Sort the Matrix Diagonally
A matrix diagonal is a diagonal line of cells starting from some cell in either the topmost row or leftmost column and going in the bottom-right direction until reaching the matrix's end. For example, the matrix diagonal starting from mat[2][0], where mat is a 6 x 3 matrix, includes cells mat[2][0], mat[3][1], and mat[4][2].
Given an m x n matrix mat of integers, sort each matrix diagonal in ascending order and return the resulting matrix.
Example 1
3 3 1 1 2 2 1 2 1 1 1 2
Input
mat = [[3,3,1,1],[2,2,1,2],[1,1,1,2]]Output
[[1,1,1,1],[1,2,2,2],[1,2,3,3]]After sorting every bottom-right diagonal in ascending order, the matrix becomes [[1,1,1,1],[1,2,2,2],[1,2,3,3]].
Example 2
11 25 66 1 69 7 23 55 17 45 15 52 75 31 36 44 58 8 22 27 33 25 68 4 84 28 14 11 5 50
Input
mat = [[11,25,66,1,69,7],[23,55,17,45,15,52],[75,31,36,44,58,8],[22,27,33,25,68,4],[84,28,14,11,5,50]]Output
[[5,17,4,1,52,7],[11,11,25,45,8,69],[14,23,25,44,58,15],[22,27,31,36,50,66],[84,28,75,33,55,68]]Each diagonal is sorted independently in ascending order to produce the returned matrix.
Constraints
- m == mat.length
- n == mat[i].length
- 1 <= m, n <= 100
- 1 <= mat[i][j] <= 100