2020/8/30

英语四级一篇

四题网络流 真就万物建模

一场cf

 

 

#include"stdio.h"
#include"string.h"
#include"stack"
#include"map"
#include"math.h"
#include"iostream"
#include"vector"
#include"queue"
#include"algorithm"
using namespace std;
#define OK printf("
");
#define Debug printf("this_ok
");
#define INF 1e18
typedef long long ll;
#define scanll(a,b) scanf("%lld%lld",&a,&b);
#define scanl(a) scanf("%lld",&a);
#define printl(a,b) if(b == 0) printf("%lld ",a); else printf("%lld
",a);
#define print_int(a,b) if(b == 0) printf("%d ",a); else printf("%d
",a);
typedef pair<int,int> PII;

inline int read(){
    int s = 0, w = 1; char ch = getchar();
    while(ch < '0' || ch > '9')   { if(ch == '-') w = -1; ch = getchar(); }
    while(ch >= '0' && ch <= '9') { s = (s << 3) + (s << 1) + (ch ^ 48); ch = getchar(); }
    return s * w;
}
const ll mod = 998244353;
const int N = 50010,M = 300010;
const  double pi = acos(-1);
const int inf = 1 << 29;
const int dirx[4] = {-1,0,1,0};
const int diry[4] = {0,1,0,-1};
int n,m,t,s,tot;
ll maxflow,sum;
int head[N],ver[M],Next[M],edge[M],d[N];
queue<int> q;
int visit[N];
vector<int> st,tmp;

void add(int x,int y,int z){
    ver[++ tot] = y; Next[tot] = head[x];  edge[tot] = z; head[x] = tot;
    ver[++ tot] = x; edge[tot] = 0; Next[tot] = head[y]; head[y] = tot;
}

bool bfs(){
    memset(d,0,sizeof(d));
    while(q.size())q.pop();
    q.push(s); d[s] = 1;
    while(q.size()){
        int x = q.front(); q.pop();
        for(int i = head[x]; i; i = Next[i])
        if(edge[i] && !d[ver[i]]){
            q.push(ver[i]); d[ver[i]] = d[x] + 1;
            if(ver[i] == t) return 1;
        }
    }
    return 0;
}

int dinic(int x,ll flow){
    if(x == t) return flow;
    ll rest = flow,k;
    for(int i = head[x]; i && rest; i = Next[i]){
         if(edge[i] && d[ver[i]] == d[x] + 1){
            k = dinic(ver[i],min(rest,(ll)edge[i]));
            if(!k) d[ver[i]] = 0;
            edge[i] -= k;
            edge[i ^ 1] += k;
            rest -= k;
         }
    }
    return flow - rest;
}
void dfs(int x){
    tmp.push_back(x);
    for(int i = head[x]; i ;i = Next[i]){
        int y = ver[i];
        if(y > n && y < s && !visit[y - n] && !edge[i]){
           visit[y - n] = 1;
           dfs(y - n);
        }
    }
}
int main(){
    n = read(),m = read();s = 2 * n + 1; t = 2 * n + 2;
    tot = 1;
    for(int i = 1; i <= n; i ++){
      //add(i,i + n,1);
      add(s,i,1); add(i + n,t,1);
    }
    for(int i = 1; i <= m; i ++){
        int x = read(),y = read();
        add(x,y + n,1);
    }

    ll flow = 0;
    while(bfs())
        while(flow = dinic(s,inf)) maxflow += flow;
    

    for(int i = n + 1; i <= n + n; i ++){
        for(int j = head[i]; j; j = Next[j]){
            if(ver[j] == t && edge[j]) st.push_back(i - n);
        }
    }
    //printf("dsf");
    for(int i = 0; i < st.size(); i ++){
      //  printf("%d x",st[i]);
        tmp.clear();
        visit[st[i]] = 1;
        dfs(st[i]);
        for(int j = 0; j < tmp.size(); j ++){
            printf("%d ",tmp[j]);
        }
        printf("
");
    }
    printf("%lld
",n - maxflow);
}
/*
3
1 2 3
2
2 6
*/

