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Jogging Trails

                                      Jogging Trails

                                                       bitwise DP 


#include <iostream>
#include <cstring>
#include <climits>
#include <cstdio>

#define INF INT_MAX
#define sf(a) scanf("%d", &a)

#define set(b, pos) ( b | (1 << pos) )
#define off(b, pos) ( b & ~( 1 << pos) )
#define test(b, pos) (b & (1 << pos) )

using namespace std;

int v, e, st, en, wt, weight, bits;

int graph[15][15];
int deg[15]; //stores degree of a node
int memo[1 << 15];

int solve(int bits)
{
    if(memo[bits] >= 0)
        return memo[bits];

    int ans = INF;
    int b;

    for(int i = 0; i < v; i++)
    {
        for(int j = i + 1; j < v; j++)
        {
            if(test(bits, i) && test(bits, j))
            {
                b = bits;
                b = off(b, i);
                b = off(b, j);

                ans = min(ans, solve(b) + graph[i][j]);
            }
        }
    }

    return memo[bits] = ans;
}

//finds the shortest distance between every node
void floyd()
{
    for(int k = 0; k < v; k++ )
    {
        for(int i = 0; i < v; i++ )
        {
            for(int j = 0; j < v; j++ )
            {
                if(graph[i][k] != INF && graph[k][j] != INF)
                    graph[i][j] = min(graph[i][k]+graph[k][j], graph[i][j]);
            }
        }
    }
}


int main()
{
    while(scanf("%d %d,", &v, &e) == 2)
    {
        for(int i = 0; i < v; i++)
        {
            for(int j = 0; j < v; j++)
            {
                graph[i][j] = INF;
            }
        }

        memset(deg, 0, sizeof(deg));
        weight = 0;
        bits = 0;

        for(int i = 0; i < e; i++)
        {
            sf(st); sf(en); sf(wt);

            st--, en--;

            graph[st][en] = graph[en][st] = min(graph[st][en], wt);

            weight += wt;

            deg[st]++, deg[en]++;
        }

        floyd();

        //sets 1 for each node that has odd degree
        for(int i = 0; i < v; i++)
        {
            if(deg[i] & 1)
            {
                bits = set(bits, i);
            }
        }

        memset(memo, -1, sizeof(memo));
        memo[0] = 0;

        weight += solve(bits);

        cout << weight << endl;
    }

    return 0;
}

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