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("\n");
#define Debug printf("this_ok\n");
#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\n",a);
#define print_int(a,b) if(b == 0) printf("%d ",a); else printf("%d\n",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("\n");
}
printf("%lld\n",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("\n");
#define Debug printf("this_ok\n");
#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\n",a);
#define print_int(a,b) if(b == 0) printf("%d ",a); else printf("%d\n",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\n"); return 0;
}
printf("1\n");
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("\n");
}
}
/*
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("\n");
#define Debug printf("this_ok\n");
#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\n",a);
#define print_int(a,b) if(b == 0) printf("%d ",a); else printf("%d\n",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!\n");
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("\n");
}
}
}
/*
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("\n");
#define Debug printf("this_ok\n");
#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\n",a);
#define print_int(a,b) if(b == 0) printf("%d ",a); else printf("%d\n",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\n",maxflow);
}
}
/*
3
1 2 3
2
2 6
*/
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