leetcode 62. 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 7 x 3 grid. How many possible unique paths are there?
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:
- Right -> Right -> Down
- Right -> Down -> Right
- Down -> Right -> Right
Example 2:
Input: m = 7, n = 3
Output: 28
Constraints:
1 <= m, n <= 100
It's guaranteed that the answer will be less than or equal to 2 * 10 ^ 9.
Solution
在每一个位置[i][j],robot要么从上面一个位置下来，要么从左边一个位置过来
所以其动态规划的状态转移方程为
dp[i][j]=dp[i-1][j]+dp[i][j-1]
class Solution {
public:
int uniquePaths(int m, int n) {
int dp[101][101];
for(int i=0;i<=m;i++)
dp[0][i]=0;
for(int i=0;i<=n;i++)
dp[i][0]=0;
dp[0][1]=1;
for(int i=1;i<=n;i++)
for(int j=1;j<=m;j++)
dp[i][j]=dp[i-1][j]+dp[i][j-1];
return dp[n][m];
}
};