专项训练之二分

Codevs 1497

Codevs 3286

Codevs 1038

Codevs 1138

Codevs 1516

Codevs 1696（洛谷 P2759）

Codevs 1766

Codevs 2072

//Codevs1497取余运算
#include<iostream>
using namespace std;
long long b,p,k;
long long ksm(long long p)
{
    if(p==0)return 1;
    int t=ksm(p/2)%k;
    t=(t*t)%k;
    if(p%2==1)t=(t*b)%k;
    return t;
}
int main()
{
    cin>>b>>p>>k;
    int tt=b;
    b%=k;
    cout<<tt<<"^"<<p<<" mod "<<k<<"="<<ksm(p)<<endl;
}
//快速幂


//Codevs 3286 火柴排队2013年NOIP全国联赛提高组
#include<cstdio>
#include<iostream>
#include<algorithm>
#define LL long long
#define M 99999997
using namespace std;
const int MAXN=100000+10;
struct node{int num,c;}l1[MAXN],l2[MAXN];
int N,goal[MAXN],bit[MAXN];
bool cmp(node a,node b){return a.c<b.c;}
int lowbit(int k){return k&(-k);}
void add(int x){while(x<=N)bit[x]++,x+=lowbit(x);}
int sum(int x)
{
    int tot=0;
    while(x>0)
    {
        tot+=bit[x];
        x-=lowbit(x);
    }
    return tot;
}
int main()
{
    scanf("%d",&N);
    for(int i=1;i<=N;i++)scanf("%d",&l1[i].c),l1[i].num=i;
    for(int i=1;i<=N;i++)scanf("%d",&l2[i].c),l2[i].num=i;
    sort(l1+1,l1+N+1,cmp);sort(l2+1,l2+N+1,cmp);
    for(int i=1;i<=N;i++)goal[l1[i].num]=l2[i].num;
    LL ans=0;
    for(int i=1;i<=N;i++)
    {
        add(goal[i]);
        ans+=i-sum(goal[i]);
        ans%=M;
    }
    printf("%lld
",ans);
    return 0;
}
//树状数组求逆序对orz


//Codevs 1038 一元三次方程求解2001年NOIP全国联赛提高组
#include<cstdio>
#include<iostream>
using namespace std;
double a,b,c,d,x1,x2,xx;
double f(double x){return a*x*x*x+b*x*x+c*x+d;}
int main()
{
    cin>>a>>b>>c>>d;
    int x;
    for(x=-100;x<=100;x++)
    {
        x1=x;x2=x+1;
        if(f(x1)==0)printf("%0.2lf ",x1);
        else if(f(x1)*f(x2)<0)
        {
            while(x2-x1>=0.001)
            {
                xx=(x1+x2)/2;
                if(f(x1)*f(xx)<=0)x2=xx;
                else x1=xx;
            }
            printf("%0.2lf ",x1);
        }
    }
    return 0;
}
//二分水题


//Codevs1138 聪明的质监员2011年NOIP全国联赛提高组
#include<iostream>
#include<cstring>
#include<cstdio>
#define N 200010
using namespace std;
long long n,m,s,ll=123456789123456789,rr=-1,mid,ans=123456789123456798;
long long w[N],v[N],le[N],ri[N],sum[N],summ[N];
bool check(int x)
{
    long long i,y=0,p;
    for(i=1;i<=n;i++)
    {
        if(w[i]>x)
        {
            sum[i]=sum[i-1]+1;
            summ[i]=summ[i-1]+v[i];
        }
        else
        {
            sum[i]=sum[i-1];
            summ[i]=summ[i-1];
        }
    }
    for(i=1;i<=m;i++)
        y=y+(sum[ri[i]]-sum[le[i]-1])*(summ[ri[i]]-summ[le[i]-1]);
    if(s>y)
    {
        p=s-y;
        i=0;
    }
    else
    {
        p=y-s;
        i=1;
    }
    if(p<ans)ans=p;
    return i;
}
int main()
{
    std::ios::sync_with_stdio(false);
    cin>>n>>m>>s;
    for(long long i=1;i<=n;i++)
    {
        cin>>w[i]>>v[i];
        if(w[i]<ll)ll=w[i];
        if(w[i]>rr)rr=w[i];
    }
    for(long long i=1;i<=m;i++)cin>>le[i]>>ri[i];
    while(ll<=rr)
    {
        mid=(ll+rr)>>1;
        if(check(mid))ll=mid+1;
        else rr=mid-1;
    }
    printf("%lld
",ans);
    return 0;
}
//二分


