POJ 3680 最小费用最大流

建图如下

若限制为k

首先将坐标离散化。

对每个区间，左端点对应的编号到右端点对应的编号建一条边，容量为k，费用为负权

然后对每个编号i,建立i到i+1的边，容量为k，费用为0

起点和编号1连边，容量为k，费用0

最后一个编号和终点连边,容量为k，费用0

然后跑费用流即可

#include <iostream>
#include <algorithm>
#include <cstring>
#include <string>
#include <cstdio>
#include <cmath>
#include <queue>
#include <map>
#include <set>
#define eps 1e-5
#define MAXN 555
#define MAXM 55555
#define INF 100000007
using namespace std;
struct EDGE
{
int v, cap, cost, next, re;    //  re记录逆边的下标。
} edge[MAXM];
int n, m, ans, flow, src, des;
int e, head[MAXN];
int que[MAXN], pre[MAXN], dis[MAXN];
bool vis[MAXN];
void init()
{
e = ans = flow = 0;
memset(head, -1, sizeof(head));
}
void add(int u, int v, int cap, int cost)
{
edge[e].v = v;
edge[e].cap = cap;
edge[e].cost = cost;
edge[e].next = head[u];
edge[e].re = e + 1;
head[u] = e++;
edge[e].v = u;
edge[e].cap = 0;
edge[e].cost = -cost;
edge[e].next = head[v];
edge[e].re = e - 1;
head[v] = e++;
}
bool spfa()
{
int i, h = 0, t = 1;
for(i = 0; i <= n; i ++)
{
dis[i] = INF;
vis[i] = false;
}
dis[src] = 0;
que[0] = src;
vis[src] = true;
while(t != h)
{
int u = que[h++];
h %= n;
vis[u] = false;
for(i = head[u]; i != -1; i = edge[i].next)
{
int v = edge[i].v;
if(edge[i].cap && dis[v] > dis[u] + edge[i].cost)
{
dis[v] = dis[u] + edge[i].cost;
pre[v] = i;
if(!vis[v])
{
vis[v] = true;
que[t++] = v;
t %= n;
}
}
}
}
if(dis[des] == INF) return false;
return true;
}
void end()
{
int u, p, mi = INF;
for(u = des; u != src; u = edge[edge[p].re].v)
{
p = pre[u];
mi = min(mi, edge[p].cap);
}
for(u = des; u != src; u = edge[edge[p].re].v)
{
p = pre[u];
edge[p].cap -= mi;
edge[edge[p].re].cap += mi;
ans += mi * edge[p].cost;     //  cost记录的为单位流量费用，必须得乘以流量。
}
flow += mi;
}
int nt, k;
int a[MAXN], b[MAXN], w[MAXN];
int x[MAXN];
int bin(int low, int high, int v)
{
while(low <= high)
{
int mid = (low + high) >> 1;
if(x[mid] == v) return mid;
else if(x[mid] > v) high = mid - 1;
else low = mid + 1;
}
return -1;
}
void build()
{
scanf("%d%d", &nt, &k);
int cnt = 0;
for(int i = 1; i <= nt; i++)
{
scanf("%d%d%d", &a[i], &b[i], &w[i]);
x[cnt++] = a[i];
x[cnt++] = b[i];
}
sort(x, x + cnt);
cnt = unique(x, x + cnt) - x;
for(int i = 1; i <= nt; i++)
{
int lx = bin(0, cnt - 1, a[i]) + 1;
int rx = bin(0, cnt - 1, b[i]) + 1;
add(lx, rx, 1, -w[i]);
}
for(int i = 1; i < cnt; i++)
add(i, i + 1, k, 0);
src = cnt + 1;
des = cnt + 2;
n = des;
add(src, 1, k, 0);
add(cnt, des, k, 0);
}
void MCMF()
{
init();
build();
while(spfa()) end();
}
int main()
{
int T;
scanf("%d", &T);
while(T--)
{
MCMF();
printf("%d\n", -ans);
}
return 0;
}

