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1477. Find Two Non-overlapping Sub-arrays Each With Target Sum (Medium)

You are given an array of integers arr and an integer target.

You have to find two non-overlapping sub-arrays of arr each with a sum equal target. There can be multiple answers so you have to find an answer where the sum of the lengths of the two sub-arrays is minimum.

Return the minimum sum of the lengths of the two required sub-arrays, or return -1 if you cannot find such two sub-arrays.

 

Example 1:

Input: arr = [3,2,2,4,3], target = 3
Output: 2
Explanation: Only two sub-arrays have sum = 3 ([3] and [3]). The sum of their lengths is 2.

Example 2:

Input: arr = [7,3,4,7], target = 7
Output: 2
Explanation: Although we have three non-overlapping sub-arrays of sum = 7 ([7], [3,4] and [7]), but we will choose the first and third sub-arrays as the sum of their lengths is 2.

Example 3:

Input: arr = [4,3,2,6,2,3,4], target = 6
Output: -1
Explanation: We have only one sub-array of sum = 6.

 

Constraints:

• 1 <= arr.length <= 105
• 1 <= arr[i] <= 1000
• 1 <= target <= 108

Related Topics

[Array] [Hash Table] [Binary Search] [Dynamic Programming] [Sliding Window]

Hints

Hint 1

Let's create two arrays prefix and suffix where prefix[i] is the minimum length of sub-array ends before i and has sum = k, suffix[i] is the minimum length of sub-array starting at or after i and has sum = k.

Hint 2

The answer we are searching for is min(prefix[i] + suffix[i]) for all values of i from 0 to n-1 where n == arr.length.

Hint 3

If you are still stuck with how to build prefix and suffix, you can store for each index i the length of the sub-array starts at i and has sum = k or infinity otherwise, and you can use it to build both prefix and suffix.