//Codevs1516 平均分数
#include<cstdio>
#include<cstring>
#include<iostream>
using namespace std;
#define M 1000006
#define LL long long
LL a[M],b[M],sum[M],t[M],N,L,R,C,ans,flag,tot;
LL gcd(LL a,LL b){return b==0?a:gcd(b,a%b);}
void merge(LL le,LL mid,LL ri,LL f[])
{
    LL i=le,j=mid+1,k=le;
    while(i<=mid&&j<=ri)
        if(f[i]<f[j]||(f[i]==f[j])*flag)t[k++]=f[i++];
        else C+=(mid+1-i),t[k++]=f[j++];
    while(i<=mid)t[k++]=f[i++];
    while(j<=ri)t[k++]=f[j++];
    for(LL o=le;o<=ri;o++)f[o]=t[o];
}
void mergesort(LL le,LL ri,LL f[])
{
    if(le<ri)
    {
        LL mid=(le+ri)>>1;
        mergesort(le,mid,f),mergesort(mid+1,ri,f);
        merge(le,mid,ri,f);
    }
}
int main()
{
    scanf("%lld%lld%lld",&N,&L,&R);
    for(LL i=1,x;i<=N;i++)
    {
        scanf("%lld",&x);
        sum[i]=sum[i-1]+x;
    }
    for(LL i=0;i<=N;i++)a[i]=L*i-sum[i],b[i]=R*i-sum[i];
    ans=flag=C=0;
    mergesort(0,N,a);
    ans=C,C=0,flag=1;
    mergesort(0,N,b);
    tot=N*(N+1)/2,ans-=C;
    if(ans==tot)printf("1
");
    else if(ans==0)printf("0
");
    else 
    {
        LL x=gcd(ans,tot);
        printf("%lld/%lld
",ans/x,tot/x);
    }
    return 0;
}
//二分
//奇怪的题目
//样例没过，提交上竟然AC了， (☄⊙ω⊙)☄


//洛谷P2759 奇怪的函数
#include<iostream>
#include<cmath>
using namespace std;
int n;
bool can(int x)
{
    if(x*(log(x)/log(10))>=n-1)return true;
    return false;
}
int findx(int x,int y)
{
    int mid=x+(y-x)/2;
    if(y-x<=1)return y;
    if(can(mid))return findx(x,mid);
    return findx(mid,y);
}
int main()
{
    cin>>n;
    int ans=findx(0,1000000000);
    cout<<ans<<endl;
    return 0;
}
//二分答案+一个灰常6的数学公式


//codevs1766装果子
#include<cstdio>
#define N 110000
long long n,m,sum=0,ans,max=0,a[N];
void find(long long le,long long ri)
{
    if(le>ri)return;
    long long mid=(le+ri)>>1,s=0,k=0;
    for(long long i=1;i<=n;i++)
    {
        s+=a[i];
        if(s>mid)k++,s=a[i];
    }
    if(s)k++;
    if(k>m)find(mid+1,ri);
    else ans=mid,find(le,mid-1);
}
int main()
{
    scanf("%lld%lld",&n,&m);
    for(long long i=1;i<=n;i++)
    {
        scanf("%lld",&a[i]);
        if(a[i]>max)max=a[i];
        sum+=a[i];
    }
    find(max,sum);
    printf("%lld
",ans);
    return 0;
}
//依旧是二分题……


//Codevs2072 分配房间
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
const int MAXN=100000+10;
int N,M,barn[MAXN];
bool cmp(int a,int b){return a<b;}
bool check(int x)
{
      int last=0;
      for(int i=1;i<M;i++)
      {
           int cnt=last+1;
           while(cnt<N&&barn[cnt]-barn[last]<x)cnt++;
           if(cnt==N)return false;
           last=cnt;
      }
      return true;
}
int main()
{
      scanf("%d%d",&N,&M);
      for(int i=0;i<N;i++)scanf("%d",&barn[i]);
      sort(barn,barn+N,cmp);
      int le=0,ri=barn[N-1]+barn[0]+1,mid;
      while(ri-le>1)
      {
           mid=(le+ri)>>1;
           if(check(mid))le=mid;
           else ri=mid;
      }
      printf("%d
",le);
      return 0;
}