leetcode -- Unique Paths

 

1.DP bottom up

 1 public int uniquePaths(int m, int n) {
 2         // Start typing your Java solution below
 3         // DO NOT write main() function
 4         int[][] steps = new int[m+2][n+2];
 5         for(int i = 0; i < n + 2; i++){
 6             steps[m+1][i] = 0;
 7         }
 8         for(int i = 0; i < m + 2; i++){
 9             steps[i][n+1] = 0;
10         }
11         steps[m][n+1] = 1;
12         for(int i = m; i >= 1; i--){
13             for(int j = n; j >= 1; j--){
14                 steps[i][j] = steps[i+1][j] + steps[i][j+1];
15             }
16         }
17         return steps[1][1];
18     }

2.DP top down

 1 public int uniquePaths(int m, int n) {
 2         // Start typing your Java solution below
 3         // DO NOT write main() function
 4         int[][] matrix = new int[m+2][n+2];
 5         for(int i = 0; i < m+2; i++){
 6             for(int j = 0; j < n+2; j++){
 7                 matrix[i][j] = -1;
 8             }
 9         }
10         
11         return dp(1, 1, m, n, matrix);
12     }
13     
14     public int dp(int r, int c, int m, int n, int[][] matrix){
15         if(r > m || c > n){
16             return 0;
17         }
18         if(r == m && c == n){
19             return 1;
20         }
21         if(matrix[r+1][c] == -1){
22             matrix[r+1][c] = dp(r+1, c, m, n, matrix);
23         }
24         if(matrix[r][c+1] == -1){
25             matrix[r][c+1] = dp(r, c+1, m, n, matrix);
26         }
27         
28         return matrix[r+1][c] + matrix[r][c+1];
29     }

 

ref:http://leetcode.com/2010/11/unique-paths.html