#include"stdio.h"
#include"string.h"
#include"stack"
#include"map"
#include"math.h"
#include"iostream"
#include"vector"
#include"queue"
#include"algorithm"
using namespace std;
#define OK printf("
");
#define Debug printf("this_ok
");
#define INF 1e18
typedef long long ll;
#define scanll(a,b) scanf("%lld%lld",&a,&b);
#define scanl(a) scanf("%lld",&a);
#define printl(a,b) if(b == 0) printf("%lld ",a); else printf("%lld
",a);
#define print_int(a,b) if(b == 0) printf("%d ",a); else printf("%d
",a);
typedef pair<int,int> PII;

inline int read(){
    int s = 0, w = 1; char ch = getchar();
    while(ch < '0' || ch > '9')   { if(ch == '-') w = -1; ch = getchar(); }
    while(ch >= '0' && ch <= '9') { s = (s << 3) + (s << 1) + (ch ^ 48); ch = getchar(); }
    return s * w;
}
const ll mod = 998244353;
const int N = 50010,M = 300010;
const  double pi = acos(-1);
const int inf = 1 << 29;
const int dirx[4] = {-1,0,1,0};
const int diry[4] = {0,1,0,-1};
int n,m,t,s,tot;
ll maxflow,sum;
int head[N],ver[M],Next[M],edge[M],d[N];
queue<int> q;

void add(int x,int y,int z){
    ver[++ tot] = y; Next[tot] = head[x];  edge[tot] = z; head[x] = tot;
    ver[++ tot] = x; edge[tot] = 0; Next[tot] = head[y]; head[y] = tot;
}

bool bfs(){
    memset(d,0,sizeof(d));
    while(q.size())q.pop();
    q.push(s); d[s] = 1;
    while(q.size()){
        int x = q.front(); q.pop();
        for(int i = head[x]; i; i = Next[i])
        if(edge[i] && !d[ver[i]]){
            q.push(ver[i]); d[ver[i]] = d[x] + 1;
            if(ver[i] == t) return 1;
        }
    }
    return 0;
}

int dinic(int x,ll flow){
    if(x == t) return flow;
    ll rest = flow,k;
    for(int i = head[x]; i && rest; i = Next[i]){
         if(edge[i] && d[ver[i]] == d[x] + 1){
            k = dinic(ver[i],min(rest,(ll)edge[i]));
            if(!k) d[ver[i]] = 0;
            edge[i] -= k;
            edge[i ^ 1] += k;
            rest -= k;
         }
    }
    return flow - rest;
}
int main(){
    n = read(),m = read();s = n + m + 1; t = s + 1;
    tot = 1; int ans = 0;
    for(int i = 1; i <= n; i ++){
        for(int j = 1; j <= m; j ++){
            add(i,j + n,1);
        }
    }
    for(int i = 1; i <= n; i ++){
        int x = read(); add(s,i,x); ans += x;
    }
    for(int i = 1; i <= m; i ++){
        int x = read();add(i + n,t,x);
    }

    ll flow = 0;
    while(bfs())
        while(flow = dinic(s,inf)) maxflow += flow;
    if(maxflow != ans){
        printf("0
"); return 0;
    }
    printf("1
");
    for(int i = 1; i <= n; i ++){
        for(int j = head[i]; j; j = Next[j]){
            if(edge[j] == 0){
                printf("%d ",ver[j] - n);
            }
        }
        printf("
");
    }
}
/*
3
1 2 3
2
2 6
*/

#include"stdio.h"
#include"string.h"
#include"stack"
#include"map"
#include"math.h"
#include"iostream"
#include"vector"
#include"queue"
#include"algorithm"
using namespace std;
#define OK printf("
");
#define Debug printf("this_ok
");
#define INF 1e18
typedef long long ll;
#define scanll(a,b) scanf("%lld%lld",&a,&b);
#define scanl(a) scanf("%lld",&a);
#define printl(a,b) if(b == 0) printf("%lld ",a); else printf("%lld
",a);
#define print_int(a,b) if(b == 0) printf("%d ",a); else printf("%d
",a);
typedef pair<int,int> PII;

inline int read(){
    int s = 0, w = 1; char ch = getchar();
    while(ch < '0' || ch > '9')   { if(ch == '-') w = -1; ch = getchar(); }
    while(ch >= '0' && ch <= '9') { s = (s << 3) + (s << 1) + (ch ^ 48); ch = getchar(); }
    return s * w;
}
const ll mod = 998244353;
const int N = 50010,M = 300010;
const  double pi = acos(-1);
const int inf = 1 << 29;
const int dirx[4] = {-1,0,1,0};
const int diry[4] = {0,1,0,-1};
int n,m,t,s,tot,k;
ll maxflow,sum;
int head[N],ver[M],Next[M],edge[M],d[N];
queue<int> q;
vector<int> st[N];

void add(int x,int y,int z){
    ver[++ tot] = y; Next[tot] = head[x];  edge[tot] = z; head[x] = tot;
    ver[++ tot] = x; edge[tot] = 0; Next[tot] = head[y]; head[y] = tot;
}

bool bfs(){
    memset(d,0,sizeof(d));
    while(q.size())q.pop();
    q.push(s); d[s] = 1;
    while(q.size()){
        int x = q.front(); q.pop();
        for(int i = head[x]; i; i = Next[i])
        if(edge[i] && !d[ver[i]]){
            q.push(ver[i]); d[ver[i]] = d[x] + 1;
            if(ver[i] == t) return 1;
        }
    }
    return 0;
}

