3446. Sort Matrix by Diagonals

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3446. Sort Matrix by Diagonals

Description

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 .

Example 1:

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Input: grid = [[1,7,3],[9,8,2],[4,5,6]]

Output: [[8,2,3],[9,6,7],[4,5,1]]

Explanation:

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:

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Input: grid = [[0,1],[1,2]]

Output: [[2,1],[1,0]]

Explanation:

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:

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Input: grid = [[1]]

Output: [[1]]

Explanation:

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

Hints/Notes

Solution

Language: C++

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class Solution {
public:
    vector<vector<int>> sortMatrix(vector<vector<int>>& grid) {
        int n = grid.size();
        vector<vector<int>> res(n, vector<int>(n));
        unordered_map<int, vector<int>> m;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                m[i - j].push_back(grid[i][j]);
            }
        }
        for (auto& [k, v] : m) {
            if (k < 0) {
                ranges::sort(v);
            } else {
                sort(v.begin(), v.end(), greater<int>());
            }
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                int val = m[i - j].front();
                m[i - j].erase(m[i - j].begin());
                res[i][j] = val;
            }
        }
        return res;
    }
};