Hdu 6178 Monkeys【树形Dp-最小点覆盖+贪心思维】

Monkeys

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 153428/153428 K (Java/Others)
Total Submission(s): 384    Accepted Submission(s): 121

Problem Description

There is a tree having N vertices. In the tree there are K monkeys (K <= N). A vertex can be occupied by at most one monkey. They want to remove some edges and leave minimum edges, but each monkey must be connected to at least one other monkey through the remaining edges.
Print the minimum possible number of remaining edges.

 

Input

The first line contains an integer T (1 <= T <= 100), the number of test cases.
Each test case begins with a line containing two integers N and K (2 <= K <= N <= 100000). The second line contains N-1 space-separated integers a1,a2,…,aN−1, it means that there is an edge between vertex ai and vertex i+1 (1 <= ai <= i).

 

Output

For each test case, print the minimum possible number of remaining edges.

 

Sample Input

2
4 4
1 2 3
4 3
1 1 1

 

Sample Output

2
2

题目大意：

给你N个点的一棵树，现在有K只猴子，猴子们不会落单，也就是说，在同一个联通块中，至少有两只猴子。

现在我们希望砍尽可能多的边，使得这K只猴子分部在若干个联通块中，使得满足上述条件。

输出剩下的最少的边数。

思路：

这题O（n）做竟然卡读入优化。。。。。。。。。。。。。。。。。。。。。。

①很显然，如果我们最终的答案是一个包含K个点的整个联通块的话，显然答案就是K-1.如果我们是两个共包含K个点的联通块的话，显然答案会对应减少。

所以我们希望分部的情况是尽可能多的联通块，那么理应我们希望将结果分成若干个两两相连的小联通块。

②我们希望构成尽可能多的这样两两相连的小联通块（只用一条边去连接）的话，很显然是需要跑最大二分匹配数。我们知道最小点覆盖==最大二分匹配数，而直接建图跑二分图匈牙利匹配的话，时间复杂度很爆炸，我们知道树形dp可以O（n）求树上的最小点覆盖问题，所以我们直接跑树形Dp即可。

③如果我们最小点覆盖数为ans个，那么分情况讨论即可：

如果k<=ans*2，那么结果就是k/2

如果k>ans*2，那么结果就是k-ans*2+ans（多出来的点直接往上加即可）

如果k是奇数，那么答案再加1.

Ac代码：

#include <bits/stdc++.h>
typedef long long int LL;
using namespace std;

const int N = 200000+6;
const int MOD = 1e9+7;
const int INF = 1e9+7;
const double eps = 1e-6;

// inline int read() {
//     int x=0,f=1;char c=getchar();
//     for(; c<'0'||'9'<c; c=getchar())if(c=='-')f=-1;
//     for(; '0'<=c&&c<='9'; c=getchar())x=(x<<3)+(x<<1)+c-'0';
//     return x*f;
// }



