BestCoder Round #76 解题报告

 

DZY Loves Partition 

【思路】

    贪心

【代码】

 

#include <iostream>
using namespace std;

typedef long long ll;
const int mod=1e9+7;

ll n,k,a[200000];

int main() 
{
    int T;
    cin>>T;
    while(T--) {
        cin>>n>>k;
        ll x=n/k;
        if(k*(k+1)/2>n)
            cout<<-1<<endl;
        else {
            if(k%2) {
                for(int i=k/2;i>0;i--) a[i]=x-(k/2-i+1);
                for(int i=k/2+1;i<=k;i++) a[i]=x+(i-k/2-1);
                int m=n%k;
                for(int i=k;m>0;m--,i--) a[i]++;
            }
            else {
                for(int i=k/2;i>0;i--) a[i]=x-(k/2-i+1);
                for(int i=k/2+1;i<=k;i++) a[i]=x+(i-k/2);
                int m=n%k;
                for(int i=k/2;i&&m;i--,m--) a[i]++;
                if(m>0)
                    for(int i=k;i>k/2&&m;i--,m--) a[i]++;
            }
            ll ans=a[1];
            for(int i=2;i<=k;i++) { ans*=a[i]; ans%=mod; }
            cout<<ans<<endl;
        }
    }
    return 0;
}

 

DZY Loves Math

【思路】

    打表

    打表ans[i,j]表示矩形i*250,j*250的答案，对于一次询问n，m，每次得到最大的ij使得i*250<n j*250<m，然后把剩下的算出来。

    一本正经地说如何打表 =_=

【代码】

 

#include<cstdio>
#include<cstring>
#define FOR(a,b,c) for(int a=b;a<=c;a++)
using namespace std;

typedef long long ll;
const int N = 250+5;

ll gcd(ll a,ll b) 
{
    return b==0? a:gcd(b,a%b);
}

int n,m;
ll ans[61][61]={
    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};

int main()
{
    int T; scanf("%d",&T);
    while(T--) {
        scanf("%d%d",&n,&m);
        ll res=0;
        FOR(i,1,61) FOR(j,1,61)
            if(i*250>n&&j*250>m) {
                i--,j--;
                res=ans[i][j];
                FOR(x,1,i*250) FOR(y,j*250+1,m)
                    res+=gcd(x&y,x|y);
                FOR(x,i*250+1,n) FOR(y,1,m)
                    res+=gcd(x&y,x|y);
                i=j=62;
            }
        printf("%I64d\n",res);
    }
    return 0;
}

 

DZY Loves Connecting

【思路】

    树形DP

    设f[u]表示经过u的所有连续集的大小之和，cnt[u]表示经过u的所有连续集的个数。枚举u的每一个儿子，假设已经统计完前S-1个儿子，则有转移式：

        f[u]=f[u]+f[u]*cnt[v]+f[v]*cnt[u]

        cnt[u]=cnt[u]+cnt[u]*cnt[v]

    感觉跟树分治的统计信息类似，大概就是因为信息可以直接由dp得出所以才采用的树DP而不是树分治。

【代码】

 

#include<set>
#include<cmath>
#include<queue>
#include<vector>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
//#pragma comment(linker, "/STACK:102400000,102400000")
#define trav(u,i) for(int i=front[u];i;i=e[i].nxt)
#define FOR(a,b,c) for(int a=(b);a<=(c);a++)
using namespace std;

typedef long long ll;
const int N = 3e5+10;
const int M = N<<1;
const int MOD = 1e9+7;

ll read() {
    char c=getchar();
    ll f=1,x=0;
    while(!isdigit(c)) {
        if(c=='-') f=-1; c=getchar();
    }
    while(isdigit(c))
        x=x*10+c-'0',c=getchar();
    return x*f;
}
struct Edge {
    int v,nxt;
    Edge(int v=0,int nxt=0):v(v),nxt(nxt){}
}e[M];
int en=1,front[N];
void adde(int u,int v) 
{
    e[++en]=Edge(v,front[u]); front[u]=en;
}

int n;
ll f[N],cnt[N];

void dp(int u,int fa)
{
    cnt[u]=f[u]=1;
    int v;
    trav(u,i) if((v=e[i].v)!=fa) {
        dp(v,u);
        f[u]=(f[u]*(cnt[v]+1)%MOD+cnt[u]*f[v]%MOD)%MOD;
        cnt[u]=cnt[u]*(cnt[v]+1)%MOD;
    }
}

int main()
{
    int T=read();
    while(T--) {
        n=read();
        en=1; memset(front,0,sizeof(front));
        FOR(i,2,n) {
            int v=read();
            adde(i,v),adde(v,i);
        }
        ll ans=0;
        dp(1,-1);
        FOR(i,1,n) ans=(ans+f[i])%MOD;
        printf("%I64d\n",ans); 
    }
    return 0;
}

