LeetCode 1983: Widest Pair of Indices With Equal Range Sum Solution

Master LeetCode problem 1983 (Widest Pair of Indices With Equal Range Sum), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

1983. Widest Pair of Indices With Equal Range Sum

Medium

Array Hash Table Prefix Sum

Problem Explanation

Explanation:

Given an array of integers nums, we need to find the widest pair of indices (i, j) such that i < j and the range sum between indices i and j is equal, i.e., sum(nums[i:k]) = sum(nums[k:j]) where i < k < j.

To solve this problem, we can iterate over all possible pairs of indices (i, j) and then for each pair, find the maximum value of k such that the range sum on both sides of k is equal. We can keep track of the widest pair of indices found so far.

Algorithm:

Initialize a variable maxWidth to store the width of the widest pair of indices found so far.
Iterate over all pairs of indices (i, j) such that i < j.
For each pair (i, j), iterate from i+1 to j-1 and find the maximum value of k such that sum(nums[i:k]) = sum(nums[k:j]).
Update maxWidth if the width of the current pair is greater than maxWidth.
Return maxWidth.

Time complexity:

The time complexity of this approach is O(n^2) where n is the size of the input array nums.

Space complexity:

The space complexity of this approach is O(1) as we are not using any extra space apart from a few variables.

: :

Solution Code

class Solution {
    public int widestPairOfIndicesWithEqualRangeSum(int[] nums) {
        int n = nums.length;
        int maxWidth = 0;
        
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                int k = i + 1;
                while (k < j && sum(nums, i, k) != sum(nums, k, j)) {
                    k++;
                }
                if (k < j) {
                    maxWidth = Math.max(maxWidth, j - i);
                }
            }
        }
        
        return maxWidth;
    }
    
    private int sum(int[] nums, int start, int end) {
        int sum = 0;
        for (int i = start; i < end; i++) {
            sum += nums[i];
        }
        return sum;
    }
}

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