【Grind75Hard】3問目42. Trapping Rain Water

grind75_hard/03_42_Trapping Rain Water/level_1.py

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+# brute force
+# 現在地より左側の最大値が左の壁、右側の最大値が右の壁となる。
+# 現在地の水位は、左右の壁の小さいほうになる。
+# 現在地が壁より低ければ、水が貯まる。
+# O(n^2)
+class Solution:
+    def trap(self, height: List[int]) -> int:
+        total_water = 0
+        for i in range(1, len(height) - 1):  # 両端には水が貯まらないので除外
+            left_wall = max(height[:i])
+            right_wall = max(height[i + 1 :])
+            water_height = min(left_wall, right_wall)
+            if water_height < height[i]:
+                continue
+            total_water += water_height - height[i]
+        return total_water
+
+
+# stackを使って実装
+# 左側の壁をstackで記憶し、右側の壁が見つかったら、貯まる水を計算する。
+class Solution:
+    def trap(self, height: List[int]) -> int:
+        left_walls = []
+        total_water = 0
+        for right in range(len(height)):
+            while left_walls and height[left_walls[-1]] <= height[right]:
+                bottom_index = left_walls.pop()
+                if not left_walls:
+                    break
+                left = left_walls[-1]
+                distance = right - left - 1
+                depth = min(height[left], height[right]) - height[bottom_index]
+                total_water += distance * depth
+            left_walls.append(right)
+        return total_water

grind75_hard/03_42_Trapping Rain Water/level_2.py

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+# DPを使って解く
+# brute forceと同じ考え方だが、左右の壁の最大値を記憶しておく
+class Solution:
+    def trap(self, height: List[int]) -> int:
+        max_left = [0] * len(height)  # [0,i]の範囲の最大値
+        max_right = [0] * len(height)  # [i,length)の範囲の最大値
+        max_left[0] = height[0]
+        max_right[-1] = height[-1]
+        for i in range(1, len(height)):
+            max_left[i] = max(max_left[i - 1], height[i])
+            max_right[-i - 1] = max(max_right[-i], height[-i - 1])
+        total_water = 0
+        for i in range(1, len(height) - 1):
+            water_height = min(max_left[i], max_right[i])
+            total_water += water_height - height[i]
+        return total_water

grind75_hard/03_42_Trapping Rain Water/level_3.py

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+class Solution:
+    def trap(self, height: List[int]) -> int:
+        max_left = [0] * len(height)
+        max_right = [0] * len(height)
+        max_left[0] = height[0]
+        max_right[-1] = height[-1]
+        for i in range(1, len(height)):
+            max_left[i] = max(max_left[i - 1], height[i])
+            max_right[-i - 1] = max(max_right[-i], height[-i - 1])
+        total_water = 0
+        for i in range(1, len(height) - 1):
+            water_height = min(max_left[i], max_right[i])
+            total_water += water_height - height[i]
+        return total_water

grind75_hard/03_42_Trapping Rain Water/level_4.py

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+# DPを使って解く
+# 変数名を修正
+# max_height_in_rightはmax_heights_in_leftとは別のループで構築する
+class Solution:
+    def trap(self, height: List[int]) -> int:
+        max_heights_in_left = [0] * len(height)  # [0,i]の範囲の最大値
+        max_height_in_right = [0] * len(height)  # [i,length)の範囲の最大値
+        max_heights_in_left[0] = height[0]
+        max_height_in_right[-1] = height[-1]
+        for i in range(1, len(height)):
+            max_heights_in_left[i] = max(max_heights_in_left[i - 1], height[i])
+        for i in range(len(height) - 2, -1, -1):
+            max_height_in_right[i] = max(max_height_in_right[i + 1], height[i])
+        total_water = 0
+        for i in range(1, len(height) - 1):
+            water_height = min(max_heights_in_left[i], max_height_in_right[i])
+            total_water += water_height - height[i]
+        return total_water
+
+
+# stackを使って実装
+# 変数名を修正
+class Solution:
+    def trap(self, height: List[int]) -> int:
+        left_wall_indexes = []
+        total_water = 0
+        for right in range(len(height)):
+            while left_wall_indexes and height[left_wall_indexes[-1]] <= height[right]:
+                bottom_index = left_wall_indexes.pop()
+                if not left_wall_indexes:
+                    break
+                left = left_wall_indexes[-1]
+                distance = right - left - 1
+                depth = min(height[left], height[right]) - height[bottom_index]
+                total_water += distance * depth
+            left_wall_indexes.append(right)
+        return total_water

grind75_hard/03_42_Trapping Rain Water/level_5.py

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+# Space: O(1)
+# 左右からポインタをずらしていく
+# 片方のポインタは今までの最大値で止まるようにしておく
+class Solution:
+    def trap(self, height: List[int]) -> int:
+        left_max = 0
+        right_max = 0
+        left = 0
+        right = len(height) - 1
+        total_water = 0
+        while left < right:
+            if height[left] < height[right]:
+                left_max = max(left_max, height[left])
+                total_water += left_max - height[left]
+                left += 1
+            else:
+                right_max = max(right_max, height[right])
+                total_water += right_max - height[right]
+                right -= 1
+        return total_water
+
+
+# DPを使って解く
+# 変数名を修正
+class Solution:
+    def trap(self, height: List[int]) -> int:
+        max_heights_in_left = [0] * len(height)  # [0,i]の範囲の最大値
+        max_heights_in_right = [0] * len(height)  # [i,length)の範囲の最大値
+        max_heights_in_left[0] = height[0]
+        max_heights_in_right[-1] = height[-1]
+        for i in range(1, len(height)):
+            max_heights_in_left[i] = max(max_heights_in_left[i - 1], height[i])
+        for i in range(len(height) - 2, -1, -1):
+            max_heights_in_right[i] = max(max_heights_in_right[i + 1], height[i])
+        total_water = 0
+        for i in range(1, len(height) - 1):
+            water_height = min(max_heights_in_left[i], max_heights_in_right[i])
+            total_water += water_height - height[i]
+        return total_water