一般图匹配带花树

一般图匹配带花树

const int maxn = 300;

int N;
bool G[maxn][maxn];
int match[maxn];
bool InQueue[maxn], InPath[maxn], InBlossom[maxn];
int head, tail;
int Queue[maxn];
int start, finish;
int NewBase;
int father[maxn], Base[maxn];
int Count;

void CreateGraph()
{
int u, v;
memset(G, 0, sizeof(G));
scanf("%d", &N);
while (scanf("%d%d",&u,&v) != EOF)
{
G[u][v] = G[v][u] = 1;
}
}

void Push(int u)
{
Queue[tail++] = u;
InQueue[u] = 1;
}

int Pop()
{
int res = Queue[head++];
return res;
}

int FindCommonAncestor (int u, int v)
{
memset(InPath, 0, sizeof(InPath));
while (true)
{
u = Base[u];
InPath[u] = 1;
if (u == start)
{
break;
}
u = father[match[u]];
}
while (true)
{
v = Base[v];
if (InPath[v])
{
break;
}
v = father[match[v]];
}
return v;
}

void ResetTrace(int u)
{
int v;
while (Base[u] != NewBase)
{
v = match[u];
InBlossom[Base[u]] = InBlossom[Base[v]] = 1;
u = father[v];
if (Base[u] != NewBase)
{
father[u] = v;
}
}
}

void BlossomContract(int u, int v)
{
NewBase = FindCommonAncestor(u, v);
memset(InBlossom, 0, sizeof(InBlossom));
ResetTrace(u);
ResetTrace(v);
if (Base[u] != NewBase)
{
father[u]=v;
}
if (Base[v] != NewBase)
{
father[v]=u;
}
for (int tu=1; tu <= N; tu++)
{
if (InBlossom[Base[tu]])
{
Base[tu] = NewBase;
if (!InQueue[tu])
{
Push(tu);
}
}
}
}

void FindAugmentingPath()
{
memset(InQueue, 0, sizeof(InQueue));
memset(father, 0, sizeof(father));
for (int i = 1; i <= N; i++)
{
Base[i] = i;
}
head = tail = 1;
Push(start);
finish = 0;
while (head < tail)
{
int u = Pop();
for (int v = 1; v <= N; v++)
{
if (G[u][v] && (Base[u] != Base[v]) && match[u] != v)
{
if ((v == start) || ((match[v] > 0) && father[match[v]] > 0))
{
BlossomContract(u, v);
}
else if (father[v] == 0)
{
father[v] = u;
if (match[v] > 0)
{
Push(match[v]);
}
else
{
finish = v;
return ;
}
}
}
}
}
}

void AugmentPath()
{
int u, v, w;
u = finish;
while (u > 0)
{
v = father[u];
w = match[v];
match[v] = u;
match[u] = v;
u = w;
}
}

void Edmonds()
{
memset(match, 0, sizeof(match));
for (int u = 1; u <= N; u++)
{
if (match[u] == 0)
{
start = u;
FindAugmentingPath();
if (finish > 0)
{
AugmentPath();
}
}
}
}

void PrintMatch()
{
Count = 0;
for (int u = 1; u <= N; u++)
{
if (match[u] > 0)
{
Count++;
}
}
printf("%d\n", Count);
for (int u = 1; u <= N; u++)
{
if (u < match[u])
{
printf("%d %d\n", u, match[u]);
}
}
}

int main()
{
CreateGraph();
Edmonds();      //  进行匹配
PrintMatch();   //  输出匹配
return 0;
}