# https://leetcode.com/problems/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:
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]]

Example 2:
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]]


Constraints:
m == mat.length
n == mat[i].length
1 <= m, n <= 100
1 <= mat[i][j] <= 100
"""


def diagonal_sort(mat: list[list[int]]) -> list[list[int]]:
    rows, cols = len(mat), len(mat[0])
    ans = [[0] * cols for _ in range(rows)]
    starts = []
    # first row
    for col in range(cols):
        starts.append((0, col))
    # first col
    for row in range(1, rows):
        starts.append((row, 0))

    for r, c in starts:
        pos = []
        vals = []
        while r < rows and c < cols:
            pos.append((r, c))
            vals.append(mat[r][c])
            r += 1
            c += 1
        vals.sort()
        for (r, c), v in zip(pos, vals):
            ans[r][c] = v

    return ans
