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AtCoder Grand Contest 083 E - Bichrome Tree

題目傳送門:https://arc083.contest.atcoder.jp/tasks/arc083_c

題目大意:

給定一棵樹,你可以給這些點任意黑白染色,並且賦上權值,現給定一個序列\(X_i\),滿足對於每一個點\(i\),整棵子樹內所有和\(i\)顏色相同的點的權值和為\(X_i\),問是否可能

首先因為權值大小任意,所以\(v\)的子樹內權值和只要不超過\(X_v\)就好,那麼對於一個點\(v\)假定其為黑色,那麼子樹中黑色總和為\(X_v\),白色總和就要儘量小,定義為\(f_v\)

那麼選定\(v\)為黑色後,假定子樹內黑色總和為\(B\),白色總和為\(W\),那麼對於每個子節點\(v\)

有兩種選擇

\(B+=X_u,W+=f_u\)\(B+=f_u,W+=X_u\)

/*program from Wolfycz*/
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define inf 0x3f3f3f3f
#define min(x,y) (x<y?x:y)
#define max(x,y) (x>y?x:y)
using namespace std;
typedef long long ll;
typedef unsigned int ui;
typedef unsigned long long ull;
inline char gc(){
    static char buf[1000000],*p1=buf,*p2=buf;
    return p1==p2&&(p2=(p1=buf)+fread(buf,1,1000000,stdin),p1==p2)?EOF:*p1++;
}
inline int frd(){
    int x=0,f=1; char ch=gc();
    for (;ch<'0'||ch>'9';ch=gc())   if (ch=='-')    f=-1;
    for (;ch>='0'&&ch<='9';ch=gc()) x=(x<<3)+(x<<1)+ch-'0';
    return x*f;
}
inline int read(){
    int x=0,f=1; char ch=getchar();
    for (;ch<'0'||ch>'9';ch=getchar())  if (ch=='-')    f=-1;
    for (;ch>='0'&&ch<='9';ch=getchar())    x=(x<<3)+(x<<1)+ch-'0';
    return x*f;
}
inline void print(int x){
    if (x<0)    putchar('-'),x=-x;
    if (x>9)    print(x/10);
    putchar(x%10+'0');
}
const int N=1e3,M=5e3;
int pre[N+10],now[N+10],child[N+10],tot;
int f[N+10],g[2][M+10],v[N+10];
void join(int x,int y){pre[++tot]=now[x],now[x]=tot,child[tot]=y;}
void dfs(int x){
    for (int p=now[x],son=child[p];p;p=pre[p],son=child[p]) dfs(son);
    memset(g[0],63,sizeof(g[0]));
    int T=0; g[T][0]=0;
    for (int p=now[x],son=child[p];p;p=pre[p],son=child[p]){
        T^=1;
        memset(g[T],63,sizeof(g[T]));
        for (int i=0;i<=v[x];i++){
            if (i>=v[son])  g[T][i]=min(g[T][i],g[T^1][i-v[son]]+f[son]);
            if (i>=f[son])  g[T][i]=min(g[T][i],g[T^1][i-f[son]]+v[son]);
        }
    }
    for (int i=0;i<=v[x];i++)   f[x]=min(f[x],g[T][i]);
}
int main(){
    int n=read();
    for (int i=2;i<=n;i++)  join(read(),i);
    for (int i=1;i<=n;i++)  v[i]=read();
    memset(f,63,sizeof(f));
    dfs(1);
    printf(f[1]<inf?"POSSIBLE\n":"IMPOSSIBLE\n");
    return 0;
}