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Sort Matrix Diagonals By Their Values | Capital One Coding Question

Quick Overview

Practice a matrix diagonal sorting problem that scans bottom-left to top-right diagonals and returns indexes ordered by their diagonal strings. The prompt targets careful indexing, deterministic tie-breaking, and translating a geometric traversal into reliable code.

Quick Overview

Sort Matrix Diagonals By Their Values

Company: Capital One

Role: Software Engineer

Category: Coding & Algorithms

Difficulty: medium

Interview Round: Technical Screen

Given an `n x n` matrix of lowercase letters, consider every diagonal that runs from bottom-left to top-right. There are `2n - 1` such diagonals. Assign each diagonal an index from `0` to `2n - 2` in the order you encounter them when scanning starting positions from the bottom row left-to-right, then the left column bottom-to-top excluding the bottom-left cell. Return the diagonal indexes sorted by the string formed from each diagonal's letters. Function signature: ```python def sort_diagonal_indexes(matrix: list[list[str]]) -> list[int]: pass ``` Constraints: - `1 <= n <= 500`. - Each cell contains one lowercase English letter. - If two diagonal strings are equal, sort by smaller diagonal index first. - The characters in a diagonal are read from bottom-left to top-right. Examples: ```text matrix = [['c','a'], ['b','d']] Diagonals: index 0 -> 'ba', index 1 -> 'd', index 2 -> 'c' Output: [0, 2, 1] ```

Quick Answer: Practice a matrix diagonal sorting problem that scans bottom-left to top-right diagonals and returns indexes ordered by their diagonal strings. The prompt targets careful indexing, deterministic tie-breaking, and translating a geometric traversal into reliable code.

Return the indexes of all bottom-left to top-right diagonals sorted by the string formed along each diagonal. Ties are broken by diagonal index.

Constraints

The matrix is square.
Each cell contains a lowercase letter.

Examples

Input: ([['c','a'],['b','d']])

Expected Output: [0,2,1]

Input: ([['a']])

Expected Output: [0]

Input: ([['a','b'],['c','d']])

Expected Output: [2,0,1]

Input: ([['b','a','c'],['a','b','a'],['c','a','b']])

Expected Output: [1,3,2,4,0]

Input: ([['z','z'],['z','z']])

Expected Output: [1,2,0]

Input: ([['m','n','o'],['j','k','l'],['a','b','c']])

Expected Output: [0,1,2,3,4]

Input: ([['c','b','a'],['f','e','d'],['i','h','g']])

Expected Output: [4,3,2,1,0]

Input: ([['a','a','b'],['a','b','a'],['b','a','a']])

Expected Output: [2,4,1,3,0]

Hints

Generate the start positions in the specified index order.
Read each diagonal upward and rightward.

Last updated: Jul 8, 2026

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