[SunaDu] Week 3

combination-sum/dusunax.py

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+'''
+# 39. Combination Sum
+
+Backtracking for find combinations.
+
+## Time and Space Complexity
+
+```
+TC: O(n^2)
+SC: O(n)
+```
+
+#### TC is O(n^2):
+- iterating through the list in backtracking recursion to find combinations. = O(n^2)
+
+#### SC is O(n):
+- using a list to store the combinations. = O(n)
+'''
+
+class Solution:
+    # Backtracking = find combination
+    # candidate is distinct & can use multiple times.
+    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
+        result = []  
+
+        def backtrack(currIdx, remain, combination):
+            if(remain == 0):
+                result.append(combination[:])
+                return
+            if(remain < 0):
+                return
+
+            for i in range(currIdx, len(candidates)):
+                combination.append(candidates[i])
+                backtrack(i, remain - candidates[i], combination) 
+                combination.pop()
+
+        backtrack(0, target, [permutations])
+        return result

maximum-subarray/dusunax.py

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+'''
+# 53. Maximum Subarray
+
+- use Kadane's Algorithm for efficiently finding the maximum subarray sum.
+
+## Time and Space Complexity
+
+```
+TC: O(n)
+SC: O(1)
+```
+
+#### TC is O(n):
+- iterating through the list just once to find the maximum subarray sum. = O(n)
+
+#### SC is O(1):
+- using a constant amount of extra space to store the current sum and the maximum sum. = O(1)
+'''
+
+class Solution:
+    def maxSubArray(self, nums: List[int]) -> int:
+        if len(nums) == 1:
+            return nums[0]
+
+        currentSum = 0 # SC: O(1)
+        maxSum = nums[0] # SC: O(1)
+
+        for i in range(len(nums)): # TC: O(n)
+            currentSum = max(currentSum + nums[i], nums[i]) # TC: O(1)
+
+            if currentSum > maxSum: # TC: O(1)
+                maxSum = currentSum
+
+        return maxSum

product-of-array-except-self/dusunax.py

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+'''
+# 238. Product of Array Except Self
+
+use prefix and suffix to calculate the product of the array, except self.
+
+## Time and Space Complexity
+
+```
+TC: O(n)
+SC: O(n)
+```
+
+### TC is O(n):
+- iterating through the list twice, to calculate both prefix and suffix products. = O(n)
+
+### SC is O(n):
+- storing the prefix and suffix in the answer list. = O(n)
+'''
+class Solution:
+    def productExceptSelf(self, nums: List[int]) -> List[int]:
+        n = len(nums)
+        answer = [1] * n
+
+        # prefix
+        for i in range(1, n):
+            answer[i] *= nums[i - 1] * answer[i - 1]
+
+        # suffix
+        suffix_product = 1
+        for i in range(n - 1, -1, -1):
+            answer[i] *= suffix_product
+            suffix_product *= nums[i]
+
+        return answer

reverse-bits/dusunax.py

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+'''
+# 190. Reverse Bits
+
+SolutionA: using bin() and int() to convert the types.
+SolutionB: using bitwise operations to reverse the bits.
+
+## Time and Space Complexity
+
+### SolutionA
+```
+TC: O(32) -> O(1)
+SC: O(1)
+```
+
+### SolutionB
+```
+TC: O(32) -> O(1)
+SC: O(1)
+```
+'''
+class Solution:
+    '''
+    SolutionA
+    - using bin() and int() to convert the number to binary and back to integer.
+    - use .zfill(32) ensures that the binary string is always 32 bits long.
+    '''
+    def reverseBitsA(self, n: int) -> int:
+        bit = bin(n)[2:].zfill(32)
+        return int(bit[::-1], 2)
+
+    '''
+    SolutionB
+    - using bitwise operations to reverse the bits.
+    - iterate through the bits and reverse them.
+    '''
+    def reverseBitsB(self, n: int) -> int:
+        result = 0
+        for i in range(32):
+            result = (result << 1) | (n & 1) # shift the result to the left & add LSB of n
+            n >>= 1 # shift n to the right & remove previous LSB
+        return result

two-sum/dusunax.py

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+'''
+# 1. Two Sum
+
+use a hash map to store the numbers and their indices.
+iterate through the list and check if the complement of the current number (target - nums[i]) is in the hash map.
+
+(assume that each input would have exactly one solution)
+- if it is a pairNum, return the indices of the two numbers.
+- if it is not, add the current number and its index to the hash map.
+
+
+## Time and Space Complexity
+
+```
+TC: O(n)
+SC: O(n)
+```
+
+#### TC is O(n):
+- iterating through the list just once to find the two numbers. = O(n)
+
+#### SC is O(n):
+- using a hash map to store the numbers and their indices. = O(n)
+'''
+
+class Solution:
+    def twoSum(self, nums: List[int], target: int) -> List[int]:
+        map = {}
+        for i in range(len(nums)):
+            pairNum = target - nums[i]
+            if pairNum in map:
+                return [map.get(pairNum), i]
+            map[nums[i]] = i