tsp problem #694

Dynamic_Programming/tsp.cpp

@@ -0,0 +1,59 @@
+#include <iostream>
+#include <vector>
+#include <algorithm>
+#include <cmath>
+#include <limits>
+
+using namespace std;
+
+struct Point {
+    int x, y;
+};
+
+double calculateDistance(const Point& p1, const Point& p2) {
+    return sqrt(pow(p2.x - p1.x, 2) + pow(p2.y - p1.y, 2));
+}
+
+double tspDynamicProgramming(const vector<Point>& cities) {
+    int numCities = cities.size();
+
+    // dp[mask][i] represents the minimum distance to visit all cities in the set represented by the bitmask 'mask', ending at city 'i'
+    vector<vector<double>> dp(1 << numCities, vector<double>(numCities, numeric_limits<double>::max()));
+
+    // Initialize base case: starting from the first city
+    dp[1][0] = 0;
+
+    // Iterate through all subsets of cities
+    for (int mask = 1; mask < (1 << numCities); ++mask) {
+        for (int i = 0; i < numCities; ++i) {
+            // Check if city 'i' is in the subset represented by the bitmask
+            if ((mask & (1 << i)) != 0) {
+                for (int j = 0; j < numCities; ++j) {
+                    // Check if city 'j' is in the subset and different from 'i'
+                    if ((mask & (1 << j)) != 0 && i != j) {
+                        dp[mask][i] = min(dp[mask][i], dp[mask ^ (1 << i)][j] + calculateDistance(cities[j], cities[i]));
+                    }
+                }
+            }
+        }
+    }
+
+    // Calculate the minimum distance to return to the starting city
+    double minDistance = numeric_limits<double>::max();
+    for (int i = 1; i < numCities; ++i) {
+        minDistance = min(minDistance, dp[(1 << numCities) - 1][i] + calculateDistance(cities[i], cities[0]));
+    }
+
+    return minDistance;
+}
+
+int main() {
+    // Example usage
+    vector<Point> cities = {{0, 0}, {1, 2}, {2, 4}, {3, 1}};
+
+    double minDistance = tspDynamicProgramming(cities);
+
+    cout << "Minimum distance: " << minDistance << endl;
+
+    return 0;
+}