63. Unique Paths II

63_unique_paths_ii/problem.md

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+## 問題: [63. Unique Paths II](https://leetcode.com/problems/unique-paths-ii/description/)

63_unique_paths_ii/step1.md

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+# Step 1
+
+- ある地点$grid[i][j]$に辿り着けるルートの数は$grid[i - 1][j]$に辿り着くルートの数と$grid[i][j - 1]$に辿り着くルートの数の和である
+
+```python
+class Solution:
+    def uniquePathsWithObstacles(self, obstacleGrid: List[List[int]]) -> int:
+        M = len(obstacleGrid)
+        N = len(obstacleGrid[0])
+
+        if obstacleGrid[M - 1][N - 1] == 1 or obstacleGrid[0][0] == 1:
+            return 0
+
+        prev_row = [0] * N
+        for i, cell in enumerate(obstacleGrid[0]):
+            if cell == 0:
+                prev_row[i] = 1
+            else:
+                break
+
+        for i in range(1, M):
+            new_row = [0] * N
+            new_row[0] = prev_row[0] if obstacleGrid[i][0] == 0 else 0
+            for j in range(1, N):
+                if obstacleGrid[i][j] == 0:
+                    new_row[j] = new_row[j - 1] + prev_row[j]
+            prev_row = new_row
+        return prev_row[N - 1]
+```
+
+時間計算量: $O(m \times n)$
+
+空間計算量: $O(n)$

63_unique_paths_ii/step2.md

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+# Step 2
+
+```python
+class Solution:
+    def uniquePathsWithObstacles(self, obstacleGrid: List[List[int]]) -> int:
+        number_of_rows = len(obstacleGrid)
+        number_of_columns = len(obstacleGrid[0])
+
+        row = [0] * number_of_columns
+        for i, cell in enumerate(obstacleGrid[0]):
+            if cell == 0:
+                row[i] = 1
+            else:
+                break
+
+        for r in range(1, number_of_rows):
+            row[0] = row[0] if obstacleGrid[r][0] == 0 else 0
+            for c in range(1, number_of_columns):
+                if obstacleGrid[r][c] == 0:
+                    row[c] += row[c - 1]
+                else:
+                    row[c] = 0
+        return row[number_of_columns - 1]
+```
+
+時間計算量: $O(m \times n)$
+
+空間計算量: $O(n)$

63_unique_paths_ii/step3.md

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+# Step 3
+
+```python
+class Solution:
+    def uniquePathsWithObstacles(self, obstacleGrid: List[List[int]]) -> int:
+        number_of_rows = len(obstacleGrid)
+        number_of_columns = len(obstacleGrid[0])
+
+        row = [0] * number_of_columns
+        for i, cell in enumerate(obstacleGrid[0]):
+            if cell == 0:
+                row[i] = 1
+            else:
+                break
+
+        for r in range(1, number_of_rows):
+            row[0] = row[0] if obstacleGrid[r][0] == 0 else 0
+            for c in range(1, number_of_columns):
+                if obstacleGrid[r][c] == 0:
+                    row[c] += row[c - 1]
+                else:
+                    row[c] = 0
+        return row[number_of_columns - 1]
+```
+
+1回目: 4分　43秒
+
+2回目: 3分　18秒
+
+3回目: 3分　29秒