Adding dynamic programming solution for unique paths problem

dynamic_programming/unique_paths.cpp

@@ -0,0 +1,134 @@
+/**
+ * @file
+ * @brief Implementation of Unique Paths (LeetCode 62) using Dynamic Programming.
+ * @details
+ * A robot is located at the top-left corner of an m × n grid.
+ * The robot can move either down or right at any point in time.
+ * This program computes the total number of unique paths to reach
+ * the bottom-right corner.
+ *
+ * Note: This is **Unique Paths I** (no obstacles). Obstacles are handled in
+ * the separate problem **Unique Paths II**.
+ *
+ * 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/
+ */
+
+#include <iostream>
+#include <vector>
+#include <cassert>
+
+/**
+ * @namespace dynamic_programming
+ * @brief Dynamic Programming algorithms
+ */
+namespace dynamic_programming {
+
+/**
+ * @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 to cache intermediate results (-1 = uncomputed)
+    std::size_t m;  ///< Number of rows in the grid
+    std::size_t n;  ///< Number of columns in the grid
+
+    /**
+     * @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));
+
+        // base cases: last column and last row
+        for (std::size_t i = 0; i < m; i++) table[i][n - 1] = 1;
+        for (std::size_t j = 0; j < n; j++) table[m - 1][j] = 1;
+
+        // fill the table from bottom-right to top-left
+        for (std::size_t i = m - 1; i-- > 0;) {
+            for (std::size_t j = n - 1; j-- > 0;) {
+                table[i][j] = table[i + 1][j] + table[i][j + 1];
+            }
+        }
+        return table[0][0];
+    }
+
+   public:
+    /**
+     * @brief Constructor initializes dimensions and memoization table
+     * @param rows number of rows in the grid (must be > 0)
+     * @param cols number of columns in the grid (must be > 0)
+     */
+    UniquePathsSolver(std::size_t rows, std::size_t cols) : m(rows), n(cols) {
+        memoization_table.assign(m, std::vector<int>(n, -1));
+    }
+
+    /**
+     * @brief Get number of unique paths using Memoization (Top-Down)
+     * @param i current row index (default = 0)
+     * @param j current column index (default = 0)
+     * @return int Number of unique paths from (i, j) to (m-1, n-1)
+     */
+    int uniquePathsMemo(std::size_t i = 0, std::size_t 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);
+
+        memoization_table.at(i).at(j) =
+            uniquePathsMemo(i + 1, j) + uniquePathsMemo(i, j + 1);
+        return memoization_table.at(i).at(j);
+    }
+
+    /**
+     * @brief Get number of unique paths using Tabulation (Bottom-Up)
+     * @return int Number of unique paths from (0, 0) to (m-1, n-1)
+     */
+    int uniquePathsTabulation() { return solveTabulation(); }
+};
+
+}  // namespace dynamic_programming
+
+/**
+ * @brief Self-test implementations
+ */
+static void test() {
+    using namespace dynamic_programming;
+
+    UniquePathsSolver solver1(3, 7);
+    assert(solver1.uniquePathsMemo() == 28);
+    assert(solver1.uniquePathsTabulation() == 28);
+
+    UniquePathsSolver solver2(3, 2);
+    assert(solver2.uniquePathsMemo() == 3);
+    assert(solver2.uniquePathsTabulation() == 3);
+
+    UniquePathsSolver solver3(1, 1);
+    assert(solver3.uniquePathsMemo() == 1);
+    assert(solver3.uniquePathsTabulation() == 1);
+
+    UniquePathsSolver solver4(2, 2);
+    assert(solver4.uniquePathsMemo() == 2);
+    assert(solver4.uniquePathsTabulation() == 2);
+
+    std::cout << "All tests have successfully passed!\n";
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on successful execution
+ */
+int main() {
+    test();  // run self-tests
+    return 0;
+}