Maximum Subarray Sum Problem Statement Given an array of integers, determine the maximum possible sum of any contiguous subarray within the array. Example: Input: array = [34, -50, 42, 14, -5, 86] Output: 137 Explanation: The maximum sum is achieved by the subarray [42, 14, -5, 86]. Input: array = [-5, -1, -8, -9] Output: -1 Explanation: The maximum sum is -1, achieved by the subarray [-1]. Constraints: 1 ≤ N ≤ 10 6 , where N is the number of elements in the array. -10 4 ≤ array[i] ≤ 10 4 Note: The solution should have a time complexity of O(N). Input: The first line contains a single integer, N, the size of the array. The second line contains N space-separated integers representing the elements of the array. Output: A single integer, the maximum subarray sum.

Find the maximum sum of any contiguous subarray within an array of integers. Iterate through the array and keep track of the maximum sum of subarrays encountered so far. At each index, decide whether to include the current element in the subarray or start a new subarray. Use Kadane's algorithm to efficiently find the maximum subarray sum in O(N) time complexity.

To solve this problem in time, we can use Kadane's Algorithm. This algorithm efficiently computes the maximum sum of a contiguous subarray in linear time. Here's the step-by-step solution: Algorithm 1. Initialize two variables: max_sum to store the maximum sum encountered so far (initialize to the smallest possible integer). current_sum to store the sum of the current subarray (initialize to 0). 2. Iterate through the array: Add the current element to current_sum. Update max_sum if current_sum is greater than max_sum. If current_sum becomes negative, reset it to 0 (as continuing with a negative sum would not maximize the result). 3. The value of max_sum at the end is the maximum sum of any contiguous subarray. Python Implementation def max_subarray_sum(n, arr): max_sum = float('-inf') current_sum = 0 for num in arr: current_sum += num if current_sum > max_sum: max_sum = current_sum if current_sum < 0: current_sum = 0 return max_sum # Input handling n = int(input()) # Size of the array arr = list(map(int, input().split())) # Array elements # Output the result print(max_subarray_sum(n, arr)) Explanation of the Example 1. Input: 6 34 -50 42 14 -5 86 Running the algorithm: Step 1: current_sum = 34, max_sum = 34 Step 2: current_sum = -16, max_sum = 34 Step 3: current_sum = 42, max_sum = 42 Step 4: current_sum = 56, max_sum = 56 Step 5: current_sum = 51, max_sum = 56 Step 6: current_sum = 137, max_sum = 137 Output: 137 2. Input: 4 -5 -1 -8 -9 Running the algorithm: Step 1: current_sum = -5, max_sum = -5, reset current_sum = 0 Step 2: current_sum = -1, max_sum = -1, reset current_sum = 0 Step 3: current_sum = -8, max_sum = -1, reset current_sum = 0 Step 4: current_sum = -9, max_sum = -1, reset current_sum = 0 Output: -1

Maximum Subarray Sum Problem Statement Given an array of int

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Maximum Subarray Sum Problem Statement

Given an array of integers, determine the maximum possible sum of any contiguous subarray within the array.

Example:

Input:

array = [34, -50, 42, 14, -5, 86]

Output:

Explanation:

The maximum sum is achieved by the subarray [42, 14, -5, 86].

Input:

array = [-5, -1, -8, -9]

Output:

-1

Explanation:

The maximum sum is -1, achieved by the subarray [-1].

Constraints:

1 ≤ N ≤ 10⁶, where N is the number of elements in the array.
-10⁴ ≤ array[i] ≤ 10⁴

Note:

The solution should have a time complexity of O(N).

Input:

The first line contains a single integer, N, the size of the array. The second line contains N space-separated integers representing the elements of the array.

Output:

A single integer, the maximum subarray sum.

AnswerBot

4mo

Find the maximum sum of any contiguous subarray within an array of integers.

Iterate through the array and keep track of the maximum sum of subarrays encountered so far.
At each index, decide whether to...read more

Usha R reddy

3mo

-1

Rolex Sir

4mo

To solve this problem in time, we can use Kadane's Algorithm. This algorithm efficiently computes the maximum sum of a contiguous subarray in linear time. Here's the step-by-step solution: Algorithm 1...read more

Anonymous

4mo

-1