Problem Link : http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem&problem=1237
Solution Idea:
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Light OJ: 1086 – Jogging Trails is a similar problem. The main idea behind this problem is Chinese Postman Problem.
For details about this theorem is described in book Competitive programming 3 by Steven Halim.
#include <bits/stdc++.h>
#define pii pair <int,int>
#define pll pair <long long,long long>
#define sc scanf
#define pf printf
#define Pi 2*acos(0.0)
#define ms(a,b) memset(a, b, sizeof(a))
#define pb(a) push_back(a)
#define MP make_pair
#define db double
#define ll long long
#define EPS 10E-10
#define ff first
#define ss second
#define sqr(x) (x)*(x)
#define D(x) cout<<#x " = "<<(x)<<endl
#define VI vector <int>
#define DBG pf("Hi\n")
#define MOD 1000000007
#define CIN ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a) (int)a.size()
#define sf(a) scanf("%d",&a)
#define sfl(a) scanf("%lld",&a)
#define sff(a,b) scanf("%d %d",&a,&b)
#define sffl(a,b) scanf("%lld %lld",&a,&b)
#define sfff(a,b,c) scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c) scanf("%lld %lld %lld",&a,&b,&c)
#define stlloop(v) for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n) for(int i=0;i<n;i++)
#define loop1(i,n) for(int i=1;i<=n;i++)
#define REP(i,a,b) for(int i=a;i<b;i++)
#define RREP(i,a,b) for(int i=a;i>=b;i--)
#define TEST_CASE(t) for(int z=1;z<=t;z++)
#define PRINT_CASE printf("Case %d: ",z)
#define LINE_PRINT_CASE printf("Case %d:\n",z)
#define CASE_PRINT cout<<"Case "<<z<<": "
#define all(a) a.begin(),a.end()
#define intlim 2147483648
#define infinity (1<<28)
#define ull unsigned long long
#define gcd(a, b) __gcd(a, b)
#define lcm(a, b) ((a)*((b)/gcd(a,b)))
using namespace std;
/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1}; // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1}; // Kings Move
//const int fx[]={-2, -2, -1, -1, 1, 1, 2, 2}; // Knights Move
//const int fy[]={-1, 1, -2, 2, -2, 2, -1, 1}; // Knights Move
/*------------------------------------------------*/
/*-----------------------Bitmask------------------*/
int Set(int N,int pos)
{
return N=N | (1<<pos);
}
int reset(int N,int pos)
{
return N= N & ~(1<<pos);
}
bool check(int N,int pos)
{
return (bool)(N & (1<<pos));
}
/*------------------------------------------------*/
ll g[16][16];
int degree[16];
ll dp[1<<16];
int n,m;
void floyed_warshal()
{
for(int k=0; k<n; k++)
for(int i=0; i<n; i++)
for(int j=0; j<n; j++)
{
if(g[i][j]>g[i][k]+g[k][j])
g[i][j]=g[i][k]+g[k][j];
}
}
ll func(int mask)
{
if(mask==0) return 0;
ll &ret=dp[mask];
if(ret!=-1) return ret;
int pos=0;
for(int i=0; i<n; i++)
if(check(mask,i))
{
pos=i;
break;
}
ret=INT_MAX;
for(int i=pos+1;i<n;i++)
{
if(check(mask,i))
{
int temp_mask=mask;
temp_mask=reset(temp_mask,pos);
temp_mask=reset(temp_mask,i);
ret=min(ret,g[pos][i]+func(temp_mask));
}
}
return ret;
}
int main()
{
// freopen("in.txt","r",stdin);
// freopen("out.txt","w",stdout);
int t;
// sf(t);
// TEST_CASE(t)
while(sf(n) && n)
{
sf(m);
// sff(n,m);
ll ans=0;
for(int i=0; i<=n; i++) for(int j=0; j<=n; j++) g[i][j]=INT_MAX;
ms(degree,0);
for(int i=0; i<m; i++)
{
ll a,b,c;
sfffl(a,b,c);
a--;
b--;
g[a][b]=min(g[a][b],c);
g[b][a]=min(g[b][a],c);
degree[a]++;
degree[b]++;
ans+=c;
}
floyed_warshal();
int mask=0;
for(int i=0; i<n; i++)
if(degree[i]%2)
mask=Set(mask,i);
// PRINT_CASE;
ms(dp,-1);
printf("%lld\n",ans+func(mask));
}
return 0;
}