Feature/maths

hashes/array_pairs_divisibility.py

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+"""
+check-if-array-pairs-are-divisible-by-k
+
+Problem statement:
+Given an array of integers arr of even length n and an integer k.
+
+Divide the array into n / 2 pairs such that the sum of each pair is divisible by k.
+
+Return true If you can find a way to do that or false otherwise.
+
+Example 1:
+
+Input: arr = [1,2,3,4,5,10,6,7,8,9], k = 5
+Output: true
+Explanation: Pairs are (1,9),(2,8),(3,7),(4,6) and (5,10).
+Example 2:
+
+Input: arr = [1,2,3,4,5,6], k = 7
+Output: true
+Explanation: Pairs are (1,6),(2,5) and(3,4).
+Example 3:
+
+Input: arr = [1,2,3,4,5,6], k = 10
+Output: false
+Explanation: You can try all possible pairs.
+See that there is no way to divide arr into 3 pairs each with sum divisible by 10.
+
+Constraints:
+
+arr.length == n
+1 <= n <= 105
+n is even.
+-109 <= arr[i] <= 109
+1 <= k <= 105
+"""
+
+# Time complexity: O(n)
+# Space complexity: O(k)
+
+# Approach:
+# 1. Create a list of size k with all elements as 0.
+# 2. For each element in the array, increment the element at index i%k.
+# 3. If the element at index 0 is odd, return False.
+# 4. Check if the number of elements at index i and k-i are equal.
+# 5. If not, return False.
+# 6. If all the conditions are satisfied, return True.
+
+
+class Solution:
+    def can_arrange(self, arr: list[int], input_num: int) -> bool:
+        """
+        Function to check if array pairs are divisible by k
+        :param arr: List of integers
+        :param k: Integer
+        :return: Boolean
+
+        Example:
+        >>> obj = Solution()
+        >>> obj.can_arrange([1, 2, 3, 4, 5, 10, 6, 7, 8, 9], 5)
+        True
+        >>> obj.can_arrange([1, 2, 3, 4, 5, 6], 7)
+        True
+        """
+        sol_arr = [0 for i in range(input_num)]
+        for i in arr:
+            sol_arr[i % input_num] += 1
+        if sol_arr[0] % 2 != 0:
+            return False
+        i, j = 1, input_num - 1
+        while j > i:
+            if sol_arr[i] == sol_arr[j]:
+                j -= 1
+                i += 1
+            else:
+                return False
+        return True
+
+
+# Driver code
+if __name__ == "__main__":
+    arr = [1, 2, 3, 4, 5, 10, 6, 7, 8, 9]
+    input_num = 5
+    s = Solution()
+    print(s.can_arrange(arr, input_num))  # Output: True

maths/reverse_polish.py

@@ -0,0 +1,94 @@
+"""
+evaluate-reverse-polish-notation
+
+Problem statement:
+Array of tokens that represents an arithmetic expression in Reverse Polish Notation.
+
+Evaluate the expression. Return an integer that represents the value of the expression.
+
+Note that:
+
+The valid operators are '+', '-', '*', and '/'.
+Each operand may be an integer or another expression.
+The division between two integers always truncates toward zero.
+There will not be any division by zero.
+The input represents a valid arithmetic expression in a reverse polish notation.
+The answer and all the intermediate calculations can be represented in a 32-bit integer.
+
+Example 1:
+
+Input: tokens = ["2","1","+","3","*"]
+Output: 9
+Explanation: ((2 + 1) * 3) = 9
+Example 2:
+
+Input: tokens = ["4","13","5","/","+"]
+Output: 6
+Explanation: (4 + (13 / 5)) = 6
+Example 3:
+
+Input: tokens = ["10","6","9","3","+","-11","*","/","*","17","+","5","+"]
+Output: 22
+Explanation: ((10 * (6 / ((9 + 3) * -11))) + 17) + 5
+= ((10 * (6 / (12 * -11))) + 17) + 5
+= ((10 * (6 / -132)) + 17) + 5
+= ((10 * 0) + 17) + 5
+= (0 + 17) + 5
+= 17 + 5
+= 22
+
+Constraints:
+
+1 <= tokens.length <= 104
+tokens[i] is an operator: "+", "-", "*", or "/".
+Or an integer in the range [-200, 200].
+"""
+
+
+class Solution:
+    def eval_rpn(self, tokens: list[str]) -> int:
+        """
+        Function to evaluate the reverse polish notation
+        :param tokens: List of strings
+        :return: int
+
+        Time complexity: O(n)
+        Space complexity: O(n)
+
+        Example:
+        >>> s = Solution()
+        >>> s.eval_rpn(["2","1","+","3","*"])
+        9
+        >>> s.eval_rpn(["4","13","5","/","+"])
+        6
+        """
+        s = []
+        for i in tokens:
+            if i not in ["+", "-", "*", "/"]:
+                s.append(int(i))
+            else:
+                b = s.pop()
+                a = s.pop()
+                if i == "+":
+                    s.append(a + b)
+                elif i == "-":
+                    s.append(a - b)
+                elif i == "*":
+                    s.append(a * b)
+                else:
+                    ele = abs(a) // abs(b)
+                    if a * b < 0:
+                        ele = -1 * ele
+                    s.append(ele)
+        return s.pop()
+
+
+if __name__ == "__main__":
+    s = Solution()
+    print(s.eval_rpn(["2", "1", "+", "3", "*"]))  # 9
+    print(s.eval_rpn(["4", "13", "5", "/", "+"]))  # 6
+    print(
+        s.eval_rpn(
+            ["10", "6", "9", "3", "+", "-11", "*", "/", "*", "17", "+", "5", "+"]
+        )
+    )  # 22