【leetcode】Unique Paths

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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题解：水题。把一个m*n的矩阵初始化第一行和第一列为1，然后遍历数组中剩下的位置，answer[i][j] = answer[i-1][j]+answer[i][j-1]

代码如下（java）

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

 当然，因为每次只需要上一行的信息，所以只用一维数组也可以完成。

JAVA代码如下：

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