Implement Trapped Rain Water algorithm. (#714)

* feat: implement Trapped Rain Water algorithm

* chore(tests): add test of empty `heights`

Author: sozelfist

README.md

@@ -314,7 +314,7 @@ Read our [Contribution Guidelines](CONTRIBUTING.md) before you contribute.
 17. [`Max`](./dynamic/knapsack.go#L11):  Max function - possible duplicate
 18. [`NthCatalanNumber`](./dynamic/catalan.go#L13):  NthCatalan returns the n-th Catalan Number Complexity: O(n²)
 19. [`NthFibonacci`](./dynamic/fibonacci.go#L6):  NthFibonacci returns the nth Fibonacci Number
-
+20. [`TrapRainWater`](./dynamic/traprainwater.go#L17): Calculate the amount of trapped rainwater between bars represented by an elevation map using dynamic programming.
 ---
 </details><details>
 	<summary> <strong> dynamicarray </strong> </summary>	

dynamic/traprainwater.go

@@ -0,0 +1,41 @@
+// filename: traprainwater.go
+// description: Provides a function to calculate the amount of trapped rainwater between bars represented by an elevation map using dynamic programming.
+// details:
+// The TrapRainWater function calculates the amount of trapped rainwater between the bars represented by the given elevation map.
+// It uses dynamic programming to precompute the maximum height of bars to the left and right of each position.
+// Then, it iterates through the array to calculate the amount of trapped rainwater at each position based on the minimum of the left and right maximum heights.
+// Finally, it sums up the trapped rainwater for all positions and returns the total amount.
+// author(s) [TruongNhanNguyen (SOZEL)](https://github.com/TruongNhanNguyen)
+package dynamic
+
+import "math"
+
+// TrapRainWater calculates the amount of trapped rainwater between the bars represented by the given elevation map.
+// It uses dynamic programming to precompute the maximum height of bars to the left and right of each position.
+// Then, it iterates through the array to calculate the amount of trapped rainwater at each position based on the minimum of the left and right maximum heights.
+// Finally, it sums up the trapped rainwater for all positions and returns the total amount.
+func TrapRainWater(height []int) int {
+	if len(height) == 0 {
+		return 0
+	}
+
+	leftMax := make([]int, len(height))
+	rightMax := make([]int, len(height))
+
+	leftMax[0] = height[0]
+	for i := 1; i < len(height); i++ {
+		leftMax[i] = int(math.Max(float64(leftMax[i-1]), float64(height[i])))
+	}
+
+	rightMax[len(height)-1] = height[len(height)-1]
+	for i := len(height) - 2; i >= 0; i-- {
+		rightMax[i] = int(math.Max(float64(rightMax[i+1]), float64(height[i])))
+	}
+
+	trappedWater := 0
+	for i := 0; i < len(height); i++ {
+		trappedWater += int(math.Min(float64(leftMax[i]), float64(rightMax[i]))) - height[i]
+	}
+
+	return trappedWater
+}

dynamic/traprainwater_test.go

@@ -0,0 +1,34 @@
+package dynamic_test
+
+import (
+	"fmt"
+	"testing"
+
+	"github.com/TheAlgorithms/Go/dynamic"
+)
+
+func TestTrapRainWater(t *testing.T) {
+	heights := [][]int{
+		{},
+		{0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1},
+		{4, 2, 0, 3, 2, 5},
+		{3, 1, 2, 4, 0, 1, 3, 2, 4},
+	}
+
+	expectedResults := []int{
+		0,
+		6,
+		9,
+		13,
+	}
+
+	for i, height := range heights {
+		expected := expectedResults[i]
+		t.Run(fmt.Sprintf("Case %d", i+1), func(t *testing.T) {
+			result := dynamic.TrapRainWater(height)
+			if result != expected {
+				t.Errorf("Expected %d, but got %d", expected, result)
+			}
+		})
+	}
+}