Algorithm for TSP giving incorrect output - c++

Question

I've spent a few hours trying to figure out what's wrong with my program, but I can't figure it out. This is a minimum tour cost program. (TSP)
c is for city and a is for arc(cost for travel between 2 cities)
Inputs I'm using to test:
c 1
c 2
c 3
c 4
c 5
a 1 2 1400
a 1 3 1800
a 1 4 4000
a 1 5 3500
a 2 3 1200
a 2 4 3400
a 2 5 3600
a 3 4 2300
a 3 5 2700
a 4 5 2100
And here is my code. The above inputs should give 10500 minTour, but its showing 5600.
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cassert>
#include <sstream>
#include <cstdlib>
#include <string>
#include <stdint.h>
using namespace std;
static char gFirstCity = 0;
static unsigned graph[50][50] = {0};
static unsigned minTour = 0xffffffff;
void swap (char *x, char *y)
{
char temp;
temp = *x;
*x = *y;
*y = temp;
}
void permute(char* cities, unsigned start, unsigned length)
{
if (start == (length-1))
{
cout << endl;
unsigned cost =0;
cost+= graph[(unsigned)gFirstCity][(unsigned)*cities];
for(unsigned i = 0; i < length-1; i++ )
{
cost+=graph[(unsigned)cities[i]][(unsigned)cities[i+1]];
for(int i = 0; i < length; i++){
cout << (int)cities[i];
}
}
cost+=graph[(unsigned)cities[length-1]][(unsigned)gFirstCity];
for(int i = 0; i < length; i++){
cout << (int)cities[i];
}
if(cost<minTour){
minTour = cost;
}
}
else
{
for (unsigned j = start; j < length; j++)
{
swap((cities + start), (cities + j));
permute(cities, start + 1, length);
swap((cities + start), (cities + j));
}
}
}
int main()
{
string cities;
string line;
char command = 0;
unsigned city = 0;
while (getline(cin, line))
{
sscanf(line.c_str(), "%c %d", &command, &city);
if (command != 'c')
break;
cities.push_back((unsigned char)city);
}
gFirstCity = cities[0];
unsigned to = 0;
unsigned from = 0;
uint32_t cost = 0;
sscanf(line.c_str(), "%c %d %d %d", &command, &to, &from, &cost);
graph[to-1][from-1]=cost;
graph[from-1][to-1]=cost;
while (getline(cin, line))
{
sscanf(line.c_str(), "%c %d %d %d", &command, &to, &from, &cost);
graph[to-1][from-1]=cost;
graph[from-1][to-1]=cost;
}
permute((char*)cities.c_str()+1, 0, cities.length()-1);
cout << minTour << endl;
return EXIT_SUCCESS;

Answer 1

After adding a bit of debugging output to the code, the biggest problem appears to be that your algorithm mixes array indexes and cities inconsistently.
For example, your gStartCity is used as an array index (0-based), but is actually a city number (1-based).
You use array indexes 1-5 when actually obtaining costs, but you assign the costs to array indexes 0-4.
I believe you can get the expected result by changing both sets of graph[][] assignments to:
graph[to][from]=cost;
graph[from][to]=cost;
The definition of graph[][] will allow this without overwriting something else, and you won't live long enough for this algorithm to compute the optimal path for 49 cities, so the difference won't matter (49 cities would require about 6E+62 possible paths; even if you could check a million paths per second, this would only take about 20,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years to compute).
Your code is very difficult to read and follow, so I'm not sure how best to fix the fundamental problem that you are off by 1 on most of your array indices, but at least this should get it running closer to the way you expect.