063_UniquePathsII63.java

/**
 * 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 UniquePathsII63 {
    public int uniquePathsWithObstacles(int[][] obstacleGrid) {
        int m = obstacleGrid.length;
        int n = obstacleGrid[0].length;
        if (m == 0) return 0;
        int[][] dp = new int[m][n];

        dp[0][0] = (obstacleGrid[0][0] == 1) ? 0 : 1;
        for (int i=1; i<m; i++) dp[i][0] = (obstacleGrid[i][0] == 1) ? 0 : dp[i-1][0];
        for (int j=1; j<n; j++) dp[0][j] = (obstacleGrid[0][j] == 1) ? 0 : dp[0][j-1];

        for (int i=1; i<m; i++) {
            for (int j=1; j<n; j++) {
                dp[i][j] = (obstacleGrid[i][j] == 1) ? 0 : dp[i][j-1] + dp[i-1][j];
            }
        }

        return dp[m-1][n-1];
    }


    public int uniquePathsWithObstacles2(int[][] obstacleGrid) {
        int m = obstacleGrid.length;
        int n = obstacleGrid[0].length;
        if (m == 0) return 0;
        int[] dp = new int[n];

        dp[0] = (obstacleGrid[0][0] == 1) ? 0 : 1;
        for (int j=1; j<n; j++) dp[j] = (obstacleGrid[0][j] == 1) ? 0 : dp[j-1];

        for (int i=1; i<m; i++) {
            dp[0] = (obstacleGrid[i][0] == 1) ? 0 : dp[0];
            for (int j=1; j<n; j++) {
                dp[j] = (obstacleGrid[i][j] == 1) ? 0 : (dp[j-1] + dp[j]);
            }
        }

        return dp[n-1];
    }

}