Travelling Salesman problem in dynamic programming

Question

i am trying to resolve the travelling salesman problem with dynamic programming in c++ and i find a way using a mask of bits, i got the min weight, but i dont know how to get the path that use, it would be very helpful if someone find a way. This is my code:

#include<iostream>
using namespace std;

#define INT_MAX 999999

int n=4;
int dist[10][10] = {
        {0,20,42,25},
        {20,0,30,34},
        {42,30,0,10},
        {25,34,10,0}
};
int VISITED_ALL = (1<<n) -1;

int dp[16][4];


int  tsp(int mask,int pos){

    if(mask==VISITED_ALL){
        return dist[pos][0];
    }
    if(dp[mask][pos]!=-1){
       return dp[mask][pos];
    }

    //Now from current node, we will try to go to every other node and take the min ans
    int ans = INT_MAX;

    //Visit all the unvisited cities and take the best route
    for(int city=0;city<n;city++){

        if((mask&(1<<city))==0){

            int newAns = dist[pos][city] + tsp( mask|(1<<city), city);
            ans = min(ans, newAns);
        }

    }

    return dp[mask][pos] = ans;
} 

int main(){
    /* init the dp array */
    for(int i=0;i<(1<<n);i++){
        for(int j=0;j<n;j++){
            dp[i][j] = -1;
        }
    }
    cout<<"Travelling Saleman Distance is "<<tsp(1,0);

return 0;
}

This needs a [example]. That means include a small but full program that reproduces your error. (in your case, your error is "I don't know how to extract the path from the parameters fed to this function"). We don't necessarily know what you are feeding into this function, so a `main` that calls this functions with small, understandable inputs would help. If possible please convert your variable names to english. It helps us read the code better than having to go back and forth between google translate. — JohnFilleau, May 18 '20 at 12:44
it is just an array initialized to -1 that stores the results (ans) to optimize the code, so that if it has already passed through mask or pos it will be reflected in the array — Alejandro Cruz Lemos, May 18 '20 at 15:11

score 0 · Accepted Answer · answered May 18 '20 at 17:09

Let's introduce a new path function that gives the entire optimal path using the previously calculated dp array.

void  path(int mask,int pos){
    if(mask==VISITED_ALL) return;
    int ans = INT_MAX, chosenCity;

    for(int city=0;city<n;city++){

        if((mask&(1<<city))==0){

            int newAns = dist[pos][city] + dp[mask|(1<<city)][city];
            if(newAns < ans){
                ans = newAns;
                chosenCity = city;
            }
        }

    }
    printf("%d ",city); // here you get the current city you need to visit
    path(mask|(1<<city),city);
}

I don't understand the two last line you've wrote... the variable city is defined in your loop, not outside of it. Could you please fix this and add comments or more description to your code so we can clearly understand ? Thank you. — polycodor, Mar 25 '21 at 03:51

Travelling Salesman problem in dynamic programming

1 Answers1