2020/8/28

英语四级

基环树学习

5题

 

#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 1e9
#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 = 2000;
const  double pi = acos(-1);

int n,m;
ll head[N],ver[N << 1],Next[N << 1],tot;
int match[N],visit[N],ans1[N];

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

bool dfs(int x){
   for(ll i = head[x];i; i = Next[i]){
      int y = ver[i];
      if(visit[y]) continue;
      visit[y] = 1;
      if(!match[y] || dfs(match[y])) {
        match[y] = x; return true;
      }
   }
   return false;
}
int main(){
    scanf("%d%d",&n,&m);
    for(int i = 1; ; i ++){
        int x = read(),y = read();
        if(x == -1) break;
        add(x,y); //add(y,x);
    }
    int ans = 0;
    for(int i = 1; i <= m; i ++){
        memset(visit,0,sizeof(visit));
        if(dfs(i)) ans ++;
    }
    for(int i = n + 1; i <= m; i ++){
        ans1[match[i]] = i;
    }
    printf("%d
",ans);
    for(int i = n + 1; i <= m; i ++){
      if(match[i] == 0) continue;
        printf("%d %d
",match[i],i);

    }
}
/*
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 + m + 1; t = n * m + m + 2;
    tot = 1;
    for(int i = 1; i <= n; i ++)
      for(int j = 1; j <= m; j ++){
         int x = read(); sum += x;
         if(((i + j) & 1) == 0){
            add(s,i * m + j,x);
         } else add(i * m + j,t,x);
         if(((i + j) & 1) == 0)
             for(int k = 0; k < 4; k ++){
                int X = i + dirx[k];
                int Y = j + diry[k];
                if(X < 1 || X > n || Y < 1 || Y > m) continue;
                add(i * m + j,X * m + Y,inf);
             }
    }
    ll flow = 0;
    while(bfs())
        while(flow = dinic(s,inf)) maxflow += flow;
    printf("%lld
",sum - maxflow);
}
/*
3
1 2 3
2
2 6
*/
#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>
#include"set"
#include"map"
using namespace std;
typedef long long ll;

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 int inf=1e9;
const int N=300,M=N*N+N+7,E=500005;
int ver[E], edge[E], Next[E], head[E];
int cost[E],d[M];
int incf[M], pre[M], v[M];
ll ans;
int n, k, tot, s, t, maxflow,m,q[E];
int store1[N],store2[N],store[N][N];


void add(int x, int y, int z, int c) {
	// 正向边，初始容量z，单位费用c
	ver[++tot] = y, edge[tot] = z, cost[tot] = c;
	Next[tot] = head[x], head[x] = tot;
	// 反向边，初始容量0，单位费用-c，与正向边“成对存储”
	ver[++tot] = x, edge[tot] = 0, cost[tot] = -c;
	Next[tot] = head[y], head[y] = tot;
}


bool spfa() {
	queue<int> q;
	for(int i = 0; i <= n + m + m + n; i ++) d[i] = inf;
	memset(v, 0, sizeof(v));
	q.push(s); d[s] = 0; v[s] = 1; // SPFA 求最长路
	incf[s] = 1 << 30; // 增广路上各边的最小剩余容量
	while (q.size()) {
		int x = q.front(); v[x] = 0; q.pop();
		for (int i = head[x]; i; i = Next[i]) {
			if (!edge[i]) continue; // 剩余容量为0，不在残量网络中，不遍历
			int y = ver[i];
			if (d[y]>d[x] + cost[i]) {
				d[y] = d[x] + cost[i];
				incf[y] = min(incf[x], edge[i]);
				pre[y] = i; // 记录前驱，便于找到最长路的实际方案
				if (!v[y]) v[y] = 1, q.push(y);
			}
		}
	}
	if (d[t] == inf) return false; // 汇点不可达，已求出最大流
	return true;
}

