Adding dynamic programming solution for unique paths problem

dynamic_programming/unique_paths.cpp

@@ -0,0 +1,91 @@
+/**
+ * @file
+ * @brief Implementation of Unique Paths problem using
+ * Dynamic Programming (Memoization + Tabulation).
+ * @details
+ * A robot is located at the top-left corner of an m x n grid.
+ * The robot can move either down or right at any point in time.
+ * The robot is trying to reach the bottom-right corner.
+ * This program computes the total number of unique paths.
+ *
+ * @see https://leetcode.com/problems/unique-paths/
+ */
+
+#include <iostream>  
+#include <vector> 
+#include <cassert>   
+using namespace std;
+
+/**
+ * @namespace dp
+ * @brief Dynamic Programming algorithms
+ */
+namespace dp {
+
+/**
+ * @brief Recursive + Memoization solution.
+ * @param i Current row index
+ * @param j Current column index
+ * @param m Number of rows
+ * @param n Number of columns
+ * @param dp Memoization table
+ * @return int Number of unique paths from (i, j) to (m-1, n-1)
+ */
+int solveMem(int i, int j, int m, int n, vector<vector<int>> &dp) {
+    if (i >= m || j >= n) return 0;
+    if (i == m - 1 && j == n - 1) return 1;
+    if (dp[i][j] != -1) return dp[i][j];
+    dp[i][j] = solveMem(i + 1, j, m, n, dp) + solveMem(i, j + 1, m, n, dp);
+    return dp[i][j];
+}
+
+/**
+ * @brief Bottom-up Tabulation solution.
+ * @param m Number of rows
+ * @param n Number of columns
+ * @return int Number of unique paths from (0, 0) to (m-1, n-1)
+ */
+int solveTab(int m, int n) {
+    vector<vector<int>> dp(m, vector<int>(n, 0));
+    for (int i = 0; i < m; i++) dp[i][n - 1] = 1;  ///< last column paths = 1
+    for (int j = 0; j < n; j++) dp[m - 1][j] = 1;  ///< last row paths = 1
+    for (int i = m - 2; i >= 0; i--) {
+        for (int j = n - 2; j >= 0; j--) {
+            dp[i][j] = dp[i + 1][j] + dp[i][j + 1];  ///< from down + right
+        }
+    }
+    return dp[0][0];
+}
+
+/**
+ * @brief Returns number of unique paths in an m x n grid.
+ * @param m Number of rows
+ * @param n Number of columns
+ * @return int Total number of unique paths
+ */
+int uniquePaths(int m, int n) {
+    vector<vector<int>> dp(m + 1, vector<int>(n + 1, -1));
+    // return solveMem(0, 0, m, n, dp);  
+    return solveTab(m, n);             
+
+}  // namespace dp
+
+/**
+ * @brief Self-test implementations
+ */
+static void test() {
+    assert(dp::uniquePaths(3, 7) == 28);
+    assert(dp::uniquePaths(3, 2) == 3);
+    assert(dp::uniquePaths(1, 1) == 1);
+    assert(dp::uniquePaths(2, 2) == 2);
+    cout << "All tests have successfully passed!\n";
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on successful execution
+ */
+int main() {
+    test();  // run self-tests
+    return 0;
+}