【leetcode每日刷题】62. Unique Paths

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

Note: m and n will be at most 100.

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right

Example 2:

Input: m = 7, n = 3
Output: 28

采用动态规划的方法，每次只能向下或者向右，所以每个格子的唯一路径数量为左边格子和上边格子的数量之和。

初始状态：dp[0][0] = 0; if(m == 1 || n == 1) return 1; dp[0][1] = 1; dp[1][0] = 1;

状态转移：dp[i][j] += dp[i-1][j] + dp[i][j-1];

public class num62 {
    public int uniquePaths(int m, int n) {
        int[][] dp = new int[m][n];
        dp[0][0] = 0;
        if(m == 1 || n == 1) return 1;
        dp[0][1] = 1;
        dp[1][0] = 1;
        for(int i=0; i<m; i++){
            for(int j=0; j<n; j++){
                if(i == 0 && j!=0){
                    dp[i][j] += dp[i][j-1];
                }else if(j == 0 && i!=0){
                    dp[i][j] += dp[i-1][j];
                }else if(j != 0 && i != 0){
                    dp[i][j] += dp[i-1][j] + dp[i][j-1];
                }
            }
        }
        return dp[m-1][n-1];
    }
    public static void main(String[] args) {
        int m=1, n=2;
        num62 s = new num62();
        System.out.println(s.uniquePaths(m, n));
    }
}