Implement Trapped Rain Water using Dynamic Programming Strategy.

dynamic_programming/trapped_rainwater.cpp

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+/**
+ * @file
+ * @brief Implementation of the [Trapped Rainwater
+ * Problem](https://www.geeksforgeeks.org/trapping-rain-water/)
+ * @details
+ * This implementation calculates the amount of rainwater that can be trapped
+ * between walls represented by an array of heights.
+ */
+
+#include <algorithm> /// For std::min and std::max
+#include <cassert> /// For assert
+#include <iostream> /// For IO operations
+#include <vector> /// For vector container
+
+/*
+ * @namespace
+ * @brief Dynamic Programming Algorithms
+ */
+namespace dynamic_programming {
+/**
+ * @brief Function to calculate the trapped rainwater
+ * @param heights Array representing the heights of walls
+ * @return The amount of trapped rainwater
+ */
+int trappedRainwater(const std::vector<int>& heights) {
+ int n = heights.size();
+ if (n <= 2)
+ return 0; // No water can be trapped with less than 3 walls
+
+ std::vector<int> leftMax(n), rightMax(n);
+
+ // Calculate the maximum height of wall to the left of each wall
+ leftMax[0] = heights[0];
+ for (int i = 1; i < n; ++i) {
+ leftMax[i] = std::max(leftMax[i - 1], heights[i]);
+ }
+
+ // Calculate the maximum height of wall to the right of each wall
+ rightMax[n - 1] = heights[n - 1];
+ for (int i = n - 2; i >= 0; --i) {
+ rightMax[i] = std::max(rightMax[i + 1], heights[i]);
+ }
+
+ // Calculate the trapped rainwater between walls
+ int trappedWater = 0;
+ for (int i = 0; i < n; ++i) {
+ trappedWater +=
+ std::max(0, std::min(leftMax[i], rightMax[i]) - heights[i]);
+ }
+
+ return trappedWater;
+}
+
+} // namespace dynamic_programming
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+ std::vector<int> heights0 = {0, 1};
+ assert(dynamic_programming::trappedRainwater(heights0) == 0);
+
+ std::vector<int> heights1 = {0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1};
+ assert(dynamic_programming::trappedRainwater(heights1) == 6);
+
+ std::vector<int> heights2 = {3, 0, 0, 2, 0, 4};
+ assert(dynamic_programming::trappedRainwater(heights2) == 10);
+
+ std::vector<int> heights3 = {1, 2, 3, 4, 5};
+ assert(dynamic_programming::trappedRainwater(heights3) == 0);
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+ test(); // run self-test implementations
+ return 0;
+}