【网络流】 POJ 3680 Intervals

我写的时候是这样构图的:先离散化,然后拆点,i和i+1连一条容量为k,费用为0的边。。s和第一个点连容量为INF,费用为0的边, t和终点两一条容量为INF, 费用为0的边。。。然后对于每条边,a的负点和b的正点连一条容量为1,费用为k的边。。。然后跑最大费用最大流。。。跑了1200ms多。。。后来上网百度。。。发现不用拆点。。i和i+1连一条容量为INF,费用为0的边, s和第一个点连容量为k,费用为0的边, t和终点两一条容量为k, 费用为0的边。。就行了。。。跑了500ms多。。。

第一个程序:

#include <iostream>
#include <queue> 
#include <stack> 
#include <map> 
#include <set> 
#include <bitset> 
#include <cstdio> 
#include <algorithm> 
#include <cstring> 
#include <climits>
#include <cstdlib>
#include <cmath>
#include <time.h>
#define maxn 1005
#define maxm 100005
#define eps 1e-10
#define mod 1000000007
#define INF 0x3f3f3f3f
#define PI (acos(-1.0))
#define lowbit(x) (x&(-x))
#define mp make_pair
#define ls o<<1
#define rs o<<1 | 1
#define lson o<<1, L, mid 
#define rson o<<1 | 1, mid+1, R
#pragma comment(linker, "/STACK:16777216")
typedef long long LL;
typedef unsigned long long ULL;
//typedef int LL;
using namespace std;
LL qpow(LL a, LL b){LL res=1,base=a;while(b){if(b%2)res=res*base;base=base*base;b/=2;}return res;}
LL powmod(LL a, LL b){LL res=1,base=a;while(b){if(b%2)res=res*base%mod;base=base*base%mod;b/=2;}return res;}
void scanf(int &__x){__x=0;char __ch=getchar();while(__ch==' '||__ch=='\n')__ch=getchar();while(__ch>='0'&&__ch<='9')__x=__x*10+__ch-'0',__ch = getchar();}
LL gcd(LL _a, LL _b){if(!_b) return _a;else return gcd(_b, _a%_b);}
// head

struct Edge
{
	int v, c, w, next;
	Edge() {}
	Edge(int v, int c, int w, int next) : v(v), c(c), w(w), next(next) {}
}E[maxm];

struct node
{
	int a, b, w;
}p[maxn];

queue<int> q;
int H[maxn], cntE;
int vis[maxn];
int dis[maxn];
int cap[maxn];
int cur[maxn];
int x[maxn];
int flow, cost, T;
int cnt, s, t, n, k, o;

void addedges(int u, int v, int c, int w)
{
	E[cntE] = Edge(v, c, w, H[u]);
	H[u] = cntE++;
	E[cntE] = Edge(u, 0, -w, H[v]);
	H[v] = cntE++;
}
bool spfa(void)
{
	memset(dis, -1, sizeof dis);
	cur[s] = -1;
	dis[s] = 0;
	cap[s] = INF;
	vis[s] = ++T;
	q.push(s);
	while(!q.empty()) {
		int u = q.front();
		q.pop();
		vis[u] = T - 1;
		for(int e = H[u]; ~e; e = E[e].next) {
			int v = E[e].v, c = E[e].c, w = E[e].w;
			if(c && dis[v] < dis[u] + w) {
				dis[v] = dis[u] + w;
				cap[v] = min(cap[u], c);
				cur[v] = e;
				if(vis[v] != T) {
					vis[v] = T;
					q.push(v);
				}
			}
		}
	}
	if(dis[t] == -1) return false;
	flow += cap[t];
	cost += cap[t] * dis[t];
	for(int e = cur[t]; ~e; e = cur[E[e ^ 1].v]) {
		E[e].c -= cap[t];
		E[e ^ 1].c += cap[t];
	}
	return true;
}

int mcmf(void)
{
	flow = cost = 0;
	while(spfa());
	return cost;
}

void init(void)
{
	cnt = cntE = T = 0;
	memset(H, -1, sizeof H);
	memset(vis, 0, sizeof vis);
}

int cmp(int a, int b)
{
	return a < b;
}

void read(void)
{
	scanf("%d%d", &n, &k);
	for(int i = 0; i < n; i++) {
		scanf("%d%d%d", &p[i].a, &p[i].b, &p[i].w);
		x[++cnt] = p[i].a;
		x[++cnt] = p[i].b;
	}
	sort(x+1, x+cnt+1, cmp);
	int j = 2;
	for(int i = 2; i <= cnt; i++) if(x[i] != x[i-1]) x[j++] = x[i];
	cnt = j - 1;
}

int find(int xx)
{
	int top = cnt, bot = 1, mid;
	while(top >= bot) {
		mid = (top + bot) >> 1;
		if(x[mid] == xx) break;
		if(x[mid] > xx) top = mid - 1;
		else bot = mid + 1;
	}
	return mid;
}

void work(void)
{
	for(int i = 0; i < n; i++) {
		p[i].a = find(p[i].a);
		p[i].b = find(p[i].b);
	}
	o = cnt, s = 0, t = 2 * o + 1;
	for(int i = 1; i <= cnt; i++) addedges(i, o + i, k, 0);
	for(int i = 0; i < n; i++) addedges(o + p[i].a, p[i].b, 1, p[i].w);
	for(int i = 1; i < cnt; i++) addedges(o + i, i+1, k, 0);
	addedges(s, 1, INF, 0);
	addedges(2 * o, t, INF, 0);
	printf("%d\n", mcmf());
}

int main(void)
{
	int _;
	while(scanf("%d", &_)!=EOF) {
		while(_--) {
			init();
			read();
			work();
		}
	}

	return 0;
}

第二个程序:

