(str1, str2, i)
-  } else {
+    return compareStr(str1, str2, i)//recalls function
+  } else {//returns false if and when two characters in the same place in the two input strings don't match up
     return false
   }
 };
@@ -263,63 +264,63 @@ var compareStr = function (str1, str2, i = 0) {
 // 16. Write a function that accepts a string and creates an array where each letter
 // occupies an index of the array.
 var createArray = function (str, newArr = [], i = 0) {
-  newArr.push(str[i]);
-  if (str[i] === str[str.length - 1]) {
+  newArr.push(str[i]);//pushes the currently selected letter into the new array
+  if (str[i] === str[str.length - 1]) {//returns the new array and ends the function when all letters have been added to the array
     return newArr;
   }
-  i++
-  return createArray(str, newArr, i);
+  i++//increases the i counter
+  return createArray(str, newArr, i);//recalls function
 };
 
 // 17. Reverse the order of an array
 var reverseArr = function (array, x = array.length, yarra = []) {
   //console.log(gnirts);
-  if (x === 0) {
+  if (x === 0) {//returns new array and ends function when said new array has finished being created
     //console.log(gnirts);
     return yarra;
   }
-  if (x > 0) {
+  if (x > 0) {//pushes the data from the input array (from back to front) to the new array (from front to back)
     x--;
     yarra.push(array[x]);
   }
-  return reverseArr(array, x, yarra);
+  return reverseArr(array, x, yarra);//recalls function
 };
 
 // 18. Create a new array with a given value and length.
 // buildList(0,5) // [0,0,0,0,0]
 // buildList(7,3) // [7,7,7]
 var buildList = function (value, length, newArr = []) {
-  if (length === 0) {
+  if (length === 0) {//ends the function and returns the new array when length reaches 0
     return newArr;
   }
-  newArr.push(value);
-  length--
-  return buildList(value, length, newArr);
+  newArr.push(value);//adds another value to the new array
+  length--//decreases length by 1
+  return buildList(value, length, newArr);//recalls function
 };
 
 // 19. Count the occurence of a value inside a list.
 // countOccurrence([2,7,4,4,1,4], 4) // 3
 // countOccurrence([2,'banana',4,4,1,'banana'], 'banana') // 2
 var countOccurrence = function (array, value, i = 0, count = 0) {
-  if (array[i] === value) {
+  if (array[i] === value) {//increases the count by 1 when the desired value is found
     count++
   }
-  if (i === array.length - 1) {
+  if (i === array.length - 1) {//ends the function and returns count when the entire array has been looked through
     return count;
   }
-  i++
-  return countOccurrence(array, value, i, count)
+  i++//increases the i counter by 1
+  return countOccurrence(array, value, i, count)//recalls function
 };
 
 // 20. Write a recursive version of map.
 // rMap([1,2,3], timesTwo); // [2,4,6]
 var rMap = function (array, callback, i = 0, newArr = []) {
-  newArr.push(callback(array[i]))
-  if (i === array.length - 1) {
+  newArr.push(callback(array[i]))//runs each value of the input array through the inputted function and pushes the results into the new array
+  if (i === array.length - 1) {//ends the function and returns the new array
     return newArr;
   }
-  i++
-  return rMap(array, callback, i, newArr)
+  i++//increases the i counter by 1
+  return rMap(array, callback, i, newArr)//recalls function
 };
 
 // 21. Write a function that counts the number of times a key occurs in an object.
@@ -354,41 +355,41 @@ var fibonacci = function (n) {
 // nthFibo(5); // 5
 // nthFibo(7); // 13
 // nthFibo(3); // 2
-var nthFibo = function (n, newArr = [0, 1], i = 1) {
-  if (n < 0) {
+var nthFibo = function (n, newArr = [0, 1], i = 1) {//the new array starts with the first 2 numbers of the Fibo sequence and the i counter starts at 1 as a result
+  if (n < 0) {//returns null when the input number is negative
     return null;
   }
-  newArr.push(newArr[newArr.length - 1] + newArr[newArr.length - 2])
-  i++
-  if (i >= n) {
+  newArr.push(newArr[newArr.length - 1] + newArr[newArr.length - 2])//adds the values of the last two numbers in the array and pushes the result onto the end of said array
+  i++//increases i counter by 1
+  if (i >= n) {//base case
     return newArr[n];
   }
-  return nthFibo(n, newArr, i)
+  return nthFibo(n, newArr, i)//recursive case
 };
 
