LeetCode第63题 – 不同路径 II

题目

解答

方案一：基于递归的方案

class Solution {

    public int uniquePathsWithObstacles(int[][] obstacleGrid) {
        int m = obstacleGrid.length;
        int n = obstacleGrid[0].length;

        if (obstacleGrid[0][0] == 1) {
            return 0;
        }

        if (obstacleGrid[m - 1][n - 1] == 1) {
            return 0;
        }

        int[][] dp = new int[m][n];

        dp[0][0] = 1;
        for (int i = 1, imax = m; i < imax; ++i) {
            if (obstacleGrid[i][0] == 1) {
                dp[i][0] = 0;
            } else {
                dp[i][0] = dp[i - 1][0];
            }
        }

        for (int j = 1, jmax = n; j < jmax; ++j) {
            if (obstacleGrid[0][j] == 1) {
                dp[0][j] = 0;
            } else {
                dp[0][j] = dp[0][j - 1];
            }
        }

        for (int i = 1, imax = m; i < imax; ++i) {
            for (int j = 1, jmax = n; j < jmax; ++j) {
                if (obstacleGrid[i][j] == 1) {
                    dp[i][j] = 0;
                } else {
                    if (obstacleGrid[i - 1][j] == 0) {
                        dp[i][j] += dp[i - 1][j];
                    }

                    if (obstacleGrid[i][j - 1] == 0) {
                        dp[i][j] += dp[i][j - 1];
                    }
                }

            }
        }

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

要点
本题目充分说明，使用动态规划解题时，初始值很重要。
另外，假如起点和终点均为障碍物的话，可以直接返回，不需要执行后续的求解操作。

准备的用例，如下

@Before
public void before() {
    t = new Solution();
}

@Test
public void test001() {
    assertEquals(2, t.uniquePathsWithObstacles(new int[][] { { 0, 0, 0 }, { 0, 1, 0 }, { 0, 0, 0 } }));
}

@Test
public void test002() {
    assertEquals(1, t.uniquePathsWithObstacles(new int[][] { { 0, 1 }, { 0, 0 } }));
}

@Test
public void test003() {
    assertEquals(1, t.uniquePathsWithObstacles(new int[][] { { 0, 0 } }));
}

@Test
public void test004() {
    assertEquals(0, t.uniquePathsWithObstacles(new int[][] { { 0, 0 }, { 1, 1 }, { 0, 0 } }));
}

@Test
public void test005() {
    assertEquals(0, t.uniquePathsWithObstacles(new int[][] { { 0, 0 }, { 0, 1 } }));
}

@Test
public void test006() {
    assertEquals(0, t.uniquePathsWithObstacles(new int[][] { { 1, 0 }, { 0, 0 } }));
}

@Test
public void test007() {
    assertEquals(0, t.uniquePathsWithObstacles(
            new int[][] { { 0, 1, 0, 0, 0 }, { 1, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0 }, { 0, 0, 0, 0, 0 } }));
}