建图方式：
我的方式为：先看从s到t的方法种数和t到s的方法种数，如果都大于1的话就是合法的。
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <set>
#include <vector>
#include <map>
#include <queue>
#include <set>
#include <algorithm>
#include <limits.h>
using namespace std;
#define MAXN 1500
#define MAXM 600000
const int INF = INT_MAX;
typedef long long LL;
struct Edge
{
int from,to,ci,next;
Edge(){}
Edge(int _from,int _to,int _ci,int _next):from(_from),to(_to),ci(_ci),next(_next){}
}e[MAXM];
int head[MAXN],tot;
int dis[MAXN];
int top,sta[MAXN],cur[MAXN];
int n,m;
inline void init(){
memset(head,-1,sizeof(head));
tot=0;
}
inline void AddEdge(int u,int v,int ci0,int ci1=0){
e[tot]=Edge(u,v,ci0,head[u]);
head[u]=tot++;
e[tot]=Edge(v,u,ci1,head[v]);
head[v]=tot++;
}
inline bool bfs(int st,int et){
memset(dis,0,sizeof(dis));
dis[st]=1;
queue <int> q;
q.push(st);
while(!q.empty()){
int now=q.front();
q.pop();
for(int i=head[now];i!=-1;i=e[i].next){
int next=e[i].to;
if(e[i].ci&&!dis[next]){
dis[next]=dis[now]+1;
if(next==et)return true;
q.push(next);
}
}
}
return false;
}
LL Dinic(int st,int et){
LL ans=0;
while(bfs(st,et)){
//printf("here\n");
top=0;
memcpy(cur,head,sizeof(head));
int u=st,i;
while(1){
if(u==et){
int pos,minn=INF;
//printf("top:%d\n",top);
for(i=0;i<top;i++)
{
if(minn>e[sta[i]].ci){
minn=e[sta[i]].ci;
pos=i;
}
//printf("%d --> %d\n",e[sta[i]].from,e[sta[i]].to);
}
for(i=0;i<top;i++){
e[sta[i]].ci-=minn;
e[sta[i]^1].ci+=minn;
}
top=pos;
u=e[sta[top]].from;
ans+=minn;
//printf("minn:%d\n\n",minn);
}
for(i=cur[u];i!=-1;cur[u]=i=e[i].next)
if(e[i].ci&&dis[u]+1==dis[e[i].to])break;
if(cur[u]!=-1){
sta[top++]=cur[u];
u=e[cur[u]].to;
}
else {
if(top==0)break;
dis[u]=0;
u=e[sta[--top]].from;
}
}
}
return ans;
}
struct point
{
double hz;
int x,y,r;
}cs[MAXN];
bool cmp(point x,point y)
{
return x.hz<y.hz;
}
bool check(int i,int j)
{
return ((cs[i].x-cs[j].x)*(cs[i].x-cs[j].x)+(cs[i].y-cs[j].y)*(cs[i].y-cs[j].y))<(cs[i].r+cs[j].r)*(cs[i].r+cs[j].r);
}
int main() {
int t;
scanf("%d",&t);
while(t--)
{
scanf("%d",&n);
for(int i=1;i<=n;i++)
scanf("%lf%d%d%d",&cs[i].hz,&cs[i].x,&cs[i].y,&cs[i].r);
sort(cs+1,cs+1+n,cmp);
init();
for(int i=1;i<n;i++)
for(int j=i+1;j<=n;j++)
{
if(cs[i].hz<cs[j].hz&&check(i,j))
{
AddEdge(i,j,1);
//printf("here1\n");
}
}
int t1=Dinic(1,n);
init();
for(int i=1;i<n;i++)
for(int j=i+1;j<=n;j++)
{
if(cs[j].hz>cs[i].hz&&check(i,j))
{
AddEdge(j,i,1);
//printf("here2\n");
}
}
int t2=Dinic(n,1);
//printf("t1:%d t2:%d\n",t1,t2);
if(t1>1&&t2>1)puts("Game is VALID");
else puts("Game is NOT VALID");
}
return 0;
}