#include <iostream>
#include <queue> 
#include <stack> 
#include <map> 
#include <set> 
#include <bitset> 
#include <cstdio> 
#include <algorithm> 
#include <cstring> 
#include <climits>
#include <cstdlib>
#include <cmath>
#include <time.h>
#define maxn 1005
#define maxm 100005
#define eps 1e-10
#define mod 1000000007
#define INF 0x3f3f3f3f
#define PI (acos(-1.0))
#define lowbit(x) (x&(-x))
#define mp make_pair
#define ls o<<1
#define rs o<<1 | 1
#define lson o<<1, L, mid 
#define rson o<<1 | 1, mid+1, R
#pragma comment(linker, "/STACK:16777216")
typedef long long LL;
typedef unsigned long long ULL;
//typedef int LL;
using namespace std;
LL qpow(LL a, LL b){LL res=1,base=a;while(b){if(b%2)res=res*base;base=base*base;b/=2;}return res;}
LL powmod(LL a, LL b){LL res=1,base=a;while(b){if(b%2)res=res*base%mod;base=base*base%mod;b/=2;}return res;}
void scanf(int &__x){__x=0;char __ch=getchar();while(__ch==' '||__ch=='\n')__ch=getchar();while(__ch>='0'&&__ch<='9')__x=__x*10+__ch-'0',__ch = getchar();}
LL gcd(LL _a, LL _b){if(!_b) return _a;else return gcd(_b, _a%_b);}
// head

struct Edge
{
	int v, c, w, next;
	Edge() {}
	Edge(int v, int c, int w, int next) : v(v), c(c), w(w), next(next) {}
}E[maxm];

struct node
{
	int a, b, w;
}p[maxn];

queue<int> q;
int H[maxn], cntE;
int vis[maxn];
int dis[maxn];
int cap[maxn];
int cur[maxn];
int x[maxn];
int flow, cost, T;
int cnt, s, t, n, k;

void addedges(int u, int v, int c, int w)
{
	E[cntE] = Edge(v, c, w, H[u]);
	H[u] = cntE++;
	E[cntE] = Edge(u, 0, -w, H[v]);
	H[v] = cntE++;
}
bool spfa(void)
{
	memset(dis, -1, sizeof dis);
	cur[s] = -1;
	dis[s] = 0;
	cap[s] = INF;
	vis[s] = ++T;
	q.push(s);
	while(!q.empty()) {
		int u = q.front();
		q.pop();
		vis[u] = T - 1;
		for(int e = H[u]; ~e; e = E[e].next) {
			int v = E[e].v, c = E[e].c, w = E[e].w;
			if(c && dis[v] < dis[u] + w) {
				dis[v] = dis[u] + w;
				cap[v] = min(cap[u], c);
				cur[v] = e;
				if(vis[v] != T) {
					vis[v] = T;
					q.push(v);
				}
			}
		}
	}
	if(dis[t] == -1) return false;
	flow += cap[t];
	cost += cap[t] * dis[t];
	for(int e = cur[t]; ~e; e = cur[E[e ^ 1].v]) {
		E[e].c -= cap[t];
		E[e ^ 1].c += cap[t];
	}
	return true;
}

int mcmf(void)
{
	flow = cost = 0;
	while(spfa());
	return cost;
}

void init(void)
{
	cnt = cntE = T = 0;
	memset(H, -1, sizeof H);
	memset(vis, 0, sizeof vis);
}

int cmp(int a, int b)
{
	return a < b;
}

void read(void)
{
	scanf("%d%d", &n, &k);
	for(int i = 0; i < n; i++) {
		scanf("%d%d%d", &p[i].a, &p[i].b, &p[i].w);
		x[++cnt] = p[i].a;
		x[++cnt] = p[i].b;
	}
	sort(x+1, x+cnt+1, cmp);
	int j = 2;
	for(int i = 2; i <= cnt; i++) if(x[i] != x[i-1]) x[j++] = x[i];
	cnt = j - 1;
}

int find(int xx)
{
	int top = cnt, bot = 1, mid;
	while(top >= bot) {
		mid = (top + bot) >> 1;
		if(x[mid] == xx) break;
		if(x[mid] > xx) top = mid - 1;
		else bot = mid + 1;
	}
	return mid;
}

void work(void)
{
	for(int i = 0; i < n; i++) {
		p[i].a = find(p[i].a);
		p[i].b = find(p[i].b);
	}
	s = 0, t = cnt + 1;
	for(int i = 0; i < n; i++) addedges(p[i].a, p[i].b, 1, p[i].w);
	for(int i = 1; i < cnt; i++) addedges(i, i + 1, INF, 0);
	addedges(s, 1, k, 0);
	addedges(cnt, t, k, 0);
	printf("%d\n", mcmf());
}

int main(void)
{
	int _;
	while(scanf("%d", &_)!=EOF) {
		while(_--) {
			init();
			read();
			work();
		}
	}

	return 0;
}


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