How should I practice Bouncing Diagonal Weights?

Start by reading the full statement, solve the visible examples, then compare the pattern against related Databricks online assessment problems in FastPrep.

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Problem · Matrix

Bouncing Diagonal Weights

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Problem statement

You are given a non-empty square integer matrix matrix.

For every starting cell in the leftmost column, trace a path that visits exactly one cell in each column:

The path initially moves one row up and one column right.
When the path reaches the top row, it changes direction and continues one row down and one column right until it reaches the rightmost column.

The weight of a starting cell is the sum of the matrix values on its path.

For every starting cell, form the pair (weight, leftmost value). Sort all pairs in ascending lexicographic order: first by weight, then by leftmost value when the weights are equal. Return the second value from each sorted pair.

Function

Diagonalweights(matrix: int[][]) → int[]

Examples

Example 1

matrix = [[2, 3, 2], [0, 2, 5], [1, 0, 1]]return = [1, 2, 0]

The paths starting in rows 0, 1, and 2 have weights 2 + 2 + 1 = 5, 0 + 3 + 5 = 8, and 1 + 2 + 2 = 5.

The corresponding pairs are (5, 2), (8, 0), and (5, 1). After sorting, they are (5, 1), (5, 2), and (8, 0), so the answer is [1, 2, 0].

Example 2

matrix = [[1, 3, 2, 5], [3, 2, 5, 0], [9, 0, 1, 3], [6, 1, 0, 8]]return = [1, 9, 3, 6]

The four path weights are 1 + 2 + 1 + 8 = 12, 3 + 3 + 5 + 3 = 14, 9 + 2 + 2 + 0 = 13, and 6 + 0 + 5 + 5 = 16.

The sorted pairs are (12, 1), (13, 9), (14, 3), and (16, 6), so the answer is [1, 9, 3, 6].

Constraints

matrix is a non-empty square matrix of integers.