Parity game poj1733

版权声明：本文为博主原创文章，未经博主允许不得转载。 https://blog.csdn.net/MrTinTin/article/details/83385889

有一个长度已知的01串，给出[l,r]这个区间中的1是奇数个还是偶数个，给出一系列语句问前几个是正确的

解法一：带权并查集。

#include<iostream>
#include<algorithm>
#define f(i,l,r) for(i=(l);i<=(r);i++)
using namespace std;
const int MAXN=5005;
int fa[MAXN<<1],d[MAXN<<1];
int m,n,L;
string s;
struct Node{
	int l,r,ans;
}q[MAXN];
int h[MAXN<<1];
inline void Makeset()
{
	int i;
	f(i,1,L){
		fa[i]=i;
	}
}
inline int Find(int x)
{
	if(fa[x]==x) return fa[x];
	int root=Find(fa[x]);
	d[x]^=d[fa[x]];
	return fa[x]=root;
}
int main()
{
	ios::sync_with_stdio(false);
	int i,j;
	cin>>m>>n;
	f(i,1,n){
		cin>>q[i].l>>q[i].r>>s;
		if(s=="even") q[i].ans=0;
		else q[i].ans=1;
		h[i+i-1]=q[i].l-1;
		h[i+i]=q[i].r;
	}
	sort(h+1,h+1+i+i);
	L=unique(h+1,h+1+i+i)-(h+1);
	Makeset();
	f(i,1,n){
		int x=lower_bound(h+1,h+1+L,q[i].l-1)-h;
		int y=lower_bound(h+1,h+1+L,q[i].r)-h;
		int fx=Find(x),fy=Find(y);
		if(fx==fy){
			if(q[i].ans!=(d[x]^d[y])){
				cout<<i-1<<endl;
				return 0;
			}
		}
		else{
			fa[fx]=fy;
			d[fx]=d[x]^d[y]^q[i].ans;
		}
	}
	cout<<n<<endl;
	return 0;
}

解法二：扩展域并查集。

#include<iostream>
#include<algorithm>
#define f(i,l,r) for(i=(l);i<=(r);i++)
using namespace std;
const int MAXN=10005;
struct Node{
	int l,r,ans;
}q[MAXN];
int fa[MAXN<<1],h[MAXN];
int L,n,m;
string s;
inline void Makeset()
{
	int i;
	f(i,1,L+L){
		fa[i]=i;
	}
}
inline int Find(int x)
{
	return fa[x]==x?x:fa[x]=Find(fa[x]);
}
inline void Union(int x,int y)
{
	x=Find(x);y=Find(y);
	fa[x]=y;
}
int main()
{
	ios::sync_with_stdio(false);
	int i,j;
	cin>>m>>n;
	f(i,1,n){
		cin>>q[i].l>>q[i].r>>s;
		if(s=="even") q[i].ans=0;
		else q[i].ans=1;
		h[i+i-1]=q[i].l-1;
		h[i+i]=q[i].r;
	}
	sort(h+1,h+1+i+i);
	L=unique(h+1,h+1+i+i)-(h+1);
	Makeset();
	f(i,1,n){
		int x=lower_bound(h+1,h+1+L,q[i].l-1)-h;
		int y=lower_bound(h+1,h+1+L,q[i].r)-h;
		if(q[i].ans==0){
			if(Find(x)==Find(y+L)){
				cout<<i-1<<endl;
				return 0;
			}
			Union(x,y);
			Union(x+L,y+L);
		}
		else{
			if(Find(x)==Find(y)){
				cout<<i-1<<endl;
				return 0;
			}
			Union(x+L,y);
			Union(x,y+L);
		}
	}
	cout<<n<<endl;
	return 0;
}