HAOI2010 软件安装

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经典树型依赖背包。唯一的区别是依赖可能成环,此时把环缩点即可。

关于树型依赖背包:

fx,yf_{x,y}表示选x,同时考虑了dfs序<xdfs序的点和x子树的点之后背包容量为y的最大价值。

然后转移就很清晰了。

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/*
Author: CNYALI_LK
LANG: C++
PROG: 2515.cpp
Mail: cnyalilk@vip.qq.com
*/
#include<bits/stdc++.h>
#define debug(...) fprintf(stderr,__VA_ARGS__)
#define DEBUG printf("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define Debug debug("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define all(x) x.begin(),x.end()
#define x first
#define y second
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const signed inf=0x3f3f3f3f;
const double eps=1e-8;
const double pi=acos(-1.0);
template<class T>int chkmin(T &a,T b){return a>b?a=b,1:0;}
template<class T>int chkmax(T &a,T b){return a<b?a=b,1:0;}
template<class T>T sqr(T a){return a*a;}
template<class T>T mmin(T a,T b){return a<b?a:b;}
template<class T>T mmax(T a,T b){return a>b?a:b;}
template<class T>T aabs(T a){return a<0?-a:a;}
template<class T>int dcmp(T a,T b){return a>b;}
template<int *a>int cmp_a(int x,int y){return a[x]<a[y];}
#define min mmin
#define max mmax
#define abs aabs
namespace io {
const int SIZE = (1 << 21) + 1;
char ibuf[SIZE], *iS, *iT, obuf[SIZE], *oS = obuf, *oT = oS + SIZE - 1, c, qu[55]; int f, qr;
// getchar
#define gc() (iS == iT ? (iT = (iS = ibuf) + fread (ibuf, 1, SIZE, stdin), (iS == iT ? EOF : *iS ++)) : *iS ++)
// print the remaining part
inline void flush () {
fwrite (obuf, 1, oS - obuf, stdout);
oS = obuf;
}
// putchar
inline void putc (char x) {
*oS ++ = x;
if (oS == oT) flush ();
}
// input a signed integer
inline void read (signed &x) {
for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
}

inline void read (long long &x) {
for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
}
inline void read (char &x) {
x=gc();
}
inline void read(char *x){
while((*x=gc())=='\n' || *x==' '||*x=='\r');
while(!(*x=='\n'||*x==' '||*x=='\r'))*(++x)=gc();
}
template<typename A,typename ...B>
inline void read(A &x,B &...y){
read(x);read(y...);
}
// print a signed integer
inline void write (signed x) {
if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
while (x) qu[++ qr] = x % 10 + '0', x /= 10;
while (qr) putc (qu[qr --]);
}

inline void write (long long x) {
if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
while (x) qu[++ qr] = x % 10 + '0', x /= 10;
while (qr) putc (qu[qr --]);
}
inline void write (char x) {
putc(x);
}
inline void write(const char *x){
while(*x){putc(*x);++x;}
}
inline void write(char *x){
while(*x){putc(*x);++x;}
}
template<typename A,typename ...B>
inline void write(A x,B ...y){
write(x);write(y...);
}
//no need to call flush at the end manually!
struct Flusher_ {~Flusher_(){flush();}}io_flusher_;
}
using io :: read;
using io :: putc;
using io :: write;
int bel[105],w[105],v[105],pre[105],f[105][505],fa[105],vis[105],n,m;
int t;
vector<int> son[105];
void findC(int x){
bel[x]=x;
++t;
while(!vis[x]){vis[x]=t;x=pre[x];}
if(vis[x]==t){
int r=x;
for(x=pre[x];x!=r;x=pre[x]){bel[x]=r;w[r]+=w[x];v[r]+=v[x];}
}
}
void dfs(int x){
for(auto i:son[x])if(w[i]<=m){
for(int j=0;j<w[i];++j)f[i][j]=-inf;
for(int j=w[i];j<=m;++j)f[i][j]=f[x][j-w[i]]+v[i];
dfs(i);
for(int j=0;j<=m;++j)chkmax(f[x][j],f[i][j]);
}
}
int main(){
#ifdef cnyali_lk
freopen("2515.in","r",stdin);
freopen("2515.out","w",stdout);
#endif
read(n,m);
for(int i=1;i<=n;++i)read(w[i]);
for(int i=1;i<=n;++i)read(v[i]);
for(int i=1;i<=n;++i)read(pre[i]);
vis[0]=1;
for(int i=1;i<=n;++i)bel[i]=i;
t=1;
for(int i=1;i<=n;++i)if(!vis[i])findC(i);
for(int i=1;i<=n;++i)if(bel[i]==i){
if(bel[pre[i]]!=i)
fa[i]=bel[pre[i]];
else
fa[i]=0;
son[fa[i]].push_back(i);
}
dfs(0);
write(f[0][m],'\n');
return 0;
}
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