 

DZY Loves Sorting

【思路】

    二分+线段树

    二分最终a[k]的值为mid，依次进行每一个操作，对于0号操作，统计区间[l,r]内比mid大的点数为x，将[l,r-x]设为0，[r-x+1,r]设为1，1号操作类似。然后用线段树提供区间赋值与区间查询的操作。

    最终看a[k]==0?，如果成立则a[k]可能更小，因为

        000[0]00111

    01分界处为mid，[]为a[k]

    太神辣，奇技淫巧系列+1

【代码】

#include<set>
#include<cmath>
#include<queue>
#include<vector>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define trav(u,i) for(int i=front[u];i;i=e[i].nxt)
#define FOR(a,b,c) for(int a=(b);a<=(c);a++)
using namespace std;

typedef long long ll;
const int N = 2e5+10;

ll read() {
    char c=getchar();
    ll f=1,x=0;
    while(!isdigit(c)) {
        if(c=='-') f=-1; c=getchar();
    }
    while(isdigit(c))
        x=x*10+c-'0',c=getchar();
    return x*f;
}

struct Tnode {
    int l,r,s,tag;
}T[N<<2];
void pushdown(int u) {
    if(T[u].tag!=-1&&T[u].l!=T[u].r) {
        int lc=u<<1,rc=lc|1;
        T[lc].tag=T[rc].tag=T[u].tag;
        if(T[u].tag) {
            T[lc].s=T[lc].r-T[lc].l+1;
            T[rc].s=T[rc].r-T[rc].l+1;
        } else
            T[lc].s=T[rc].s=0;
        T[u].tag=-1;
    }
}
void maintain(int u) {
    T[u].s=T[u<<1].s+T[u<<1|1].s;
}
void update(int u,int L,int R,int v) {
    pushdown(u);
    if(L<=T[u].l&&T[u].r<=R) {
        T[u].tag=v;
        if(v==1) T[u].s=T[u].r-T[u].l+1;
        else T[u].s=0;
    } else {
        int mid=T[u].l+T[u].r>>1;
        if(L<=mid) update(u<<1,L,R,v);
        if(mid<R)  update(u<<1|1,L,R,v);
        maintain(u);
    }
}
int query(int u,int L,int R) {
    pushdown(u);
    if(L<=T[u].l&&T[u].r<=R) return T[u].s;
    else {
        int mid=T[u].l+T[u].r>>1,ans=0;;
        if(L<=mid) ans+=query(u<<1,L,R);
        if(mid<R)  ans+=query(u<<1|1,L,R);
        return ans;
     }
}

struct Node {
    int op,l,r;
}q[N];
int n,m,K,a[N],M;

void build(int u,int l,int r) 
{
    T[u].l=l,T[u].r=r; T[u].s=0;
    T[u].tag=-1;
    if(l==r) { T[u].s=a[l]>M; return ; }
    int mid=l+r>>1;
    build(u<<1,l,mid);
    build(u<<1|1,mid+1,r);
    maintain(u);
}
int can() 
{
    build(1,1,n);
    FOR(i,1,m) {
        if(q[i].op==0) {
            int x=query(1,q[i].l,q[i].r);
            update(1,q[i].l,q[i].r,0);
            if(x) update(1,q[i].r-x+1,q[i].r,1);
        } else {
            int x=query(1,q[i].l,q[i].r);
            update(1,q[i].l,q[i].r,0);
            if(x) update(1,q[i].l,q[i].l+x-1,1);
        }
    }
    return query(1,K,K)==0;
}

int main()
{
    int kase=read();
    while(kase--) {
        n=read(),m=read();
        int L=0,R=0,ans=0;
        FOR(i,1,n) a[i]=read(),R=max(R,a[i]);
        FOR(i,1,m)
            q[i].op=read(),q[i].l=read(),q[i].r=read();
        K=read();
        while(L<=R) {
            M=L+R>>1;
            if(can()) R=M-1,ans=M; else L=M+1;
        }
        printf("%d\n",ans);
    }
    return 0;
}