【Leetcode 62】

题目

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

分析

采用动态规划，用填表法。

从最后一排最后一列开始遍历，计算到终点所经历的sum值。

源代码

int uniquepaths(int m, int n) {
	int roads[110][110];
	for (int i = m - 1; i >= 0; i--)
	{
		for (int j = n - 1; j >= 0; j--)
		{
			if (i == m - 1||j==n-1)
				roads[i][j] = 1;
			else
			{
				roads[i][j] = roads[i + 1][j] + roads[i][j + 1];
			}
		}
	}
	return roads[0][0];
}