1439. Find the Kth Smallest Sum of a Matrix With Sorted Rows

https://leetcode.com/problems/find-the-kth-smallest-sum-of-a-matrix-with-sorted-rows

Description

You are given an m * n matrix, mat, and an integer k, which has its rows sorted in non-decreasing order.

You are allowed to choose exactly 1 element from each row to form an array. Return the Kth smallest array sum among all possible arrays.

Example 1:

**Input:** mat = [[1,3,11],[2,4,6]], k = 5
**Output:** 7
**Explanation:** Choosing one element from each row, the first k smallest sum are:
[1,2], [1,4], [3,2], [3,4], [1,6]. Where the 5th sum is 7.  

Example 2:

**Input:** mat = [[1,3,11],[2,4,6]], k = 9
**Output:** 17

Example 3:

**Input:** mat = [[1,10,10],[1,4,5],[2,3,6]], k = 7
**Output:** 9
**Explanation:** Choosing one element from each row, the first k smallest sum are:
[1,1,2], [1,1,3], [1,4,2], [1,4,3], [1,1,6], [1,5,2], [1,5,3]. Where the 7th sum is 9.  

Example 4:

**Input:** mat = [[1,1,10],[2,2,9]], k = 7
**Output:** 12

Constraints:

• m == mat.length

• n == mat.length[i]

• 1 <= m, n <= 40

• 1 <= k <= min(200, n ^ m)

• 1 <= mat[i][j] <= 5000

• mat[i] is a non decreasing array.

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