Unique paths for leetcode topic resolution

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

Construct a two-dimensional array dpm, among

image.png

among dpm-1 It's the result .

    public int uniquePaths(int m, int n) {
        if (m <= 0 || n <= 0) {
            return 0;
        }
        int[][] dp = new int[m][n];
        for (int y = 1; y < n; y++) {
            dp[0][y] = 1;
        }
        for (int x = 1; x < m; x++) {
            dp[x][0] = 1;
        }
        for (int y = 1; y < n; y++) {
            for (int x = 1; x < m; x++) {
                dp[x][y] = dp[x - 1][y] + dp[x][y - 1];
            }
        }
        return dp[m - 1][n - 1];
    }