LeetCode 62. Unique Paths

LeetCode 62. 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?

Note: m and n will be at most 100.

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分析：

首先初始化第一行和第一列为1，因为从起点开始到第一行第一列只有一条路径，然后第二行第二列的数为其左边和其上边两个数之和，因为只能往右往下走，走到第二行第二列只能从左边来或者从上边来，所以到第二行第二列的路径数目为第一行第二列（上边）和第二行第一列（左边）的路径数目之和。

三行七列求解：

代码如下：

class Solution {
public:
	int uniquePaths(int m, int n) {
		int a[100][100];
		for (int i = 0; i < m; i++) {
			for (int j = 0; j < n; j++) {
				if (i == 0 || j == 0) a[i][j] = 1;
				else a[i][j] = a[i][j - 1] + a[i - 1][j];
			}
		}
		return a[m - 1][n - 1];
	}
};