add : trapped water program under dynamic programming

dynamic_programming/trapped_water.py

@@ -0,0 +1,58 @@
+"""
+Given an array of non-negative integers representing an elevation map where
+the width of each bar is 1,this program calculates how much rainwater can be trapped.
+
+Example - height = [0,1,0,2,1,0,1,3,2,1,2,1]
+Output: 6
+This problem can be solved using the concept of "DYNAMIC PROGRAMMING".
+
+We calculate the maximum height of bars on the left and right of every bar in array.
+Then iterate over the width of structure and at each index.
+The amount of water that will be stored is equal to minimum of maximum height of bars
+on both sides minus height of bar at current position.
+"""
+
+
+def trapped_rainwater(height: list[int] = None) -> int:
+    """
+    The trapped_rainwater function calculates the total amount of rainwater
+    that can be trapped given an array of bar heights.
+    It uses a dynamic programming approach, determining the maximum height of bars
+    on both sides for each bar, and then computing the trapped water above each bar.
+    The function returns the total trapped water.
+
+    trapped_rainwater([0,1,0,2,1,0,1,3,2,1,2,1])
+    >>> 6
+    trapped_rainwater([7,1,5,3,6,4])
+    >>> 9
+    """
+    if not height:
+        return 0
+    if any(height < 0):
+        raise ValueError("No height can be negative")
+    length = len(height)
+
+    left_max = [0] * length
+    left_max[0] = height[0]
+    for i in range(1, length):
+        left_max[i] = max(height[i], left_max[i - 1])
+
+    right_max = [0] * length
+    right_max[length - 1] = height[length - 1]
+    for i in range(length - 2, -1, -1):
+        right_max[i] = max(height[i], right_max[i + 1])
+
+    trapped_water: int = 0
+
+    for i in range(length):
+        water_level = min(left_max[i], right_max[i])
+        trapped_water += water_level - height[i]
+
+    return trapped_water
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    print(f"{trapped_rainwater([0,1,0,2,1,0,1,3,2,1,2,1])}")