solve Unique Paths III

Author: saubhik

problems/unique_paths_iii.py

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+from typing import List
+
+
+class Solution:
+    # We have the following grid:
+    # 1, 0, 0,  0
+    # 0, 0, 0,  0
+    # 0, 0, 2, -1
+    # Walk over every non-obstacle square exactly once.
+    #
+    # 1, 0, 0, 0
+    # 0, 0, 0, 0
+    # 0, 0, 0, 2
+    #
+    # Straight Forward DFS.
+    # Time: O(4 ^ (r * c)), exponential time.
+    # Space: O(r * c)
+    # where r and c are the number of rows or columns.
+    #
+    # Since r * c <= 20, this solution is accepted.
+    def uniquePathsIII(self, grid: List[List[int]]) -> int:
+        rows, cols, paths, visited, num_valid_squares, start_i, start_j = (
+            len(grid),
+            len(grid[0]),
+            0,
+            set(),
+            0,
+            None,
+            None,
+        )
+
+        for i in range(rows):
+            for j in range(cols):
+                if grid[i][j] in (0, 1):
+                    num_valid_squares += 1
+                    if grid[i][j] == 1:
+                        start_i, start_j = i, j
+
+        def dfs(i, j):
+            if grid[i][j] == 2:
+                if len(visited) == num_valid_squares:
+                    nonlocal paths
+                    paths += 1
+
+                return
+
+            visited.add((i, j))
+
+            for dir in ((1, 0), (0, -1), (-1, 0), (0, 1)):
+                nbr_i, nbr_j = i + dir[0], j + dir[1]
+                if (
+                    0 <= nbr_i < rows
+                    and 0 <= nbr_j < cols
+                    and grid[nbr_i][nbr_j] != -1
+                    and (nbr_i, nbr_j) not in visited
+                ):
+                    dfs(i=nbr_i, j=nbr_j)
+
+            visited.remove((i, j))
+
+        dfs(i=start_i, j=start_j)
+
+        return paths

tests/test_unique_paths_iii.py

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+import unittest
+
+from unique_paths_iii import Solution
+
+
+class TestUniquePathsIII(unittest.TestCase):
+    def test_example_1(self):
+        grid = [[1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 2, -1]]
+        assert Solution().uniquePathsIII(grid=grid) == 2
+
+    def test_example_2(self):
+        grid = [[1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 2]]
+        assert Solution().uniquePathsIII(grid=grid) == 4
+
+    def test_example_3(self):
+        grid = [[0, 1], [2, 0]]
+        assert Solution().uniquePathsIII(grid=grid) == 0