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| 1 | +/** |
| 2 | + * @file |
| 3 | + * @brief Implementation of the [Trapped Rainwater |
| 4 | + * Problem](https://www.geeksforgeeks.org/trapping-rain-water/) |
| 5 | + * @details |
| 6 | + * This implementation calculates the total trapped rainwater using a |
| 7 | + * two-pointer approach. It maintains two pointers (`left` and `right`) and |
| 8 | + * tracks the maximum height seen so far from both ends (`leftMax` and |
| 9 | + * `rightMax`). At each step, the algorithm decides which side to process based |
| 10 | + * on which boundary is smaller, ensuring O(n) time and O(1) space complexity. |
| 11 | + * @author [kanavgoyal898](https://github.com/kanavgoyal898) |
| 12 | + */ |
| 13 | + |
| 14 | +#include <algorithm> /// For std::min and std::max |
| 15 | +#include <cassert> /// For assert |
| 16 | +#include <cstddef> /// For std::size_t |
| 17 | +#include <cstdint> /// For std::uint32_t |
| 18 | +#include <vector> /// For std::vector |
| 19 | + |
| 20 | +/* |
| 21 | + * @namespace |
| 22 | + * @brief Dynamic Programming Algorithms |
| 23 | + */ |
| 24 | +namespace dynamic_programming { |
| 25 | +/** |
| 26 | + * @brief Function to calculate the trapped rainwater |
| 27 | + * @param heights Array representing the heights of walls |
| 28 | + * @return The amount of trapped rainwater |
| 29 | + */ |
| 30 | +uint32_t trappedRainwater(const std::vector<uint32_t>& heights) { |
| 31 | + std::size_t n = heights.size(); |
| 32 | + if (n <= 2) |
| 33 | + return 0; // Not enough walls to trap water |
| 34 | + |
| 35 | + std::size_t left = 0, right = n - 1; |
| 36 | + uint32_t leftMax = 0, rightMax = 0, trappedWater = 0; |
| 37 | + |
| 38 | + // Traverse from both ends towards the center |
| 39 | + while (left < right) { |
| 40 | + if (heights[left] < heights[right]) { |
| 41 | + // Water trapped depends on the tallest wall to the left |
| 42 | + if (heights[left] >= leftMax) |
| 43 | + leftMax = heights[left]; // Update left max |
| 44 | + else |
| 45 | + trappedWater += |
| 46 | + leftMax - heights[left]; // Water trapped at current left |
| 47 | + ++left; |
| 48 | + } else { |
| 49 | + // Water trapped depends on the tallest wall to the right |
| 50 | + if (heights[right] >= rightMax) |
| 51 | + rightMax = heights[right]; // Update right max |
| 52 | + else |
| 53 | + trappedWater += |
| 54 | + rightMax - |
| 55 | + heights[right]; // Water trapped at current right |
| 56 | + --right; |
| 57 | + } |
| 58 | + } |
| 59 | + |
| 60 | + return trappedWater; |
| 61 | +} |
| 62 | + |
| 63 | +} // namespace dynamic_programming |
| 64 | + |
| 65 | +/** |
| 66 | + * @brief Self-test implementations |
| 67 | + * @returns void |
| 68 | + */ |
| 69 | +static void test() { |
| 70 | + std::vector<uint32_t> test_basic = {0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1}; |
| 71 | + assert(dynamic_programming::trappedRainwater(test_basic) == 6); |
| 72 | + |
| 73 | + std::vector<uint32_t> test_peak_under_water = {3, 0, 2, 0, 4}; |
| 74 | + assert(dynamic_programming::trappedRainwater(test_peak_under_water) == 7); |
| 75 | + |
| 76 | + std::vector<uint32_t> test_bucket = {5, 1, 5}; |
| 77 | + assert(dynamic_programming::trappedRainwater(test_bucket) == 4); |
| 78 | + |
| 79 | + std::vector<uint32_t> test_skewed_bucket = {4, 1, 5}; |
| 80 | + assert(dynamic_programming::trappedRainwater(test_skewed_bucket) == 3); |
| 81 | + |
| 82 | + std::vector<uint32_t> test_empty = {}; |
| 83 | + assert(dynamic_programming::trappedRainwater(test_empty) == 0); |
| 84 | + |
| 85 | + std::vector<uint32_t> test_flat = {0, 0, 0, 0, 0}; |
| 86 | + assert(dynamic_programming::trappedRainwater(test_flat) == 0); |
| 87 | + |
| 88 | + std::vector<uint32_t> test_no_trapped_water = {1, 1, 2, 4, 0, 0, 0}; |
| 89 | + assert(dynamic_programming::trappedRainwater(test_no_trapped_water) == 0); |
| 90 | + |
| 91 | + std::vector<uint32_t> test_single_elevation = {5}; |
| 92 | + assert(dynamic_programming::trappedRainwater(test_single_elevation) == 0); |
| 93 | + |
| 94 | + std::vector<uint32_t> test_two_point_elevation = {5, 1}; |
| 95 | + assert(dynamic_programming::trappedRainwater(test_two_point_elevation) == |
| 96 | + 0); |
| 97 | + |
| 98 | + std::vector<uint32_t> test_large_elevation_map_difference = {5, 1, 6, 1, |
| 99 | + 7, 1, 8}; |
| 100 | + assert(dynamic_programming::trappedRainwater( |
| 101 | + test_large_elevation_map_difference) == 15); |
| 102 | +} |
| 103 | + |
| 104 | +/** |
| 105 | + * @brief Main function |
| 106 | + * @returns 0 on exit |
| 107 | + */ |
| 108 | +int main() { |
| 109 | + test(); // run self-test implementations |
| 110 | + return 0; |
| 111 | +} |
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