【LeetCode】62. Unique Paths

問題描述

https://leetcode.com/problems/unique-paths/#/description

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.

算法

動態規劃解題f(i,j)，i<m，j<n爲從左上角到(i,j)的方法，則有：

1. f(0,j) = 1, 0<=j<n，第一行的各個位置均只有一條路徑，即一直向右走
2. f(i,0) = 1, 0<=i<m，第一列的也只有一條路徑，即一直往下走
3. f(i,j) = f(i-1,j) + f(i, j-1), i>=1 & j>=1，其它位置直接來源有兩條，一個是上面的往下走，一個是左邊的往右走

代碼

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