 // 26. Given an array of words, return a new array containing each word capitalized.
 // var words = ['i', 'am', 'learning', 'recursion'];
 // capitalizedWords(words); // ['I', 'AM', 'LEARNING', 'RECURSION']
 var capitalizeWords = function (input, i = 0) {
-  if (i === input.length) {
+  if (i === input.length) {//base case
     return input
   }
-  input[i] = input[i].toUpperCase();
-  i++
-  return capitalizeWords(input, i)
+  input[i] = input[i].toUpperCase();//runs each word in the input array through the .toUpperCase function, which capitalizes all of the letters in each word
+  i++//increases the i counter by 1
+  return capitalizeWords(input, i)//recursive case
 };
 
 // 27. Given an array of strings, capitalize the first letter of each index.
 // capitalizeFirst(['car', 'poop', 'banana']); // ['Car', 'Poop', 'Banana']
 var capitalizeFirst = function (array, i = 0) {
-  if (i === array.length) {
+  if (i === array.length) {//base case
     return array
   }
-  let word = array[i];
-
-  array[i] = word[0].toUpperCase() + word.substring(1);
-  i++
-  return capitalizeFirst(array, i)
+  let word = array[i];//creates a new variable equal to the first letter in the currently selected word from the input array
+//It may be a good idea to rename the word variable to be the letter variable instead, which makes more sense.
+  array[i] = word[0].toUpperCase() + word.substring(1);//capitalizes the word variable, removes the first letter from the currently selected word, and adds the capitalized letter (word variable) to the front of the word
+  i++//increases the i counter by 1
+  return capitalizeFirst(array, i)//recursive case
 };
 
 // 28. Return the sum of all even numbers in an object containing nested objects.
@@ -411,16 +412,16 @@ var flatten = function (arrays) {
 // 30. Given a string, return an object containing tallies of each letter.
 // letterTally('potato'); // {'p':1, 'o':2, 't':2, 'a':1}
 var letterTally = function (str, obj = {}, i = 0) {
-  if (i === str.length) {
+  if (i === str.length) {//base case
     return obj;
   }
-  if (!obj[str[i]]) {
+  if (!obj[str[i]]) {//creates a counter key-value pair for the currently-selected character if one doesn't already exist in the object
     obj[str[i]] = 1
-  } else {
+  } else {//adds 1 to the counter when another instance of a character is found
     obj[str[i]]++
   }
-  i++
-  return letterTally(str, obj, i)
+  i++//increases the i counter by 1
+  return letterTally(str, obj, i)//recursive case
 };
 
 // 31. Eliminate consecutive duplicates in a list.  If the list contains repeated
@@ -429,21 +430,21 @@ var letterTally = function (str, obj = {}, i = 0) {
 // Example: compress([1, 2, 2, 3, 4, 4, 5, 5, 5]) // [1, 2, 3, 4, 5]
 // Example: compress([1, 2, 2, 3, 4, 4, 2, 5, 5, 5, 4, 4]) // [1, 2, 3, 4, 2, 5, 4]
 var compress = function (list, i = 0, obj = {}) {
-  if (i === list.length) {
+  if (i === list.length) {//base case
     return list
   }
-  if (!obj[list[i]]) {
+  if (!obj[list[i]]) {//creates a counter key-value pair for the currently-selected character if one doesn't already exist in the object
     obj[list[i]] = 1
-    i++
-  } else if (list[i] !== list[i - 1]) {
+    i++//increases the i counter by 1
+  } else if (list[i] !== list[i - 1]) {//adds 1 to the counter when another instance of a character is found and said instance isn't one that came right after another instance of the same character
     obj[list[i]]++
-    i++
+    i++//increases the i counter by 1
   }
-  else {
+  else {//removes the character when it is determined to be a consecutive duplicate
     obj[list[i]]++
     list.splice(i, 1);
   }
-  return compress(list, i, obj)
+  return compress(list, i, obj)//recursive case
 };
 
