UVA10735 Euler Circuit题解

/* UVa 10735: find euler tour in a mixed graph */
#include <stdio.h>
#include <string.h>
#include <vector>
using namespace std;

int war[128][128], deg[128], need[128], seen[128], n, m;
int ex[1024], ey[1024], ed[1024], em[1024];
vector<int> adj[128];

void tour(int x)
{
while (adj[x].size() > 0) {
int y = adj[x].back();
adj[x].pop_back();
tour(y);
}
printf(m++ ? " %d" : "%d", x);
}

int aug(int x)
{
if (seen[x]) return 0;
seen[x] = 1;

for (int i = 0; i < adj[x].size(); i++) {
int y = adj[x][i];
if (em[y] == 0 || aug(em[y])) {
em[y] = x;
return 1;
}
}

return 0;
}

int solve()
{
int i, j, k;

memset(war, 0, sizeof(war));
memset(deg, 0, sizeof(deg));

/* check connectedness */

for (i = 0; i < m; i++) {
war[ex[i]][ey[i]] = war[ey[i]][ex[i]] = 1;
deg[ex[i]]++; deg[ey[i]]++;
}

for (k = 1; k <= n; k++)
for (war[k][k]=1, i = 1; i <= n; i++)
if (war[i][k])
for (j = 1; j <= n; j++)
war[i][j] |= war[k][j];
for(i = 1; i <= n; i++)
for (j = 1; j <= n; j++)
if (war[i][j] == 0) return 0;

/* underlying undirected graph must have an euler tour... */
for (i = 1; i <= n; i++)
if ((deg[i] % 2) != 0) return 0;

/* prepare matching */

memset(em, 0, sizeof(em));

for (i = 1; i <= n; i++)
need[i] = deg[i] / 2;

for (i = 1; i <= n; i++)
adj[i].clear();

for (i = 0; i < m; i++)
if (!ed[i]) {
adj[ex[i]].push_back(i);
adj[ey[i]].push_back(i);
}

for (i = 0; i < m; i++)
if (ed[i] && --need[em[i]=ey[i]] < 0) return 0;

/* now find a perfect matching... */
for (i = 1; i <= n; i++)
for (; need[i] > 0; need[i]--) {
memset(seen, 0, sizeof(seen));
if (!aug(i)) return 0;
}

/* construct fully directed graph from the matching, and
find euler tour in it with a classical algorithm */

/* edges' directions are reversed, so that tour() can
immediately print the tour's vertices */

for (i = 1; i <= n; i++)
adj[i].clear();

for (i = 0; i < m; i++)
if (ed[i] || ey[i]==em[i])
adj[ey[i]].push_back(ex[i]);
else
adj[ex[i]].push_back(ey[i]);

m = 0;
tour(1);
printf("\n");

return 1;
}

int main()
{
int i, t;
char d;

for (scanf("%d", &t); t-- > 0 && scanf("%d %d", &n, &m) == 2;) {
for (i = 0; i < m; i++) {
scanf("%d %d %c", &ex[i], &ey[i], &d);
ed[i] = (d == 'D' || d == 'd');
}

if (!solve()) printf("No euler circuit exist\n");
if (t) printf("\n");
}

return 0;
}