DSAPROB21 - Editorial

editorial
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Problem Link - Finding the Subarray with Minimum Sum of Size K

Problem statement:
You are given an array of integers and you need to find a subarray of size K that has the minimum sum in all the subarray of size K.

Approach:
To solve this problem efficiently, we can use the sliding window technique. First, we calculate the sum of the first subarray of size K and keep that as our initial minimum sum. As we slide the window to the right, we update the sum by adding the next element and subtracting the element that is left behind. This allows us to maintain the sum of each subarray without recalculating it from scratch.

Step-by-Step Explanation:

  1. Initial Sum Calculation:
    Start by calculating the sum of the first K elements in the array. This gives us our initial sum to work with.

  2. Set Minimum Sum:
    Store this initial sum as the minimum sum encountered so far.

  3. Slide the Window:

    • Move the window one element to the right.
    • Add the new element that enters the window.
    • Subtract the element that is left behind (exits the window).

  4. Update Minimum Sum:
    After updating the sum for the current window, compare it with the minimum sum found so far. If the current sum is smaller, update the minimum sum.

  5. Repeat:
    Continue sliding the window across the array until you reach the end.

Time Complexity:
The time complexity is O(n), where n is the size of the array.

Space Complexity:
The space complexity is O(1), since we only use a few extra variables to keep track of the sum and the indices for the sliding window.