 // 32. Augment every element in a list with a new value where each element is an array
@@ -456,20 +457,20 @@ var augmentElements = function (array, aug) {
 // minimizeZeroes([2,0,0,0,1,4]) // [2,0,1,4]
 // minimizeZeroes([2,0,0,0,1,0,0,4]) // [2,0,1,0,4]
 var minimizeZeroes = function (array, i = 0, obj = {}) {
-  if (i === array.length) {
+  if (i === array.length) {//base case
     return array
   }
-  if (!obj[array[i]] && array[i] === 0) {
+  if (!obj[array[i]] && array[i] === 0) {//creates a counter for 0 if one doesn't exist already
     obj[array[i]] = 1
     i++
   }
-  else if (array[i] === 0 && array[i - 1] === 0) {
-    obj[array[i]]++
+  else if (array[i] === 0 && array[i - 1] === 0) {//removes the 0 from the array if it occurs right after another 0
+    obj[array[i]]++//adds 1 to the 0 counter
     array.splice(i, 1);
   } else {
-    i++
+    i++//increases the i counter by 1
   }
-  return minimizeZeroes(array, i, obj)
+  return minimizeZeroes(array, i, obj)//recursive case
 };
 
 // 34. Alternate the numbers in an array between positive and negative regardless of
@@ -477,31 +478,31 @@ var minimizeZeroes = function (array, i = 0, obj = {}) {
 // alternateSign([2,7,8,3,1,4]) // [2,-7,8,-3,1,-4]
 // alternateSign([-2,-7,8,3,-1,4]) // [2,-7,8,-3,1,-4]
 var alternateSign = function (array, i = 0) {
-  if (i === array.length) {
+  if (i === array.length) {//base case
     return array
   }
 
-  if (i === 0 && array[i] < 0) {
+  if (i === 0 && array[i] < 0) {//forces the first number in the array to be positive
     array[i] = array[i] * -1
-  } else if (array[i - 1] < 0 && array[i] < 0) {
+  } else if (array[i - 1] < 0 && array[i] < 0) {//compares the current number and the one that came before it and changes the sign of the second value if the values are both negative
     array[i] = array[i] * -1
-  } else if (array[i - 1] > 0 && array[i] > 0) {
+  } else if (array[i - 1] > 0 && array[i] > 0) {//compares the current number and the one that came before it and changes the sign of the second value if the values are both positive
     array[i] = array[i] * -1
   }
-  i++
-  return alternateSign(array, i)
+  i++//increases the i counter by 1
+  return alternateSign(array, i)//recursive case
 };
 
 // 35. Given a string, return a string with digits converted to their word equivalent.
 // Assume all numbers are single digits (less than 10).
 // numToText("I have 5 dogs and 6 ponies"); // "I have five dogs and six ponies"
 var numToText = function (str, i = 0) {
-  if (i === str.length) {
+  if (i === str.length) {//base case
     return str
   }
-  str = str.replace(1, 'one')
-  str = str.replace(2, 'two')
-  str = str.replace(3, 'three')
+  str = str.replace(1, 'one')//each of these replaces any instance of a number in the string with their letter-based counterpart
+  str = str.replace(2, 'two')//recursion isn't really needed as these check the whole string at once, but trying to check the string one word at a time proved to be problematic.
+  str = str.replace(3, 'three')//though this can probably be improved with code that checks if the currently selected character is a number and then runs the replace code on the whole string for the number and replaces said number with the corresponding string from an array
   str = str.replace(4, 'four')
   str = str.replace(5, 'five')
   str = str.replace(6, 'six')
@@ -511,8 +512,8 @@ var numToText = function (str, i = 0) {
   str = str.replace(0, 'zero')
 
   if (i < str.length) {
-    i++
-    return numToText(str, i)
+    i++//increases the i counter by 1
+    return numToText(str, i)//recursive case
   }
 };