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题意:给定n个昆虫和m个判断x, y,表示x和y是异性。求判断是否错误。
法一:带权并查集
#include <cstdio>
using namespace std;
const int N = 2010;
int fa[N],relation[N];//0:相同,1不同
int n, m;
int findf(int x)
{
if(x != fa[x])
{
int f = findf(fa[x]);
relation[x] = (relation[x]+relation[fa[x]])%2;//与朴素的不同
fa[x] = f;
}
return fa[x];
}
bool merge_(int x, int y)
{
int f1 = findf(x);
int f2 = findf(y);
if(f1==f2)
{
if((relation[x]+relation[y])%2==0)
return 1;
return 0;
}
fa[f2] = f1;
relation[f2] = (relation[x]+relation[y]+1)%2;//保证更新后x,y为异性
return 0;
}
int main()
{
int t;
scanf("%d", &t);
for(int cas = 1; cas <= t; ++cas)
{
scanf("%d %d", &n, &m);
for(int i = 0; i <= n; ++i)
{
fa[i] = i;
relation[i] = 0;
}
bool flag = 0;
while(m--)
{
int x, y;
scanf("%d %d", &x, &y);
if(merge_(x, y))
flag = 1;
}
if(flag) printf("Scenario #%d:\nSuspicious bugs found!\n\n", cas);
else printf("Scenario #%d:\nNo suspicious bugs found!\n\n", cas);
}
return 0;
}
法二:把一个点i分成两个点i和i+n,一个表示相同,一个表示不同
#include <cstdio>
using namespace std;
const int N = 2010;
int fa[N<<1];
int n, m;
int findf(int x)
{
return x==fa[x]?x:fa[x]=findf(fa[x]);
}
void merge_(int x, int y)
{
int f1 = findf(x);
int f2 = findf(y);
if(f1!=f2)
fa[f1] = f2;
}
int main()
{
int t;
scanf("%d", &t);
for(int cas = 1; cas <= t; ++cas)
{
scanf("%d %d", &n, &m);
for(int i = 0; i <= 2*n; ++i) fa[i] = i;
bool flag = 0;
while(m--)
{
int x, y;
scanf("%d %d", &x, &y);
if(findf(x)==findf(y)) flag = 1;
else
{
merge_(x, y+n);
merge_(x+n, y);
}
}
if(flag) printf("Scenario #%d:\nSuspicious bugs found!\n\n", cas);
else printf("Scenario #%d:\nNo suspicious bugs found!\n\n", cas);
}
return 0;
}
法三:dif[x]表示与x性别不同的昆虫
#include <cstdio>
using namespace std;
const int N = 2010;
int fa[N<<1],dif[N<<1];
int n, m;
int findf(int x)
{
return x==fa[x]?x:fa[x]=findf(fa[x]);
}
void merge_(int x, int y)
{
int f1 = findf(x);
int f2 = findf(y);
if(f1!=f2)
fa[f1] = f2;
}
int main()
{
int t;
scanf("%d", &t);
for(int cas = 1; cas <= t; ++cas)
{
scanf("%d %d", &n, &m);
for(int i = 0; i <= 2*n; ++i)
{
fa[i] = i;
dif[i] = 0;
}
bool flag = 0;
while(m--)
{
int x, y;
scanf("%d %d", &x, &y);
if(findf(x)==findf(y)) flag = 1;
else if(dif[x]+dif[y]==0)
{
dif[x] = y;
dif[y] = x;
}
else if(!dif[x])
{
dif[x] = y;
merge_(x, dif[y]);
}
else if(!dif[y])
{
dif[y] = x;
merge_(y, dif[x]);
}
else
{
merge_(x, dif[y]);
merge_(y, dif[x]);
}
}
if(flag) printf("Scenario #%d:\nSuspicious bugs found!\n\n", cas);
else printf("Scenario #%d:\nNo suspicious bugs found!\n\n", cas);
}
return 0;
}