LeetCode: Unique Paths 解题报告

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.

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SOLUTION 1:

使用DP解决之。很简单。某一个cell有2种可能到达，从上面来，以及从左边来，只需要把每一个cell的可能数计算好，并且把它们相加即可。

另外，在第一行，第一列，以及左上角需要特别处理，因为我们上面、左边并没有cells.

public class Solution {
    public int uniquePaths(int m, int n) {
        if (m <= 0 || n <= 0) {
            return 0;
        }
        
        int[][] D = new int[m][n];
        
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (i == 0 && j == 0) {
                    D[i][j] = 1;
                } else if (i == 0) {
                    D[i][j] = D[i][j - 1];
                } else if (j == 0) {
                    D[i][j] = D[i - 1][j];
                } else {
                    D[i][j] = D[i - 1][j] + D[i][j - 1];
                }
            }
        }
        
        return D[m  - 1][n - 1];
    }
}