lintcode_114 a different path

Topic

There is a robot that is located in the upper left corner of an MXN grid (labeled ' Start ' in the middle).

Robots can only move one step down or to the right each time. The robot tries to reach the lower-right corner of the grid (labeled ' Finish '). Q. How many different paths are there?

Precautions

N and M are not more than 100

Sample Example

The	The	1,3	1,4	1,5	1,6	1,7
2,1
3,1						3,7

How many different paths are there in the above 3 x 7 grid?

Ideas

DP's idea to solve

DP[0][J] = 1;

Dp[i][0] = 1;

DP[I][J] = Dp[i-1][j] + dp[i][j-1];

Space complexity can be reduced to O (n)

Dp[i] = Dp[i] + dp[i-1];

C + + code

1 intUniquepaths (intMintN) {2         //Wirte Your code here3vector<int> DP (N,1);4          for(inti =1; I < m; ++i)5         {6              for(intj =1; J < N; ++j)7             {8DP[J] + = dp[j-1];9             }Ten         } One         returnDp[n-1]; A}

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lintcode_114 a different path