// 更新最长增广路及其反向边的剩余容量
void update() {
	int x = t;
	while (x != s) {
		int i = pre[x];
		edge[i] -= incf[t];
		edge[i ^ 1] += incf[t]; // 利用“成对存储”的xor 1技巧
		x = ver[i ^ 1];
	}
	maxflow += incf[t];
	ans += d[t] * incf[t];
	//printf("%d %d sd
 ",d[t],incf[t]);
}

int main() {
        n = read(); m = read();  tot = 1;
        t = n + m + 2;
        s =  n + m + 1;
        for(int i = 1; i <= n; i ++) {
            scanf("%d",&store1[i]);
            add(s,i,store1[i],0);
        }
        for(int i = 1; i <= m; i ++) {
            scanf("%d",&store2[i]);
            add(i + n,t,store2[i],0);
        }
        for(int i = 1; i <= n; i ++){
            for(int j = 1; j <= m; j ++){
               int x; scanf("%d",&x);
               store[i][j] = x;
               add(i,j + n,inf,x);
            }
        }
        maxflow = ans = 0;
        while(spfa()){
         update();
         //printf("%lld %lld
",maxflow,ans);
        }
        printf("%lld
",ans);


        memset(head,0,sizeof(head)); tot = 1;
        for(int i = 1; i <= n; i ++) {
            add(s,i,store1[i],0);
        }
        for(int i = 1; i <= m; i ++) {
            add(i + n,t,store2[i],0);
        }
        for(int i = 1; i <= n; i ++){
            for(int j = 1; j <= m; j ++){
               add(i,j + n,inf,-store[i][j]);
            }
        }
        maxflow = ans = 0;
        while(spfa()){
         update();
        // printf("%lld %lld
",maxflow,ans);
        }
        printf("%lld
",-ans);
}
#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 1e9
#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 = 300100;
const  double pi = acos(-1);
int n,m;
int head[N],ver[N << 1],Next[N << 1],tot;
int d[N],a[N],far[N];
int k,t;
int id[N];
int f[N][20];

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

void bfs(int x){
    queue<int> Q;Q.push(x);
    d[x] = 1;
    while(!Q.empty()){
        int x = Q.front(); Q.pop();
        for(int i = head[x]; i; i = Next[i]){
            int y = ver[i];
            if(d[y]) continue;
            d[y] = d[x] + 1;
            f[y][0] = x;
            for(int j = 1; j <= t; j ++)
                f[y][j] = f[f[y][j - 1]][j - 1];
            Q.push(y);
        }
    }
}
int lca(int x,int y){
    if(d[x] > d[y]) swap(x,y);
    for(int i = t; i >= 0; i --)
        if(d[f[y][i]] >= d[x]) y = f[y][i];
    if(x == y) return x;
    for(int i = t; i >= 0; i --)
        if(f[x][i] != f[y][i]) x = f[x][i],y = f[y][i];
    return f[x][0];
}

int cmp(int x,int y){
    return d[x] > d[y];
}
int main()
{
    n = read(); m = read();
    t = (int)(log(n) / log(2)) + 1;
    far[1] = 1;
    for(int i = 1; i < n; i ++){
        int x = read(),y = read();
        add(x,y); add(y,x);
    }
    bfs(1);
    while(m --){
      int a, b, c;
        scanf("%d%d%d", &a, &b, &c);

        int x = lca(a, b), y = lca(a, c), z = lca(b, c);

        if(x == y)  swap(y, z);
        if(d[x] < d[y])  swap(x, y);

        int sum = d[a] + d[b] + d[c] - d[y] * 3 - (d[x] - d[y]);
        printf("%d %d
", x, sum);
    }
}
/*
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 1e9
#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 = 300100;
const  double pi = acos(-1);

int n,m,match[N];
bool G[250][250];
bool vis[N],succ[N];
int hide[N];

bool dfs(int x){
    for(int i = 1; i <= n; i ++){
        if(G[x][i] && !vis[i]){
            vis[i] = true;
            if(!match[i] || dfs(match[i])){
                match[i] = x; return true;
            }
        }
    }
    return false;
}


int main(){
    n = read(); m = read();
    for(int i = 1; i <= m; i ++){
        int x = read(),y = read();
        G[x][y] = 1;
    }
    for(int i = 1; i <= n; i ++) G[i][i] = 1;
    for(int k = 1; k <= n; k ++)
        for(int i = 1; i <= n; i ++)
            for(int j = 1; j <= n; j ++)
               G[i][j] |= G[i][k] & G[k][j];
    for(int i = 1; i <= n; i ++) G[i][i] = 0;
    int ans = n;
    for(int i = 1; i <= n; i ++){
        memset(vis,0,sizeof(vis));
        ans -= dfs(i);
    }
    printf("%d
",ans);
}