gym101239J Pipe Stream

题意

已知 $x$ 满足 $l\leq x\leq r$ ，现在每次能询问一个 $y(0\leq y\leq s)$ ，第 $i$ 次会回答 $ix\geq y$是否成立。

求最少的次数，使得能确定 $x$ 在一个长度 $\leq t$ 的区间内。

$q\leq 100$。

题解

考虑从 $r$ 开始往下每长度 $t$ 分一段，现在变成判断 $x$ 在哪一段内。

考虑把询问看成在一个有段数个叶子的bst上搜索，其中要求第$i$个叶子的深度不超过$d_i$。

那么我们从上到下每次加一层，每次把自由叶子数 $\times 2$，然后把必须放这一层的放在这一层($-$个数)，直到够放剩下的叶子即可。

正确性显然。

代码

/*
Author: QAQAutoMaton
Lang: C++
Code: G.cpp
Mail: lk@qaq-am.com
Blog: https://www.qaq-am.com/
*/
#include<bits/stdc++.h>
#define int long long
#define debug(...) fprintf(stderr,__VA_ARGS__)
#define DEBUG printf("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define Debug debug("Passing [%s] in LINE %d\n",__FUNCTION__,__LINE__)
#define all(x) x.begin(),x.end()
#define x first
#define y second
using namespace std;
typedef unsigned uint;
typedef long long ll;
typedef unsigned long long ull;
typedef complex<double> cp;
typedef pair<int,int> pii;
int inf;
const double eps=1e-8;
const double pi=acos(-1.0);
template<class T,class T2>int chkmin(T &a,T2 b){return a>b?a=b,1:0;}
template<class T,class T2>int chkmax(T &a,T2 b){return a<b?a=b,1:0;}
template<class T>T sqr(T a){return a*a;}
template<class T,class T2>T mmin(T a,T2 b){return a<b?a:b;}
template<class T,class T2>T mmax(T a,T2 b){return a>b?a:b;}
template<class T>T aabs(T a){return a<0?-a:a;}
template<class T>int dcmp(T a,T b){return a>b;}
template<int *a>int cmp_a(int x,int y){return a[x]<a[y];}
template<class T>bool sort2(T &a,T &b){return a>b?swap(a,b),1:0;}
#define min mmin
#define max mmax
#define abs aabs
struct __INIT__{
    __INIT__(){
        fill((unsigned char*)&inf,(unsigned char*)&inf+sizeof(inf),0x3f);
    }
}__INIT___;
namespace io {
    const int SIZE = (1 << 21) + 1;
    char ibuf[SIZE], *iS, *iT, obuf[SIZE], *oS = obuf, *oT = oS + SIZE - 1, c, qu[55]; int f, qr;
    // getchar
    #define gc() (iS == iT ? (iT = (iS = ibuf) + fread (ibuf, 1, SIZE, stdin), (iS == iT ? EOF : *iS ++)) : *iS ++)
    // print the remaining part
    inline void flush () {
        fwrite (obuf, 1, oS - obuf, stdout);
        oS = obuf;
    }
    // putchar
    inline void putc (char x) {
        *oS ++ = x;
        if (oS == oT) flush ();
    }
    template<typename A>
    inline bool read (A &x) {
        for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;else if(c==EOF)return 0;
        for (x = 0; c <= '9' && c >= '0'; c = gc()) x = x * 10 + (c & 15); x *= f;
        return 1;
    }
    inline bool read (char &x) {
        while((x=gc())==' '||x=='\n' || x=='\r');
        return x!=EOF;
    }
    inline bool read(char *x){
        while((*x=gc())=='\n' || *x==' '||*x=='\r');
        if(*x==EOF)return 0;
        while(!(*x=='\n'||*x==' '||*x=='\r'||*x==EOF))*(++x)=gc();
        *x=0;
        return 1;
    }
    template<typename A,typename ...B>
    inline bool read(A &x,B &...y){
        return read(x)&&read(y...);
    }
    template<typename A>
    inline bool write (A x) {
        if (!x) putc ('0'); if (x < 0) putc ('-'), x = -x;
        while (x) qu[++ qr] = x % 10 + '0',  x /= 10;
        while (qr) putc (qu[qr --]);
        return 0;
    }
    inline bool write (char x) {
        putc(x);
        return 0;
    }
    inline bool write(const char *x){
        while(*x){putc(*x);++x;}
        return 0;
    }
    inline bool write(char *x){
        while(*x){putc(*x);++x;}
        return 0;
    }
    template<typename A,typename ...B>
    inline bool write(A x,B ...y){
        return write(x)||write(y...);
    }
    //no need to call flush at the end manually!
    struct Flusher_ {~Flusher_(){flush();}}io_flusher_;
}
using io :: read;
using io :: putc;
using io :: write;
namespace run{
    int s,l,r,t,c;
    int xcount(int x){
        return (r-x)/t;
    }
    int get(int c){
        return max(xcount(max(s/(c+1)+1,l))-xcount(min(s/c+1,r)),0);
//        r/c .. r/(c+1)    
    }
    bool main(){
        read(s,l,r,t,c);
        l*=c;r*=c;t*=c;
        if(r-l<=t)return write("0\n");
        int w=(r-l-1)/t+1,cur=1,cnt=0;
        if(r-t>s)return write("impossible\n");
        while(cur<w){
            if(cur<0)return write("impossible\n");
            ++cnt;    
            cur<<=1;
            int c=get(cnt);
            w-=c;
            cur-=c;
        }
        return write(cnt,'\n');
    }
}
signed main(){
#ifdef QAQAutoMaton 
    freopen("G.in","r",stdin);
    freopen("G.out","w",stdout);
#endif
    int t;
    read(t);
    for(;t;--t)run::main();
    return 0;
}