cogs #743

来源：互联网发布：华师网络教育远程教育编辑：程序博客网时间：2024/05/17 22:00

题目链接

最大费用最大流

如何构图？

设源点为 S，汇点为 T 。

将所有的端点离散化，

S 点向第一个点连边，每个点向下一个点连边，最后一个点向 T 点连边，流量都为 k，费用都为 0 。

对于每条线段，从左端点向右端点连边，流量为 1，费用为其长度。

这样就限制了选择的线段数量，同时使得总长度最大。

#include <cstdio>#include <cstdlib>#include <cstring>#include <cmath>#include <ctime>#include <string>#include <map>#include <vector>#include <stack>#include <queue>#include <utility>#include <iostream>#include <algorithm>template<class Num>void read(Num &x){    char c; int flag = 1;    while((c = getchar()) < '0' || c > '9')        if(c == '-') flag *= -1;    x = c - '0';    while((c = getchar()) >= '0' && c <= '9')        x = (x<<3) + (x<<1) + (c-'0');    x *= flag;    return;}template<class Num>void write(Num x){    if(x < 0) putchar('-'), x = -x;    static char s[20];int sl = 0;    while(x) s[sl++] = x%10 + '0',x /= 10;    if(!sl) {putchar('0');return;}    while(sl) putchar(s[--sl]);}#define REP(__i,__start,__end) for(int __i = (__start); __i <= (__end); __i++)const int maxn = 510, node = maxn << 1, edgenum = node << 2, INF = 0x3f3f3f3f;int n, _k;struct Edge{    int v, cap, cost, next;    Edge(int v = 0,int cap = 0,int cost = 0,int next = 0):v(v), cap(cap), cost(cost), next(next){}}edge[edgenum];#define St first#define Ed secondstd::pair<int, int> seg[maxn];int bowl[node], bsize;int head[node], el = 1, S, T, ind;int dist[node], fr[node], fd[node];void newedge(int u,int v,int cap,int cost){    edge[++el] = Edge(v, cap, cost, head[u]), head[u] = el;    edge[++el] = Edge(u, 0, -cost, head[v]), head[v] = el;}bool SPFA(){    static int line[node];    static bool hash[node];    int f = 0, r = 0;    REP(i, 1, ind) dist[i] = -INF, fr[i] = fd[i] = 0;    dist[S] = 0, line[r] = S, r = (r + 1)%node;    hash[S] = true;    while(f != r)    {        int x = line[f], p, calc;        line[f] = 0, f = (f + 1)%node;        hash[x] = false;        for(int i = head[x]; i; i = edge[i].next)            if(edge[i].cap)            {                p = edge[i].v, calc = dist[x] + edge[i].cost;                if(calc > dist[p])                {                    dist[p] = calc, fr[p] = x, fd[p] = i;                    if(!hash[p])                    {                        if(dist[p] <= dist[line[f]])                            f = (f - 1 + node)%node, line[f] = p;                        else                            line[r] = p, r = (r + 1)%node;                        hash[p] = true;                    }                }            }    }    return (dist[T] > -INF);}int change(int a,int flow){    if(a != S)    {        flow = std::min(flow, edge[fd[a]].cap);        flow = change(fr[a], flow);        edge[fd[a]].cap -= flow;        edge[fd[a]^1].cap += flow;    }    return flow;}void init(){    int u, v;    read(n), read(_k);    REP(i, 1, n)    {        read(u), read(v);        seg[i] = std::make_pair(u, v);    }}void prework(){    REP(i, 1, n)    {        bowl[i<<1] = seg[i].St;        bowl[(i<<1) - 1] = seg[i].Ed;    }    std::sort(bowl + 1, bowl + (n << 1) + 1);    bsize = std::unique(bowl + 1, bowl + (n << 1) + 1) - (bowl + 1);    S = bsize + 1, T = bsize + 2, ind = T;    REP(i, 1, bsize - 1) newedge(i, i + 1, INF, 0);    newedge(S, 1, _k, 0), newedge(bsize, T, _k, 0);    REP(i, 1, n)    {        int len = seg[i].Ed - seg[i].St;        seg[i].St = std::lower_bound(bowl + 1, bowl + bsize + 1, seg[i].St) - bowl;        seg[i].Ed = std::lower_bound(bowl + 1, bowl + bsize + 1, seg[i].Ed) - bowl;        newedge(seg[i].St, seg[i].Ed, 1, len);    }}int solve(){    int maxcost = 0, maxflow = 0;    while(SPFA())    {        maxcost += dist[T];        maxflow += change(T, INF);    }    return maxcost;}int main(){    freopen("interv.in","r",stdin);    freopen("interv.out","w",stdout);    init(), prework(), write(solve());    fclose(stdin);    fclose(stdout);    return 0;}

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