/********************************************/
namespace fastIO{
    #define BUF_SIZE 100000
    #define OUT_SIZE 100000
    #define ll long long
    //fread->read
    bool IOerror=0;
    inline char nc(){
        static char buf[BUF_SIZE],*p1=buf+BUF_SIZE,*pend=buf+BUF_SIZE;
        if (p1==pend){
            p1=buf; pend=buf+fread(buf,1,BUF_SIZE,stdin);
            if (pend==p1){IOerror=1;return -1;}
            //{printf("IO error!\n");system("pause");for (;;);exit(0);}
        }
        return *p1++;
    }
    inline bool blank(char ch){return ch==' '||ch=='\n'||ch=='\r'||ch=='\t';}
    inline void read(int &x){
        bool sign=0; char ch=nc(); x=0;
        for (;blank(ch);ch=nc());
        if (IOerror)return;
        if (ch=='-')sign=1,ch=nc();
        for (;ch>='0'&&ch<='9';ch=nc())x=x*10+ch-'0';
        if (sign)x=-x;
    }
    inline void read(ll &x){
        bool sign=0; char ch=nc(); x=0;
        for (;blank(ch);ch=nc());
        if (IOerror)return;
        if (ch=='-')sign=1,ch=nc();
        for (;ch>='0'&&ch<='9';ch=nc())x=x*10+ch-'0';
        if (sign)x=-x;
    }
    inline void read(double &x){
        bool sign=0; char ch=nc(); x=0;
        for (;blank(ch);ch=nc());
        if (IOerror)return;
        if (ch=='-')sign=1,ch=nc();
        for (;ch>='0'&&ch<='9';ch=nc())x=x*10+ch-'0';
        if (ch=='.'){
            double tmp=1; ch=nc();
            for (;ch>='0'&&ch<='9';ch=nc())tmp/=10.0,x+=tmp*(ch-'0');
        }
        if (sign)x=-x;
    }
    inline void read(char *s){
        char ch=nc();
        for (;blank(ch);ch=nc());
        if (IOerror)return;
        for (;!blank(ch)&&!IOerror;ch=nc())*s++=ch;
        *s=0;
    }
    inline void read(char &c){
        for (c=nc();blank(c);c=nc());
        if (IOerror){c=-1;return;}
    }
    //getchar->read
    inline void read1(int &x){
        char ch;int bo=0;x=0;
        for (ch=getchar();ch<'0'||ch>'9';ch=getchar())if (ch=='-')bo=1;
        for (;ch>='0'&&ch<='9';x=x*10+ch-'0',ch=getchar());
        if (bo)x=-x;
    }
    inline void read1(ll &x){
        char ch;int bo=0;x=0;
        for (ch=getchar();ch<'0'||ch>'9';ch=getchar())if (ch=='-')bo=1;
        for (;ch>='0'&&ch<='9';x=x*10+ch-'0',ch=getchar());
        if (bo)x=-x;
    }
    inline void read1(double &x){
        char ch;int bo=0;x=0;
        for (ch=getchar();ch<'0'||ch>'9';ch=getchar())if (ch=='-')bo=1;
        for (;ch>='0'&&ch<='9';x=x*10+ch-'0',ch=getchar());
        if (ch=='.'){
            double tmp=1;
            for (ch=getchar();ch>='0'&&ch<='9';tmp/=10.0,x+=tmp*(ch-'0'),ch=getchar());
        }
        if (bo)x=-x;
    }
    inline void read1(char *s){
        char ch=getchar();
        for (;blank(ch);ch=getchar());
        for (;!blank(ch);ch=getchar())*s++=ch;
        *s=0;
    }
    inline void read1(char &c){for (c=getchar();blank(c);c=getchar());}
    //scanf->read
    inline void read2(int &x){scanf("%d",&x);}
    inline void read2(ll &x){
        #ifdef _WIN32
            scanf("%I64d",&x);
        #else
        #ifdef __linux
            scanf("%lld",&x);
        #else
            puts("error:can't recognize the system!");
        #endif
        #endif
    }
    inline void read2(double &x){scanf("%lf",&x);}
    inline void read2(char *s){scanf("%s",s);}
    inline void read2(char &c){scanf(" %c",&c);}
    inline void readln2(char *s){gets(s);}
    //fwrite->write
    struct Ostream_fwrite{
        char *buf,*p1,*pend;
        Ostream_fwrite(){buf=new char[BUF_SIZE];p1=buf;pend=buf+BUF_SIZE;}
        void out(char ch){
            if (p1==pend){
                fwrite(buf,1,BUF_SIZE,stdout);p1=buf;
            }
            *p1++=ch;
        }
        void print(int x){
            static char s[15],*s1;s1=s;
            if (!x)*s1++='0';if (x<0)out('-'),x=-x;
            while(x)*s1++=x%10+'0',x/=10;
            while(s1--!=s)out(*s1);
        }
        void println(int x){
            static char s[15],*s1;s1=s;
            if (!x)*s1++='0';if (x<0)out('-'),x=-x;
            while(x)*s1++=x%10+'0',x/=10;
            while(s1--!=s)out(*s1); out('\n');
        }
        void print(ll x){
            static char s[25],*s1;s1=s;
            if (!x)*s1++='0';if (x<0)out('-'),x=-x;
            while(x)*s1++=x%10+'0',x/=10;
            while(s1--!=s)out(*s1);
        }
        void println(ll x){
            static char s[25],*s1;s1=s;
            if (!x)*s1++='0';if (x<0)out('-'),x=-x;
            while(x)*s1++=x%10+'0',x/=10;
            while(s1--!=s)out(*s1); out('\n');
        }
        void print(double x,int y){
            static ll mul[]={1,10,100,1000,10000,100000,1000000,10000000,100000000,
                1000000000,10000000000LL,100000000000LL,1000000000000LL,10000000000000LL,
                100000000000000LL,1000000000000000LL,10000000000000000LL,100000000000000000LL};
            if (x<-1e-12)out('-'),x=-x;x*=mul[y];
            ll x1=(ll)floor(x); if (x-floor(x)>=0.5)++x1;
            ll x2=x1/mul[y],x3=x1-x2*mul[y]; print(x2);
            if (y>0){out('.'); for (size_t i=1;i<y&&x3*mul[i]<mul[y];out('0'),++i); print(x3);}
        }
        void println(double x,int y){print(x,y);out('\n');}
        void print(char *s){while (*s)out(*s++);}
        void println(char *s){while (*s)out(*s++);out('\n');}
        void flush(){if (p1!=buf){fwrite(buf,1,p1-buf,stdout);p1=buf;}}
        ~Ostream_fwrite(){flush();}
    }Ostream;
    inline void print(int x){Ostream.print(x);}
    inline void println(int x){Ostream.println(x);}
    inline void print(char x){Ostream.out(x);}
    inline void println(char x){Ostream.out(x);Ostream.out('\n');}
    inline void print(ll x){Ostream.print(x);}
    inline void println(ll x){Ostream.println(x);}
    inline void print(double x,int y){Ostream.print(x,y);}
    inline void println(double x,int y){Ostream.println(x,y);}
    inline void print(char *s){Ostream.print(s);}
    inline void println(char *s){Ostream.println(s);}
    inline void println(){Ostream.out('\n');}
    inline void flush(){Ostream.flush();}
    //puts->write
    char Out[OUT_SIZE],*o=Out;
    inline void print1(int x){
        static char buf[15];
        char *p1=buf;if (!x)*p1++='0';if (x<0)*o++='-',x=-x;
        while(x)*p1++=x%10+'0',x/=10;
        while(p1--!=buf)*o++=*p1;
    }
    inline void println1(int x){print1(x);*o++='\n';}
    inline void print1(ll x){
        static char buf[25];
        char *p1=buf;if (!x)*p1++='0';if (x<0)*o++='-',x=-x;
        while(x)*p1++=x%10+'0',x/=10;
        while(p1--!=buf)*o++=*p1;
    }
    inline void println1(ll x){print1(x);*o++='\n';}
    inline void print1(char c){*o++=c;}
    inline void println1(char c){*o++=c;*o++='\n';}
    inline void print1(char *s){while (*s)*o++=*s++;}
    inline void println1(char *s){print1(s);*o++='\n';}
    inline void println1(){*o++='\n';}
    inline void flush1(){if (o!=Out){if (*(o-1)=='\n')*--o=0;puts(Out);}}
    struct puts_write{
        ~puts_write(){flush1();}
    }_puts;
    inline void print2(int x){printf("%d",x);}
    inline void println2(int x){printf("%d\n",x);}
    inline void print2(char x){printf("%c",x);}
    inline void println2(char x){printf("%c\n",x);}
    inline void print2(ll x){
        #ifdef _WIN32
            printf("%I64d",x);
        #else
        #ifdef __linux
            printf("%lld",x);
        #else
            puts("error:can't recognize the system!");
        #endif
        #endif
    }
    inline void println2(ll x){print2(x);printf("\n");}
    inline void println2(){printf("\n");}
    #undef ll
    #undef OUT_SIZE
    #undef BUF_SIZE
};
using namespace fastIO;


