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Find the Kth Smallest Sum of a Matrix With Sorted Rows - Practice Coding | SlaveCode

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

Hard

50 Points

Array

Binary Search

Heap (Priority Queue)

Matrix

You are given an m x n matrix mat that has its rows sorted in non-decreasing order and an integer k. You are allowed to choose exactly one element from each row to form an array. Return the kth smallest array sum among all possible arrays.

Examples

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.

Constraints

m == mat.length
n == mat.length[i]
1 <= m, n <= 40
1 <= mat[i][j] <= 5000
1 <= k <= min(200, nm)
mat[i] is a non-decreasing array.

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

Hard

50 Points

Array

Binary Search

Heap (Priority Queue)

Matrix

You are given an m x n matrix mat that has its rows sorted in non-decreasing order and an integer k. You are allowed to choose exactly one element from each row to form an array. Return the kth smallest array sum among all possible arrays.

Examples

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.

Constraints

m == mat.length
n == mat.length[i]
1 <= m, n <= 40
1 <= mat[i][j] <= 5000
1 <= k <= min(200, nm)
mat[i] is a non-decreasing array.