https://codeforces.com/contest/1104/problem/D

题解:倍增+二分

先特判等于1的情况

因为如果查询的两个数都在左边的话,肯定返回y,所以按倍增查找

1 2

2 4

4 8

8 16

的顺序倍增查询, 查出来目标在哪个区间

对区间【l,r】进行变形二分查找

先固定左边界 l 询问 l+l/2如果返回y代表目标不在【l,l+l/2】上,查询【l+l/2,3*l/4】

以此类推

最终可以得到答案

/*
*@Author:   STZG
*@Language: C++
*/
#include <bits/stdc++.h>
#include<iostream>
#include<algorithm>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<string>
#include<vector>
#include<bitset>
#include<queue>
#include<deque>
#include<stack>
#include<cmath>
#include<list>
#include<map>
#include<set>
//#define DEBUG
#define RI register int
using namespace std;
typedef long long ll;
//typedef __int128 lll;
const int N=100000+10;
const int MOD=1e9+7;
const double PI = acos(-1.0);
const double EXP = 1E-8;
const int INF = 0x3f3f3f3f;
int t,n,m,k,q;
int ans,cnt,flag,temp;
int a[N];
char str[N];
int main()
{
#ifdef DEBUG
	freopen("input.in", "r", stdin);
	//freopen("output.out", "w", stdout);
#endif
    //scanf("%d",&n);
    //scanf("%d",&t);
    //while(t--){}
    fflush(stdout);
    ll x,y;
    ll pos=0;
    scanf("%s",str);
    while(1){

        if(str[0]=='s'){
            x=1,y=2;
            pos=0;
            printf("? %I64d %I64d\n",x,y);
            fflush(stdout);
            scanf("%s",str);
            if(str[0]=='x'){
                printf("? %I64d %I64d\n",2ll,3ll);
                fflush(stdout);
                scanf("%s",str);
                if(str[0]=='x'){
                    printf("! %I64d\n",1ll);
                    fflush(stdout);
                }else{
                    printf("! %I64d\n",2ll);
                    fflush(stdout);
                }
            }else{
                x*=2;
                y*=2;
                printf("? %I64d %I64d\n",x,y);
                fflush(stdout);
            }
        }else if(str[0]=='x'){
            pos=x;
            x/=2;
            while(x){
                printf("? %I64d %I64d\n",pos,pos+x);
                fflush(stdout);
                scanf("%s",str);
                if(str[0]=='y')
                    pos+=x;
                x/=2;
            }
            printf("! %I64d\n",pos+1);
            fflush(stdout);
        }else if(str[0]=='y'){
            x*=2;
            y*=2;
                printf("? %I64d %I64d\n",pos+x,pos+y);
                fflush(stdout);
        }else{
            break;
        }
        scanf("%s",str);
    }

    //cout << "Hello world!" << endl;
    return 0;
}