Kos [最大流(TLE)]

$Kos$

有 $n$ 个人，之间会有 $m$ 场比赛。你可以设定所有比赛的结果。你希望获胜场次最
多的人获胜的场次数最少，问这个最小值是多少。

$1 le n le 10^4$, $0 le m le 10^4$ .

---

$color{red}{正解部分}$

最多的人获胜最少 $ightarrow$ 二分答案 .

二分答案得出 $mid$, 然后 $chk$ ,

先建图 $downarrow$

• $s ightarrow 比赛 (1)$
• $比赛 ightarrow 人 (-)$
• $人 ightarrow t (mid)$

然后检查最大流是否等于 $M$, 即可 $chk$ .

---

$color{red}{实现部分}$

重新跑 $Dinic$ 需要注意以下内容

• $num0$ 的重置
• $haed$ 的重置
• $M$ 和 $N$ 之间的区分 .

重置时又需要注意点的范围为 $[0, M+N] ∪ f_t$ .

#include<bits/stdc++.h>
#define reg register

const int maxn = 20004;
const int inf = 0x3f3f3f3f;

int N;
int M;
int Ans;
int tim_reg;
int f_s = 0;
int f_t;
int num0 = 1;
int cur[maxn<<2];
int dep[maxn<<2];
int head[maxn<<2];
int tmp_head[maxn<<2];

struct Edge{ int nxt, to, w, flow; } edge[maxn << 3];

void Add(int from, int to, int w, int flow = 0){
        edge[num0] = (Edge){ head[from], to, w, flow };
        head[from] = num0 ++;
}

bool BFS(){
	for(reg int i = 0; i <= M+N; i ++) cur[i] = head[i];
	cur[f_t] = head[f_t];
        memset(dep, 0, sizeof dep);
        std::queue <int> Q; Q.push(f_s);
	dep[f_s] = 1; // !
        while(!Q.empty()){
                int ft = Q.front(); Q.pop();
                for(reg int i = head[ft]; ~i; i = edge[i].nxt){
                        int to = edge[i].to;
                        if(dep[to] || edge[i].flow >= edge[i].w) continue ;
                        dep[to] = dep[ft] + 1;
                        Q.push(to);
                        if(to == f_t) return 1;
                }
        }
        return dep[f_t];
}

int DFS(int k, int Min_w){
        if(k == f_t) return Min_w;
        for(reg int &i = cur[k]; ~i; i = edge[i].nxt){
                int to = edge[i].to, t = edge[i].w - edge[i].flow;
                if(dep[to] != dep[k] + 1 || t <= 0) continue ;
                int tmp = DFS(to, std::min(Min_w, t));
                if(tmp){
                        edge[i].flow += tmp, edge[i^1].flow -= tmp;
                        return tmp;
                }
        }
        return 0; // !
}

int Dinic(){
        int res = 0;
        for(reg int i = 0; i <= num0; i ++) edge[i].flow = 0;
        while(BFS()) res += DFS(f_s, inf);
        return res;
}

bool chk(int mid){
	for(reg int i = 0; i <= M+N+1; i ++) head[i] = tmp_head[i];
        num0 = tim_reg;
        for(reg int i = 1; i <= N; i ++) Add(M+i, f_t, mid), Add(f_t, M+i, -mid);
        return Dinic() >= M;
}

int main(){
	freopen("kos.in", "r", stdin);
	freopen("kos.out", "w", stdout);
	memset(head, -1, sizeof head);
	scanf("%d%d", &N, &M);
	for(reg int i = 1; i <= M; i ++){
                Add(f_s, i, 1), Add(i, f_s, -1);
                int a, b;
                scanf("%d%d", &a, &b);
                Add(i, M+a, inf), Add(M+a, i, -inf);
                Add(i, M+b, inf), Add(M+b, i, -inf);
        }
        f_t = N+M+1;
        for(reg int i = 0; i <= M+N+1; i ++) tmp_head[i] = head[i];
        tim_reg = num0;  Ans = inf;
        
        int l = 1, r = M;
        while(l <= r){
                int mid = l+r >> 1;
                if(chk(mid)) Ans = std::min(Ans, mid), r = mid - 1;
                else l = mid + 1;
        }
        printf("%d
", Ans);
	return 0;
}

---

#include<bits/stdc++.h>
using namespace std;
const int N=4e4+5;
const int M=2e6+5;
const int inf=2147483647;
int s,n,m,cnt,now=1,v[M],w[M],cr[N],nex[M],head[N],deep[N];
void add(int x,int y,int z){
	nex[++now]=head[x],w[now]=z;
	head[x]=now,v[now]=y;
}
queue<int>que;
struct each{
	int x,y;
}a[N];
bool bfs(){
	for(int i=0;i<=s;i++)	cr[i]=head[i];
	for(int i=0;i<s;i++)	deep[i]=0;
	que.push(s),deep[s]=1;
	while(!que.empty()){
		int x=que.front();que.pop();
		for(int i=head[x];i;i=nex[i])
			if(w[i]&&!deep[v[i]]){
				deep[v[i]]=deep[x]+1;
				que.push(v[i]);
			}
	}
	return deep[0];
}
int dfs(int x,int f){
	if(!x||!f)	return f;
	int ans=0;
	for(int &i=cr[x];i;i=nex[i])
		if(w[i]&&deep[v[i]]==deep[x]+1){
			int d=dfs(v[i],min(w[i],f));
			if(!d)	continue;
			w[i]-=d,ans+=d;
			w[i^1]+=d,f-=d;
			if(!f)	break;
		}
	if(!ans)	deep[x]=0;
	return ans;
}
bool check(int x){
	int ans=0;
	now=1,cnt=n;
	for(int i=0;i<=s;i++)	head[i]=0;
	for(int i=1;i<=n;i++)	add(i,0,x),add(0,i,0);
	for(int i=1;i<=m;i++){
		++cnt,add(s,cnt,1),add(cnt,s,0);
		add(cnt,a[i].x,1),add(a[i].x,cnt,0);
		add(cnt,a[i].y,1),add(a[i].y,cnt,0);
	}
	while(bfs())
	while(int d=dfs(s,inf))	ans+=d;
	return ans==m;
}
int main(){
	freopen("kos.in","r",stdin);
	freopen("kos.out","w",stdout);
	scanf("%d%d",&n,&m),s=n+m+1;
	for(int i=1;i<=m;i++)
		scanf("%d%d",&a[i].x,&a[i].y);
	int l=1,r=m;
	while(l<r){
		int mid=l+r>>1;
		if(check(mid))	r=mid;
		else	l=++mid;
	}
	printf("%d
",l);
	return 0;
}