Sort Matrix by Diagonals

arraysortingmatrix

Problem Statement

You are given an n x n square matrix of integers grid . Return the matrix such that:

The diagonals in the bottom-left triangle (including the middle diagonal) are sorted in non-increasing order .

The diagonals in the top-right triangle are sorted in non-decreasing order .

Examples

Example 1

Input: grid = [[1,7,3],[9,8,2],[4,5,6]]
Output: [[8,2,3],[9,6,7],[4,5,1]]
The diagonals with a black arrow (bottom-left triangle) should be sorted in non-increasing order: 
 
 [1, 8, 6] becomes [8, 6, 1] . 
 [9, 5] and [4] remain unchanged. 
 
 The diagonals with a blue arrow (top-right triangle) should be sorted in non-decreasing order: 
 
 [7, 2] becomes [2, 7] . 
 [3] remains unchanged.

Example 2

Input: grid = [[0,1],[1,2]]
Output: [[2,1],[1,0]]
The diagonals with a black arrow must be non-increasing, so [0, 2] is changed to [2, 0] . The other diagonals are already in the correct order.

Example 3

Input: grid = [[1]]
Output: [[1]]
Diagonals with exactly one element are already in order, so no changes are needed.

Constraints

grid.length == grid[i].length == n

1 <= n <= 10

-10 ^5 <= grid[i][j] <= 10 ^5

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Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicSorting