【DFS求树的最大二分匹配+输入外挂】HDU 6178 Monkeys

http://acm.hdu.edu.cn/showproblem.php?pid=6178

【题意】

• 给定一棵有n个结点的树，现在有k个猴子分布在k个结点上，我们可以删去树上的一些边，使得k个猴子每个猴子都至少和其他一个猴子相连
• 问树上最少保留多少条边

【思路】

• 每个猴子要至少和一个猴子相连，考虑保留的边最少，那么最优的情况一定是一条边的两个顶点放两个猴子，这些边的顶点都不重合
• 我们现在要找到给定的树中最多有多少条这样的边，即最大二分匹配
• O(n)的DFS，对于每个结点，优先与叶子结点形成一条边

【AC】

#include<bits/stdc++.h>
using namespace std; 
typedef long long ll;
namespace IO
{
    const int MX=1e8;
    char buf[MX];
    int c,sz;
    void begin()
    {
        c=0;
        sz=fread(buf,1,MX,stdin);
    }
    inline bool read(int &x)
    {
        while(c<sz && buf[c]!='-' && (buf[c]<'0'||buf[c]>'9')) ++c;
        if(c>=sz) return false;
        bool flag=0;
        if(buf[c]=='-') flag=1,++c;
        for(x=0;c<sz&&buf[c]>='0'&&buf[c]<='9';++c)
            x=x*10+buf[c]-'0';
        if(flag) x=-x;
        return true;
    }
}

int n,k;
const int maxn=1e5+2;
const int maxm=maxn*2;
bool vis[maxn];
struct edge
{
    int to;
    int nxt;
}e[maxm];
int head[maxn];
int tot;
//int dp[maxn][2];
int flag;
int cnt;
void init()
{
    memset(head,-1,sizeof(head));
    tot=0;
  //  memset(dp,0,sizeof(dp));
      memset(vis,false,sizeof(vis));
      cnt=0;
}
void addedge(int u,int v)
{
    e[tot].to=v;
    e[tot].nxt=head[u];
    head[u]=tot++;
}

void dfs(int u,int pa)
{
    for(int i=head[u];i!=-1;i=e[i].nxt)
    {
        int v=e[i].to;
        if(v==pa) continue;
        dfs(v,u);
        if(!vis[u]&&!vis[v])
        {
            cnt++;
            vis[u]=vis[v]=true;
        }
    }
}
int main()
{
    IO::begin();
    int T;
      IO::read(T);
   // scanf("%d",&T);
    while(T--)
    {
        init();
      //  scanf("%d%d",&n,&k);
        IO::read(n);IO::read(k);
        int x;
        for(int i=2;i<=n;i++)
        {
            //scanf("%d",&x);
            IO::read(x);
            addedge(i,x);
            addedge(x,i);
        }
        dfs(1,-1);
        int tmp=cnt*2;
        int ans;
        if(k<=tmp)
        {
            ans=k/2;
            if(k%2) ans++;
        }
        else
        {
            ans=cnt+k-tmp;
        }
        printf("%d\n",ans);
    }
    return 0;
}

#include<bits/stdc++.h>
namespace fastIO {
#define BUF_SIZE 1100000
#define OUT_SIZE 1100000
#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;
typedef long long ll;
int n,k;
const int maxn=1e5+2;
const int maxm=maxn*2;
struct edge
{
    int to;
    int nxt;
}e[maxm];
int head[maxn];
int tot;
int dp[maxn][2];

void init()
{
    memset(head,-1,sizeof(head));
    tot=0;
    memset(dp,0,sizeof(dp));
}
void addedge(int u,int v)
{
    e[tot].to=v;
    e[tot].nxt=head[u];
    head[u]=tot++;
}

bool dfs(int u,int pa)
{
    int flag=0;
    dp[u][0]=0;
    for(int i=head[u];i!=-1;i=e[i].nxt)
    {
        int v=e[i].to;
        if(v==pa) continue;
        if(dfs(v,u))
        {
            flag=1;
        }
        dp[u][0]+=dp[v][1];
    }
    if(flag)
    {
        dp[u][1]=dp[u][0]+1;
        return false;
    }
    else
    {
        dp[u][1]=dp[u][0];
        return true;
    }
}
int main()
{
    int T;
    //scanf("%d",&T);
    read(T);
    //cout<<T<<endl;
    while(T--)
    {
        init();
        read(n);
        read(k);
        //cout<<n<<k<<endl;
        //scanf("%d%d",&n,&k);
        int x;
        for(int i=2;i<=n;i++)
        {
            read(x);
            //scanf("%d",&x);
            addedge(i,x);
            addedge(x,i);
        }
        dfs(1,-1);
        int cnt=dp[1][1];
        int tmp=cnt*2;
        int ans;
        if(k<=tmp)
        {
            ans=k/2;
            if(k%2) ans++;
        }
        else
        {
            ans=cnt+k-tmp;
        }
        printf("%d\n",ans);
    }
    return 0;
}

树形dp的代码比赛是wa了，赛后才发现，原来是我dfs里开了全局变量flag,flag在其他层里被修改，改成局部变量就A了orz