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a73323e
Adding dynamic programming solution for unique paths problem
singhsayan ba22f9f
Update unique_paths.cpp
singhsayan d87ca7c
Refactor Unique Paths as requested in code review
singhsayan 8dce8c6
Update unique_paths.cpp
singhsayan 548c500
Updated code
singhsayan 1a71f3b
Updated_code
singhsayan eb39769
Merge branch 'master' into feat/grid_unique_path
singhsayan 5e5b2cd
Update unique_paths.cpp
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| @@ -0,0 +1,122 @@ | ||
| /** | ||
| * @file | ||
| * @brief Implementation of Unique Paths problem using Dynamic Programming. | ||
| * @details | ||
| * A robot is located at the top-left corner of an m ×ばつ n grid. | ||
| * The robot can move either down or right at any point in time. | ||
|
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. could add a brief comparison between memoization and tabulation? |
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| * This program computes the total number of unique paths to reach | ||
| * the bottom-right corner. | ||
| * | ||
| * Approaches: | ||
| * - **Memoization (Top-Down)**: Recursively explores solutions while | ||
| * storing intermediate results in a cache (`memoization_table`) to avoid redundant | ||
| * computation. Typically more intuitive and easy to write, but | ||
| * relies on recursion and has associated call-stack overhead. | ||
| * | ||
| * - **Tabulation (Bottom-Up)**: Iteratively builds the solution using | ||
| * a DP table, starting from the base cases and filling up the table. | ||
| * Offers consistent performance without recursion overhead and | ||
| * is generally more space-efficient when optimized. | ||
| * | ||
| * @see https://leetcode.com/problems/unique-paths/ | ||
| */ | ||
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| #include <iostream> | ||
| #include <vector> | ||
| #include <cassert> | ||
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| /** | ||
| * @namespace dynamic_programming | ||
| * @brief Dynamic Programming algorithms | ||
| */ | ||
| namespace dynamic_programming { | ||
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| /** | ||
| * @class UniquePathsSolver | ||
| * @brief Solves the Unique Paths problem using both memoization and tabulation. | ||
| */ | ||
| class UniquePathsSolver { | ||
| private: | ||
| std::vector<std::vector<int>> memoization_table; ///< Memoization table | ||
| int m, n; | ||
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| /** | ||
| * @brief Bottom-up Tabulation solution. | ||
| * @return int Number of unique paths from (0, 0) to (m-1, n-1) | ||
| */ | ||
| int solveTabulation() { | ||
| std::vector<std::vector<int>> table(m, std::vector<int>(n, 0)); | ||
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| for (int i = 0; i < m; i++) table[i][n - 1] = 1; ///< last column | ||
| for (int j = 0; j < n; j++) table[m - 1][j] = 1; ///< last row | ||
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| for (int i = m - 2; i >= 0; i--) { | ||
| for (int j = n - 2; j >= 0; j--) { | ||
| table[i][j] = table[i + 1][j] + table[i][j + 1]; | ||
| } | ||
| } | ||
| return table[0][0]; | ||
| } | ||
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| public: | ||
| /** | ||
| * @brief Constructor initializes dimensions and memoization table | ||
| */ | ||
| UniquePathsSolver(int rows, int cols) : m(rows), n(cols) { | ||
| memoization_table.assign(m, std::vector<int>(n, -1)); | ||
| } | ||
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| /** | ||
| * @brief Get number of unique paths using Memoization (Top-Down) | ||
| */ | ||
| int uniquePathsMemo(int i = 0, int j = 0) { | ||
| if (i >= m || j >= n) return 0; | ||
| if (i == m - 1 && j == n - 1) return 1; | ||
| if (memoization_table.at(i).at(j) != -1) return memoization_table.at(i).at(j); | ||
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| memoization_table.at(i).at(j) = | ||
| uniquePathsMemo(i + 1, j) + uniquePathsMemo(i, j + 1); | ||
| return memoization_table.at(i).at(j); | ||
| } | ||
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| /** | ||
| * @brief Get number of unique paths using Tabulation (Bottom-Up) | ||
| */ | ||
| int uniquePathsTabulation() { return solveTabulation(); } | ||
| }; | ||
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| } // namespace dynamic_programming | ||
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| /** | ||
| * @brief Self-test implementations | ||
| */ | ||
| static void test() { | ||
| using namespace dynamic_programming; | ||
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| UniquePathsSolver solver1(3, 7); | ||
| assert(solver1.uniquePathsMemo() == 28); | ||
| assert(solver1.uniquePathsTabulation() == 28); | ||
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| UniquePathsSolver solver2(3, 2); | ||
| assert(solver2.uniquePathsMemo() == 3); | ||
| assert(solver2.uniquePathsTabulation() == 3); | ||
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| UniquePathsSolver solver3(1, 1); | ||
| assert(solver3.uniquePathsMemo() == 1); | ||
| assert(solver3.uniquePathsTabulation() == 1); | ||
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| UniquePathsSolver solver4(2, 2); | ||
| assert(solver4.uniquePathsMemo() == 2); | ||
| assert(solver4.uniquePathsTabulation() == 2); | ||
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| std::cout << "All tests have successfully passed!\n"; | ||
| } | ||
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| /** | ||
| * @brief Main function | ||
| * @returns 0 on successful execution | ||
| */ | ||
| int main() { | ||
| test(); // run self-tests | ||
| return 0; | ||
| } | ||
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