"Leetcode" Unique Paths

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 is there?

Above is a 3 x 7 grid. How many possible unique paths is there?

Note: m and N would be is at most 100.

Can be pushed to the formula, for m+1,n+1, only need to go to the right M step, go down n steps, you can reach the end, we put down and to the right, all the permutation is the result result= (m+n)!/(m!*n!) The direct request will go out of scope, so simplify a little bit: m+1 (m/2+1) ... (m/n+1)

1 classSolution {2  Public:3    4     intUniquepaths (intMintN) {5        6         intresult=0;7         Doubletmp=1;8m--;9n--;Ten          for(intI=0; i<n;i++) One         { ATmp*= (Double) (m)/(i+1)+1; -         } -         theresult=round (TMP); -         returnresult; -     } -};

Direct use of dynamic programming

1 classSolution {2  Public:3    4     intUniquepaths (intMintN) {5        6         if(m==0|| n==0)return 0;7  8         intdp[101][101];9        Tendp[0][0]=1; One         A          for(intI=1; i<m;i++) -         { -dp[i][0]=1; the         } -         -          for(intj=1; j<n;j++) -         { +dp[0][j]=1; -         } +         A          for(intI=1; i<m;i++) at         { -              for(intj=1; j<n;j++) -             { -dp[i][j]=dp[i][j-1]+dp[i-1][j]; -             } -         } in         returndp[m-1][n-1]; -     } to};

"Leetcode" Unique Paths