wayetan
12/29/2013 - 3:19 AM

## Unique Paths

Unique Paths

``````/**
* Follow up for "Unique Paths":
* Now consider if some obstacles are added to the grids. How many unique paths would there be?
* An obstacle and empty space is marked as 1 and 0 respectively in the grid.
* For example,
* There is one obstacle in the middle of a 3x3 grid as illustrated below.
* [
[0,0,0],
[0,1,0],
[0,0,0]
]
* The total number of unique paths is 2.
* Note: m and n will be at most 100.
*/

public class Solution {
public int uniquePathsWithObstacles(int[][] obstacleGrid) {
if(obstacleGrid[0][0] == 1)
return 0;
int[][] paths = new int[obstacleGrid.length][obstacleGrid[0].length];
// Initialization
paths[0][0] = 1;
for(int i = 1; i < obstacleGrid.length; i++){
if(obstacleGrid[i][0] == 0)
paths[i][0] = paths[i - 1][0];
}
for(int i = 1; i < obstacleGrid[0].length; i++){
if(obstacleGrid[0][i] == 0)
paths[0][i] = paths[0][i - 1];
}
for(int i = 1; i < obstacleGrid.length; i++){
for(int j = 1; j < obstacleGrid[0].length; j++)
if(obstacleGrid[i][j] == 0)
paths[i][j] = paths[i - 1][j] + paths[i][j - 1];
}
return paths[obstacleGrid.length - 1][obstacleGrid[0].length - 1];
}
}``````
``````/**
* 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?
* Note: m and n will be at most 100.
*/

public class Solution {
public int uniquePaths(int m, int n) {
int[][] paths = new int[m][n];
// Initialization
for(int i = 0; i < m; i++){
paths[i][0] = 1;
}
for(int i = 0; i < n; i++){
paths[0][i] = 1;
}
for(int i = 1; i < m; i++){
for(int j = 1; j < n; j++){
paths[i][j] = paths[i - 1][j] + paths[i][j - 1];
}
}
return paths[m - 1][n - 1];
}
}``````