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63. Unique Paths II 👍

Approach 1: 2D DP

  • Time: $O(mn)$
  • Space: $O(mn)$
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class Solution {
 public:
  int uniquePathsWithObstacles(vector<vector<int>>& obstacleGrid) {
    const int m = obstacleGrid.size();
    const int n = obstacleGrid[0].size();
    // dp[i][j] := the number of unique paths from (0, 0) to (i, j)
    vector<vector<long>> dp(m + 1, vector<long>(n + 1, 0));
    dp[0][1] = 1;  // Can also set dp[1][0] = 1.

    for (int i = 1; i <= m; ++i)
      for (int j = 1; j <= n; ++j)
        if (!obstacleGrid[i - 1][j - 1])
          dp[i][j] = dp[i - 1][j] + dp[i][j - 1];

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

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class Solution {
  public int uniquePathsWithObstacles(int[][] obstacleGrid) {
    final int m = obstacleGrid.length;
    final int n = obstacleGrid[0].length;
    // dp[i][j] := the number of unique paths from (0, 0) to (i, j)
    long[][] dp = new long[m + 1][n + 1];
    dp[0][1] = 1; // Can also set dp[1][0] = 1.

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

    return (int) dp[m][n];
  }
}

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class Solution:
  def uniquePathsWithObstacles(self, obstacleGrid: list[list[int]]) -> int:
    m = len(obstacleGrid)
    n = len(obstacleGrid[0])
    # dp[i][j] := the number of unique paths from (0, 0) to (i, j)
    dp = [[0] * (n + 1) for _ in range(m + 1)]
    dp[0][1] = 1  # Can also set dp[1][0] = 1.

    for i in range(1, m + 1):
      for j in range(1, n + 1):
        if obstacleGrid[i - 1][j - 1] == 0:
          dp[i][j] = dp[i - 1][j] + dp[i][j - 1]

    return dp[m][n]

Approach 2: 1D DP

  • Time: $O(mn)$
  • Space: $O(n)$
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class Solution {
 public:
  int uniquePathsWithObstacles(vector<vector<int>>& obstacleGrid) {
    const int m = obstacleGrid.size();
    const int n = obstacleGrid[0].size();
    vector<long> dp(n);
    dp[0] = 1;

    for (int i = 0; i < m; ++i)
      for (int j = 0; j < n; ++j)
        if (obstacleGrid[i][j])
          dp[j] = 0;
        else if (j > 0)
          dp[j] += dp[j - 1];

    return dp[n - 1];
  }
};

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class Solution {
  public int uniquePathsWithObstacles(int[][] obstacleGrid) {
    final int m = obstacleGrid.length;
    final int n = obstacleGrid[0].length;
    int[] dp = new int[n];
    dp[0] = 1;

    for (int i = 0; i < m; ++i)
      for (int j = 0; j < n; ++j)
        if (obstacleGrid[i][j] == 1)
          dp[j] = 0;
        else if (j > 0)
          dp[j] += dp[j - 1];

    return dp[n - 1];
  }
}

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class Solution:
  def uniquePathsWithObstacles(self, obstacleGrid: list[list[int]]) -> int:
    m = len(obstacleGrid)
    n = len(obstacleGrid[0])
    dp = [0] * n
    dp[0] = 1

    for i in range(m):
      for j in range(n):
        if obstacleGrid[i][j]:
          dp[j] = 0
        elif j > 0:
          dp[j] += dp[j - 1]

    return dp[n - 1]