From fe89149911899fde0baf56da7a312d06dafcdee2 Mon Sep 17 00:00:00 2001
From: Ishan Pandhare <91841626+Ishanned@users.noreply.github.com>
Date: Sat, 7 Oct 2023 13:54:50 +0530
Subject: [PATCH] Create travelling-salesman-dp

added dp implementation of travelling salesman problem
---
 c++/travelling-salesman-dp | 42 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 42 insertions(+)
 create mode 100644 c++/travelling-salesman-dp

diff --git a/c++/travelling-salesman-dp b/c++/travelling-salesman-dp
new file mode 100644
index 0000000..8068fae
--- /dev/null
+++ b/c++/travelling-salesman-dp
@@ -0,0 +1,42 @@
+#include <iostream>
+
+using namespace std;
+const int n = 4;
+const int MAX = 1000000;
+
+int dist[n + 1][n + 1] = {
+	{ 0, 0, 0, 0, 0 }, { 0, 0, 10, 15, 20 },
+	{ 0, 10, 0, 25, 25 }, { 0, 15, 25, 0, 30 },
+	{ 0, 20, 25, 30, 0 },
+};
+int memo[n + 1][1 << (n + 1)];
+
+int fun(int i, int mask)
+{
+	if (mask == ((1 << i) | 3))
+		return dist[1][i];
+	if (memo[i][mask] != 0)
+		return memo[i][mask];
+
+	int res = MAX;
+
+	for (int j = 1; j <= n; j++)
+		if ((mask & (1 << j)) && j != i && j != 1)
+			res = std::min(res, fun(j, mask & (~(1 << i)))
+									+ dist[j][i]);
+	return memo[i][mask] = res;
+}
+
+int main()
+{
+	int ans = MAX;
+	for (int i = 1; i <= n; i++)
+		
+		ans = std::min(ans, fun(i, (1 << (n + 1)) - 1)
+								+ dist[i][1]);
+
+	printf("The cost of most efficient tour = %d", ans);
+
+	return 0;
+}
+