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.

 1 public class Solution {
 2     public int uniquePaths(int m, int n) {
 3         if (m <= 0 || n <= 0) {
 4             return 0;
 5         }
 6
 7         int[][] D = new int[m][n];
 8
 9         for (int i = 0; i < m; i++) {
10             for (int j = 0; j < n; j++) {
11                 if (i == 0 && j == 0) {
12                     D[i][j] = 1;
13                 } else if (i == 0) {
14                     D[i][j] = D[i][j - 1];
15                 } else if (j == 0) {
16                     D[i][j] = D[i - 1][j];
17                 } else {
18                     D[i][j] = D[i - 1][j] + D[i][j - 1];
19                 }
20             }
21         }
22
23         return D[m  - 1][n - 1];
24     }
25 }