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 3 x 7 grid. How many possible unique paths are there?
Note: m and n will be at most 100.
 
[解题思路]
一维DP。 Step[i][j] = Step[i-1][j] + Step[i][j-1];
 
 1 public class Solution {
 2     public int uniquePaths(int m, int n) {
 3         int[][] ways = new int[m+1][n+1];
 4         ways[0][1] = 1;
 5         for(int i =1; i<= m; i++){
 6             for(int j = 1; j<=n; j++){
 7                 ways[i][j] = ways[i-1][j]+ways[i][j-1];
 8             }
 9         }
10         
11         return ways[m][n];
12     }
13 }

 

 
 
滚动数组
 1 public class Solution {
 2      public int uniquePaths(int m, int n) {
 3          int row = m;
 4          int col = n;
 5          int[] paths = new int[col];
 6          for(int i = 0; i < col; i++){
 7              paths[i] = 1;
 8          }
 9          for(int i = 1; i < row; i++){
10              for(int j = 1; j < col; j++){
11                  paths[j] = paths[j] + paths[j-1];
12              }
13          }
14          return paths[col-1];
15      }
16 }

 

 
 
bottom up
public class Solution {
    public int uniquePaths(int m, int n) {
        int[][] steps = new int[m+1][n+1];
        for(int i = 0; i < n+1; i++){
            steps[m][i] = 0;
        }
        
        for(int i = 0; i < m+1; i++){
            steps[i][n] = 0;
        }
        
        // 此处的初始化是为了 让 steps[m-1][n-1] 为 1（即右下角的终点）
        steps[m-1][n] =1;
        
        for(int i = m-1; i>= 0; i--){
            for(int j = n-1; j >=0; j--){
                steps[i][j] = steps[i+1][j] + steps[i][j+1];
            }
        }
        
        return steps[0][0];
    }
}

 

top down

public int uniquePaths(int m, int n) {
        // Start typing your Java solution below
        // DO NOT write main() function
        int[][] matrix = new int[m+2][n+2];
        for(int i = 0; i < m+2; i++){
            for(int j = 0; j < n+2; j++){
                matrix[i][j] = -1;
            }
        }
        
        return dp(1, 1, m, n, matrix);
    }
    
    public int dp(int r, int c, int m, int n, int[][] matrix){
        if(r > m || c > n){
            return 0;
        }
        if(r == m && c == n){
            return 1;
        }
        if(matrix[r+1][c] == -1){
            matrix[r+1][c] = dp(r+1, c, m, n, matrix);
        }
        if(matrix[r][c+1] == -1){
            matrix[r][c+1] = dp(r, c+1, m, n, matrix);
        }
        
        return matrix[r+1][c] + matrix[r][c+1];
    }

 

 

ref : http://www.cnblogs.com/feiling/p/3270618.html

http://fisherlei.blogspot.com/2013/01/leetcode-unique-paths.html

posted @ 2014-02-05 02:29  Razer.Lu  阅读(281)  评论(0)  编辑  收藏  举报