Beautiful Matrix - The Idea

The insight: you don't need to simulate the swaps. If the $1$ is at position $(r, c)$ and needs to reach $(3, 3)$, the number of moves is the Manhattan distance: $|r - 3| + |c - 3|$.

Each step moves you one position closer in either rows or columns. Manhattan distance counts how many horizontal and vertical steps you need.

First, find where the $1$ is located by scanning the matrix with nested loops.