int dinic(int x,ll flow){
    if(x == t) return flow;
    ll rest = flow,k;
    for(int i = head[x]; i && rest; i = Next[i]){
         if(edge[i] && d[ver[i]] == d[x] + 1){
            k = dinic(ver[i],min(rest,(ll)edge[i]));
            if(!k) d[ver[i]] = 0;
            edge[i] -= k;
            edge[i ^ 1] += k;
            rest -= k;
         }
    }
    return flow - rest;
}
int main(){
    m = read(),n = read();s = n + m + 1; t = s + 1; tot = 1;
    int ans = 0;
    for(int i = 1; i <= m; i ++){
        int x = read(); add(i + n,t,x);
        ans += x;
    }
    for(int i = 1; i <= n; i ++){
        add(s,i,1);
    }
    for(int i = 1; i <= n; i ++){
        int k = read();
        while(k --){
            int x = read();
            add(i,x + n,1);
        }
    }
    ll flow = 0;
    while(bfs())
        while(flow = dinic(s,inf)) maxflow += flow;
    if(maxflow != ans) printf("No Solution!
");
    else {
        for(int i = 1; i <= m; i ++){
            printf("%d:",i);
            for(int x = 1; x <= n; x ++){

                for(int j = head[x]; j; j = Next[j]){
                     if(ver[j] != i + n) continue;
                     if(edge[j]) continue;
                     if(ver[j] == s || ver[j] == t) continue;
                     printf(" %d",x);
                }
            }
            printf("
");
        }
    }
}
/*
3
1 2 3
2
2 6
*/

#include"stdio.h"
#include"string.h"
#include"stack"
#include"map"
#include"math.h"
#include"iostream"
#include"vector"
#include"queue"
#include"algorithm"
using namespace std;
#define OK printf("
");
#define Debug printf("this_ok
");
#define INF 1e18
typedef long long ll;
#define scanll(a,b) scanf("%lld%lld",&a,&b);
#define scanl(a) scanf("%lld",&a);
#define printl(a,b) if(b == 0) printf("%lld ",a); else printf("%lld
",a);
#define print_int(a,b) if(b == 0) printf("%d ",a); else printf("%d
",a);
typedef pair<int,int> PII;

inline int read(){
    int s = 0, w = 1; char ch = getchar();
    while(ch < '0' || ch > '9')   { if(ch == '-') w = -1; ch = getchar(); }
    while(ch >= '0' && ch <= '9') { s = (s << 3) + (s << 1) + (ch ^ 48); ch = getchar(); }
    return s * w;
}
const ll mod = 998244353;
const int N = 50010,M = 300010;
const  double pi = acos(-1);
const int inf = 1 << 29;
int n,m,t,s,tot;
ll maxflow,sum;
int head[N],ver[M],Next[M],edge[M],d[N];
queue<int> q;

void add(int x,int y,int z){
    ver[++ tot] = y; Next[tot] = head[x];  edge[tot] = z; head[x] = tot;
    ver[++ tot] = x; edge[tot] = 0; Next[tot] = head[y]; head[y] = tot;
}

bool bfs(){
    memset(d,0,sizeof(d));
    while(q.size())q.pop();
    q.push(s); d[s] = 1;
    while(q.size()){
        int x = q.front(); q.pop();
        for(int i = head[x]; i; i = Next[i])
        if(edge[i] && !d[ver[i]]){
            q.push(ver[i]); d[ver[i]] = d[x] + 1;
            if(ver[i] == t) return 1;
        }
    }
    return 0;
}

int dinic(int x,ll flow){
    if(x == t) return flow;
    ll rest = flow,k;
    for(int i = head[x]; i && rest; i = Next[i]){
         if(edge[i] && d[ver[i]] == d[x] + 1){
            k = dinic(ver[i],min(rest,(ll)edge[i]));
            if(!k) d[ver[i]] = 0;
            edge[i] -= k;
            edge[i ^ 1] += k;
            rest -= k;
         }
    }
    return flow - rest;
}
int main(){
    int T = read();
    int cont = 1;
    while(T --){
        n = read(),m = read();s = 1; t = n;
        memset(head,0,sizeof(head));
        tot = 1;
        for(int i = 1; i <= m; i ++){
         int x = read(),y = read(),w = read();
           add(x,y,w);
        }
        ll flow = 0; maxflow = 0;
        while(bfs())
            while(flow = dinic(s,inf)) maxflow += flow;
        printf("Case %d: ",cont ++);
        printf("%lld
",maxflow);
    }
}
/*
3
1 2 3
2
2 6
*/