Is Widest Pair of Indices With Equal Range Sum easy or hard?

The problem is typically classified as Medium. The brute force idea is simple, but recognizing that equal range sums translate into matching prefix differences requires familiarity with prefix sum patterns.

Widest Pair of Indices With Equal Range Sum Python/Java solution

Implement a single pass through both arrays while tracking the prefix difference between them. Store the first index of each difference in a dictionary or HashMap. When the same value reappears, compute the width and update the maximum result. The same logic applies across Python, Java, C++, Go, and TypeScript.

How to solve Widest Pair of Indices With Equal Range Sum in O(n)?

Maintain a running value diff = prefixSum(nums1) - prefixSum(nums2). Store the first index where each diff appears in a hash map. When the same diff occurs again at index j, compute the width using the earlier stored index. The widest such pair across the traversal is the answer.

What is the best approach for Widest Pair of Indices With Equal Range Sum?

The most efficient approach uses a prefix sum difference combined with a hash table. Track the running difference between prefix sums of nums1 and nums2 while iterating through the arrays. When the same difference appears again, the indices between them form a valid range with equal sums. This method runs in O(n) time and O(n) space.

Is Widest Pair of Indices With Equal Range Sum asked at Google/Amazon/Meta?

Problems based on prefix sums and hash maps frequently appear in interviews at companies like Amazon, Google, and Meta. Variants involving equal subarray sums, prefix differences, or longest matching ranges are common interview patterns.

What data structure is used in Widest Pair of Indices With Equal Range Sum?

The key data structure is a hash table that maps a prefix difference value to its earliest index. This allows constant-time lookups to determine whether the same difference has appeared before.

What is the time complexity of Widest Pair of Indices With Equal Range Sum?

The optimal solution runs in O(n) time because each index is processed once and hash table lookups are constant time. Space complexity is O(n) to store the earliest occurrence of each prefix difference value.

Description Hints 4 Solution Video 17:10

1983. Widest Pair of Indices With Equal Range Sum

Medium54.0% acceptance1 companyPremium elsewhere, free here

You are given two 0-indexed binary arrays nums1 and nums2. Find the widest pair of indices (i, j) such that i <= j and nums1[i] + nums1[i+1] + ... + nums1[j] == nums2[i] + nums2[i+1] + ... + nums2[j].

The widest pair of indices is the pair with the largest distance between i and j. The distance between a pair of indices is defined as j - i + 1.

Return the distance of the widest pair of indices. If no pair of indices meets the conditions, return 0.

Example 1:

Input: nums1 = [1,1,0,1], nums2 = [0,1,1,0]
Output: 3
Explanation:
If i = 1 and j = 3:
nums1[1] + nums1[2] + nums1[3] = 1 + 0 + 1 = 2.
nums2[1] + nums2[2] + nums2[3] = 1 + 1 + 0 = 2.
The distance between i and j is j - i + 1 = 3 - 1 + 1 = 3.

Example 2:

Input: nums1 = [0,1], nums2 = [1,1]
Output: 1
Explanation:
If i = 1 and j = 1:
nums1[1] = 1.
nums2[1] = 1.
The distance between i and j is j - i + 1 = 1 - 1 + 1 = 1.

Example 3:

Input: nums1 = [0], nums2 = [1]
Output: 0
Explanation:
There are no pairs of indices that meet the requirements.

Constraints:

n == nums1.length == nums2.length
1 <= n <= 10⁵
nums1[i] is either 0 or 1.
nums2[i] is either 0 or 1.

Asked at 1 company

Microsoft

Topics

Hints open one at a time

Hint 1

Keep prefix sums of both arrays.

Hint 2

Can the difference between the prefix sums at an index help us?

Hint 3

What happens if the difference between the two prefix sums at an index a is x, and x again at a different index b?

Hint 4

This means that the sum of nums1 from index a + 1 to index b is equal to the sum of nums2 from index a + 1 to index b.

17:10

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Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

[1,1,0,1]
[0,1,1,0]

Input

[0,1]
[1,1]

Input

[0]
[1]

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