How hard is LeetCode 980. Unique Paths III?

LeetCode 980. Unique Paths III is rated Hard on LeetCode.

What is the time complexity of LeetCode 980. Unique Paths III?

The Python solution on this page runs in O(3^{m \times n}).

What is the space complexity of LeetCode 980. Unique Paths III?

The Python solution on this page uses O(m \times n) auxiliary space.

What topics does LeetCode 980. Unique Paths III cover?

LeetCode 980. Unique Paths III is tagged Bit Manipulation, Array, Backtracking and Matrix on LeetCode.

Unique Paths III — LeetCode 980 Python Solution

HardBit ManipulationArrayBacktrackingMatrix

Problem: #980
Pattern: Backtracking
Reading time: 4 min
Source: leetcode.com

The problem

You are given an m x n integer array grid where grid[i][j] could be: 1 representing the starting square. There is exactly one starting square.

Example

Input: grid = [[1,0,0,0],[0,0,0,0],[0,0,2,-1]]
Output: 2
Explanation: We have the following two paths:

Python solution

Python

class Solution:
    def uniquePathsIII(self, grid: List[List[int]]) -> int:
        def dfs(i: int, j: int, k: int) -> int:
            if grid[i][j] == 2:
                return int(k == cnt + 1)
            ans = 0
            for a, b in pairwise(dirs):
                x, y = i + a, j + b
                if 0 <= x < m and 0 <= y < n and (x, y) not in vis and grid[x][y] != -1:
                    vis.add((x, y))
                    ans += dfs(x, y, k + 1)
                    vis.remove((x, y))
            return ans

        m, n = len(grid), len(grid[0])
        start = next((i, j) for i in range(m) for j in range(n) if grid[i][j] == 1)
        dirs = (-1, 0, 1, 0, -1)
        cnt = sum(row.count(0) for row in grid)
        vis = {start}
        return dfs(*start, 0)

Complexity

Measure	Complexity
Time	O(3^{m \times n})
Space	O(m \times n) auxiliary

Pattern: Backtracking

Build candidates one choice at a time and abandon a branch the moment it cannot work. LeetCode 980. Unique Paths III is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Backtracking.

The backtracking guide has the Python template for the pattern and the 105 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 980. Unique Paths III?: LeetCode 980. Unique Paths III is rated Hard on LeetCode.
What is the time complexity of LeetCode 980. Unique Paths III?: The Python solution on this page runs in O(3^{m \times n}).
What is the space complexity of LeetCode 980. Unique Paths III?: The Python solution on this page uses O(m \times n) auxiliary space.
What topics does LeetCode 980. Unique Paths III cover?: LeetCode 980. Unique Paths III is tagged Bit Manipulation, Array, Backtracking and Matrix on LeetCode.