zkw版 貌似比原作者写的指针版本的慢了不少，不过这种图zkw费用流本来就不擅长

#include <iostream>
#include <algorithm>
#include <cstring>
#include <string>
#include <cstdio>
#include <cmath>
#include <queue>
#include <deque>
#include <map>
#include <set>
#define eps 1e-5
#define MAXN 5555
#define MAXM 55555
#define INF 100000007
using namespace std;
struct EDGE
{
int cost, cap, v;
int next, re;
}edge[MAXM];
int head[MAXN], e;
int vis[MAXN], d[MAXN];
int ans, cost, src, des, n;
void init()
{
memset(head, -1, sizeof(head));
e = 0;
ans = cost = 0;
}
void add(int u, int v, int cap, int cost)
{
edge[e].v = v;
edge[e].cap = cap;
edge[e].cost = cost;
edge[e].re = e + 1;
edge[e].next = head[u];
head[u] = e++;
edge[e].v = u;
edge[e].cap = 0;
edge[e].cost = -cost;
edge[e].re = e - 1;
edge[e].next = head[v];
head[v] = e++;
}
int aug(int u, int f)
{
if(u == des)
{
ans += cost * f;
return f;
}
vis[u] = 1;
int tmp = f;
for(int i = head[u]; i != -1; i = edge[i].next)
if(edge[i].cap && !edge[i].cost && !vis[edge[i].v])
{
int delta = aug(edge[i].v, tmp < edge[i].cap ? tmp : edge[i].cap);
edge[i].cap -= delta;
edge[edge[i].re].cap += delta;
tmp -= delta;
if(!tmp) return f;
}
return f - tmp;
}
bool modlabel()
{
for(int i = 0; i <= n; i++) d[i] = INF;
d[des] = 0;
deque<int>Q;
Q.push_back(des);
while(!Q.empty())
{
int u = Q.front(), tmp;
Q.pop_front();
for(int i = head[u]; i != -1; i = edge[i].next)
if(edge[edge[i].re].cap && (tmp = d[u] - edge[i].cost) < d[edge[i].v])
(d[edge[i].v] = tmp) <= d[Q.empty() ? src : Q.front()] ? Q.push_front(edge[i].v) : Q.push_back(edge[i].v);
}
for(int u = 1; u <= n; u++)
for(int i = head[u]; i != -1; i = edge[i].next)
edge[i].cost += d[edge[i].v] - d[u];
cost += d[src];
return d[src] < INF;
}
void costflow()
{
while(modlabel())
{
do
{
memset(vis, 0, sizeof(vis));
}while(aug(src, INF));
}
}
int nt, k;
int a[MAXN], b[MAXN], w[MAXN];
int x[MAXN];
int bin(int low, int high, int v)
{
while(low <= high)
{
int mid = (low + high) >> 1;
if(x[mid] == v) return mid;
else if(x[mid] > v) high = mid - 1;
else low = mid + 1;
}
return -1;
}
void build()
{
scanf("%d%d", &nt, &k);
int cnt = 0;
for(int i = 1; i <= nt; i++)
{
scanf("%d%d%d", &a[i], &b[i], &w[i]);
x[cnt++] = a[i];
x[cnt++] = b[i];
}
sort(x, x + cnt);
cnt = unique(x, x + cnt) - x;
for(int i = 1; i <= nt; i++)
{
int lx = bin(0, cnt - 1, a[i]) + 1;
int rx = bin(0, cnt - 1, b[i]) + 1;
add(lx, rx, 1, -w[i]);
}
for(int i = 1; i < cnt; i++)
add(i, i + 1, k, 0);
src = cnt + 1;
des = cnt + 2;
n = des;
add(src, 1, k, 0);
add(cnt, des, k, 0);
}
int main()
{
int T;
scanf("%d", &T);
while(T--)
{
init();
build();
costflow();
printf("%d\n", -ans);
}
return 0;
}