Uva 10852 - Less Prime

 
// Accepted

// Header file begin
#include<iostream>
#include<cstdio>
#include<cstring>
#include<map>
#include<string>
#include<vector>
#include<cmath>
#include<cctype>
#include<sstream>
#include<set>
#include<list>
#include<stack>
#include<utility>
#include<queue>
#include<algorithm>
#include<cstdlib>
// End
//..........
// Macro
#define sf scanf
#define pf printf
#define lp1(i,n) for(i=0;i<n;i++)
#define lp2(i,n) for(i=1;i<=n;i++)
#define mem(c,v) memset(c,v,sizeof(c))
#define cp(a) cout<<" "<<a<<" "
#define nl puts("")
#define sq(x) ((x)*(x))
#define all(x) x.begin(),x.end()
#define reall(x) x.rbegin(),x.rend()
#define s_wap(x,y) x^=y;y^=x;x^=y;
#define sz size()
#define gc getchar()
#define pb push_back
#define freader freopen("input.txt","r",stdin)
// End.........

// Size
#define mx7 20000100
#define mx6 1500000
#define mx5 100005
#define mx4 1000100
#define inf 1<<30                                           //infinity value
#define eps 1e-9
#define mx (65540)
#define mod 1000000007
#define pi acos(-1.0)

// Macros for Graph

#define white 1
#define gray 2
#define black 3
#define nil 0

using namespace std;
/***************/

// typedef

typedef long long LL;
typedef long L;
typedef unsigned long long ull;
typedef unsigned long ul;
typedef unsigned int ui;
typedef pair<int, int> pii;
typedef vector<int>vi;
typedef vector<long long> vll;
typedef vector<long>vl;
typedef vector<char>vch;
typedef vector<string>vs;
typedef map<int,int>mpii;
typedef map<int,bool>mpbi;
typedef map<long,bool>mpbl;
typedef map<long long,bool>mpbll;
typedef map<char,int>mpci;
typedef map<char,bool>mpbc;
typedef map<string,int>mpsi;
typedef map<long long,long long>mpll;

// template

template<class T> T gcd(T a, T b ) {return b!=0?gcd<T>(b,a%b):a;}
template<class T> T large(T a, T b ) {return a>b?a:b;}
template<class T> T small(T a, T b ) {return a<b?a:b;}
template<class T> T diffrnce(T a, T b) {return a-b<0?b-a:a-b;}

int prime[(mx4>>6)+1],prm[(mx4>>1)+9],plen=0;

#define setbit(n) (prime[n>>6] |= (1<<((n>>1)&31)))
#define checkbit(n) (prime[n>>6] & (1<<((n>>1)&31)))

void sieve()
{
    int i,j;
    for(i=3;sq(i)<=mx4;i+=2)
    {
        if(!checkbit(i))
        {
           for(j=i*i;j<=mx4;j+=i+i)
           {
                setbit(j);
           }
        }
    }

    prm[plen++]=2;

    for(i=3;i<=mx4;i+=2)
    {
        if(!checkbit(i))
        {
            prm[plen++]=i;
        }
    }

    //lp1(i,100)cp(prm[i]);
}

int b_search(int lo, int hi, int target)
{
    int mid;

    while(lo <= hi)
    {
        mid = lo + (hi-lo)/2;

        if(prm[mid] == target)
        {
            return mid;
        }

        else if(prm[mid] < target)
        {
            lo = mid + 1;
        }

        else
        {
            hi = mid - 1;
        }
    }

    return lo;
}

int main()
{
    sieve();
    int test;
    sf("%d",&test);

    while(test--)
    {
        int num;
        sf("%d",&num);

        int half = (num / 2) + 1; // p = 2;
        int res = b_search(1,plen,half);
        //cp(res); nl; cp(prm[res]);
        pf("%d\n",prm[res]);
    }

    return 0;
}

/*

***   Binary Search ****
binary_search(lo, hi, p):
   while lo < hi:
      mid = lo + (hi-lo)/2
      if p(mid) == true:
         hi = mid
      else:
         lo = mid+1

   if p(lo) == false:
      complain                // p(x) is false for all x in S!

   return lo         // lo is the least x for which p(x) is true

Source :: Top Coder :)


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