[Leetcode] Unique Paths

Unique PathsTotal accepted:36748 Total submissions:112531my submissions QuestionSolution

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.

Hide TagsArray Dynamic ProgrammingIdea one: Dynamic planning, f[i][j] = F[i-1][j] + f[i][j-1], and f[i][0] = 0, f[0][j]=0, f[1][1] = 1, time complexity O (m*n), Space complexity O (m*n)

classSolution { Public:        intUniquepaths (intMintN) {vector<int> Row (n +1,0); Vector<vector<int> > F (M +1, Row); f[1][1] =1;  for(inti =1; I <= m; i + +)             {                    for(intj =1; J <= N; J + +)                 {                       if(i = =1&& J = =1)                        Continue; F[I][J]= f[i-1][J] + f[i][j-1]; }               }               returnF[m][n]; }   };

Idea Two: space complexity can also be optimized, f[][] is changed to f[], optimization, time complexity, Space complexity O (n)

classSolution { Public:#if0intUniquepaths (intMintN) {vector<int> Row (n +1,0); Vector<vector<int> > F (M +1, Row); f[1][1] =1;  for(inti =1; I <= m; i + +)            {                 for(intj =1; J <= N; J + +)                {                    if(i = =1&& J = =1)                        Continue; F[I][J]= f[i-1][J] + f[i][j-1]; }            }            returnF[m][n]; }#endif        intUniquepaths (intMintN) {vector<int> f (n +1,0); f[1] =1;  for(inti =1; I <= m; i + +)            {                 for(intj =1; J <= N; J + +)                {                    if(i = =1&& J = =1)                        Continue; F[J]= F[j] + f[j-1]; }            }            returnF[n]; }};

[Leetcode] Unique Paths