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Find The Maximum Sum Subarray

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 8

Write a C# program to implement the MaximumSumSubarray(int[] arr, int k) function to find the maximum sum subarray of size K in a given array of integers. The algorithm should efficiently find the contiguous subarray of size K that has the maximum sum.

Example 1
    

  • Input: arr = [2, 1, 5, 1, 3, 2], K = 3
    • 

  • Output: 9
    • 

  • Explanation:

      

    • Step 1: Use a sliding window of size K = 3 to efficiently compute sums.

        

      • Window [2, 1, 5] has sum 8
        • 

      • Window [1, 5, 1] has sum 7
        • 

      • Window [5, 1, 3] has sum 9
        • 

      • Window [1, 3, 2] has sum 6
        • 

      

      • 

    • Step 2: Track the maximum sum encountered (9 from window [5, 1, 3]).
      • 

    • Step 3: Return the maximum sum, which is 9.
      • 

    •
Example 2
    

  • Input: arr = [1, 4, 2, 10, 23, 3, 1, 0, 20], K = 4
    • 

  • Output: 39
    • 

  • Explanation:

      

    • Step 1: Use a sliding window of size K = 4 to efficiently compute sums.

        

      • Window [1, 4, 2, 10] has sum 17
        • 

      • Window [4, 2, 10, 23] has sum 39
        • 

      • Window [2, 10, 23, 3] has sum 38
        • 

      • Window [10, 23, 3, 1] has sum 37
        • 

      • Window [23, 3, 1, 0] has sum 27
        • 

      • Window [3, 1, 0, 20] has sum 24
        • 

      

      • 

    • Step 2: Track the maximum sum encountered (39 from window [4, 2, 10, 23]).
      • 

    • Step 3: Return the maximum sum, which is 39.
      • 

    •
Constraints
    

  • 1 ≤ arr.length ≤ 10^5
    • 

  • -10^4 ≤ arr[i] ≤ 10^4
    • 

  • 1 ≤ K ≤ arr.length
    • 

  • Time Complexity: O(n) where n is the length of the input array
    • 

  • Space Complexity: O(1) using constant extra space
    •
ArraysKPMGSwiggy
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Hint
Solution

Solution Hints

    
  
  • Use the sliding window technique to avoid recalculation
    • 
  
  • Calculate the sum of first K elements
    • 
  
  • Slide the window by one element and keep updating the maximum sum
    • 
  
  • Avoid the brute force approach of recalculating the sum for each window
    •

Steps to solve by this approach:

 Step 1: Check if the array length is less than K. If so, return an error.

 Step 2: Calculate the sum of the first K elements in the array.

 Step 3: Initialize the maximum sum as the sum of the first window.

 Step 4: Slide the window by adding the next element and removing the first element of the previous window.

 Step 5: Update the maximum sum if the current window sum is greater.

 Step 6: Repeat steps 4-5 until the end of the array.

 Step 7: Return the maximum sum found.

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