Unique Paths

Leetcode

題意：

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?

解題思路：

使用一維陣列的dp來解

public class Solution {
    public int uniquePaths(int m, int n) {
        if (m < 0 || n < 0) {
            return 0;
        }

        int[] res = new int[n];
        res[0] = 1;
        for (int i = 0; i < m; i++) {
            for (int j = 1; j < n; j++) {
                res[j] += res[j - 1];
            }
        }

        return res[n - 1];
    }
}

使用二維陣列來解

public class Solution {
    public int uniquePaths(int m, int n) {
        if (m == 0 || n == 0) {
            return 1;
        }

        int[][] count = new int[m][n];
        for (int i = 0; i < m; i++) {
            count[i][0] = 1;
        }

        for (int i = 1; i < n; i++) {
            count[0][i] = 1;
        }

        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                count[i][j] = count[i - 1][j] + count[i][j - 1];
            }
        }

        return count[m - 1][n - 1];
    }
}