[LightOJ-1356] Prime Independence 二分图+素数分解

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int MAXN = 50010;
const int MAXM = 1010*1010;
const int INF = 0x3f3f3f3f;
int N;
struct Node {
	int x,y;
} p[MAXN],it[MAXN];
int v[MAXN];

struct Edge {
	int v;
	int next;
} edge[MAXM];

int nx, ny;
int cnt;
int t;
int dis;

int first[MAXN];
int xlink[MAXN], ylink[MAXN];
/*xlink[i]表示左集合顶点所匹配的右集合顶点序号，ylink[i]表示右集合i顶点匹配到的左集合顶点序号。*/
int dx[MAXN], dy[MAXN];
/*dx[i]表示左集合i顶点的距离编号，dy[i]表示右集合i顶点的距离编号*/
int vis[MAXN]; //寻找增广路的标记数组
void init() {
	cnt = 0;
	memset(first, -1, sizeof(first));
	memset(xlink, -1, sizeof(xlink));
	memset(ylink, -1, sizeof(ylink));
}

void AddEdge(int u, int v) {
	edge[cnt].v = v;
	edge[cnt].next = first[u], first[u] = cnt++;
}

int bfs() {
	queue<int> q;
	dis = INF;
	memset(dx, -1, sizeof(dx));
	memset(dy, -1, sizeof(dy));
	for(int i = 1; i <= nx; i++) {
		if(xlink[i] == -1) {
			q.push(i);
			dx[i] = 0;
		}
	}
	while(!q.empty()) {
		int u = q.front();
		q.pop();
		if(dx[u] > dis) break;
		for(int e = first[u]; e != -1; e = edge[e].next) {
			int v = edge[e].v;
			if(dy[v] == -1) {
				dy[v] = dx[u] + 1;
				if(ylink[v] == -1) dis = dy[v];
				else {
					dx[ylink[v]] = dy[v]+1;
					q.push(ylink[v]);
				}
			}
		}
	}
	return dis != INF;
}

int find(int u) {
	for(int e = first[u]; e != -1; e = edge[e].next) {
		int v = edge[e].v;
		if(!vis[v] && dy[v] == dx[u]+1) {
			vis[v] = 1;
			if(ylink[v] != -1 && dy[v] == dis) continue;
			if(ylink[v] == -1 || find(ylink[v])) {
				xlink[u] = v, ylink[v] = u;
				return 1;
			}
		}
	}
	return 0;
}

int MaxMatch() {
	int ans = 0;
	while(bfs()) {
		memset(vis, 0, sizeof(vis));
		for(int i = 1; i <= nx; i++)
			if(xlink[i] == -1)
				ans += find(i);
	}
	return ans;
}

const int MAXV = 50005;
int prime[MAXV];
bool notprime[MAXV*10];
void pre() {
	int up  = MAXV *10;
	memset(notprime,0,sizeof(notprime));
	notprime[0] = notprime[1] = true;
	memset(prime,0,sizeof(prime));
	for(int i=2; i<up; ++i) {
		if(!notprime[i]) prime[++prime[0]] = i;
		for(int j=1 ; j<=prime[0] && prime[j] <= up / i ; ++j) {
			notprime[prime[j]*i] = true;
			if(i%prime[j]==0) break;
		}
	}
}

int pos[MAXV*10];
int num[MAXV];
int fac[MAXV];
bool jo[MAXV*10];
void ADD(int num,int pt) {
	int sum = 0;
	int tmp = num;
	for(int i=1; prime[i]*prime[i]<=tmp; i++) {
		if(tmp%prime[i]==0) {
			fac[sum++] = prime[i];
			while(tmp%prime[i]==0) tmp/=prime[i];
		}
	}
	if(tmp>1) fac[sum++] = tmp;
	for(int i=0; i<sum; ++i) {
		int x = num/fac[i];
		if(pos[x]) {
			AddEdge(pt,pos[x]);
			AddEdge(pos[x],pt);
		}
	}
}

int main() {
	pre();
	int T,cas=1;
	scanf("%d",&T);
	while(T--) {
		int N;
		scanf("%d",&N);
		init();
		memset(pos,0,sizeof(pos));
		for(int i=1; i<=N; ++i) {
			scanf("%d",&num[i]);
			pos[num[i]] = i;
		}
		nx = ny =0;
		for(int i=1; i<=N; ++i) {
			ADD(num[i],i);
		}
		nx = ny = N;
		int res= N - MaxMatch()/2;
		printf("Case %d: %d\n",cas++,res);
	}
	return 0;
}