vector<int>mp[100050];
int dp[100050][3];
void DP(int u,int from)
{
    dp[u][0]=1;
    dp[u][1]=0;
    for(int i=0;i<mp[u].size();i++)
    {
        int v=mp[u][i];
        if(v==from)continue;
        DP(v,u);
        dp[u][0]+=min(dp[v][0],dp[v][1]);
        dp[u][1]+=dp[v][0];
    }
}
int main()
{

//    freopen("in.txt","r",stdin);
//    freopen("out.txt","w",stdout);
    int t;
//    scanf("%d",&t);
    read(t);
    while(t--)
    {
        int n,k;
//        scanf("%d%d",&n,&k);
        read(n),read(k);
        for(int i=1;i<=n;i++)mp[i].clear();
        for(int i=2;i<=n;i++)
        {
            int x;
//            scanf("%d",&x);
            read(x);
            mp[i].push_back(x);
            mp[x].push_back(i);
        }
        DP(1,-1);
        int ans=min(dp[1][0],dp[1][1]);
        if(k%2==0)
        {
            if(k<=ans*2)
            {
                printf("%d\n",k/2);
            }
            else printf("%d\n",(k-ans*2)+ans);
        }
        else
        {
            k-=1;
            if(k<=ans*2)
            {
                printf("%d\n",k/2+1);
            }
            else printf("%d\n",(k-ans*2)+ans +1);
        }
    }
}