竞技编程中的交互问题

交互式问题是我们的解决方案或代码与法官实时交互的那些问题。当我们为交互问题开发解决方案时，提供给我们解决方案的输入数据可能不是预先确定的，而是专门为该问题构建的。解决方案与法官进行一系列数据交换，在对话结束时，法官决定我们的解决方案是否正确。

猜数字(一个互动问题)

在这个问题中，用户必须在与法官交流期间猜测数字。用户有上限和下限，他/她可以询问判断一个数字是否是要猜的数字。如果数字小于要猜的数字，则法官回复-1，如果数字大于要猜的数字，则为1，如果等于要猜的数字，则为0。

方法一：线性猜测

用户可以查询下限和上限之间的所有数字的判断来找到解决方案。

C++

#include 
using namespace std;
 
int main()
{
    int lower_bound = 2;
    int upper_bound = 10;
 
    // Number to be guessed is 6
 
    // Iterating from lower_bound to upper_bound
    for (int i = lower_bound; i <= upper_bound; i++) {
        cout << i << endl;
 
        // Input the response from the judge
        int response;
        cin >> response;
 
        if (response == 0) {
            cout << "Number guessed is :" << i;
            break;
        }
    }
 
    return 0;
}
 
// This code is contributed by divyeshrabadiya07

Java

import java.util.*;
class GFG {
    public static void main(String[] args)
    {
        Scanner sc1 = new Scanner(System.in);
        int lower_bound = 2;
        int upper_bound = 10;
 
        // Number to be guessed is 6
 
        // Iterating from lower_bound to upper_bound
        for (int i = lower_bound; i <= upper_bound; i++) {
            System.out.println(i);
 
            // Input the response from the judge
            int response = sc1.nextInt();
 
            if (response == 0) {
                System.out.println("Number guessed is :" + i);
                break;
            }
        }
    }
}

Python3

if __name__=='__main__':
    lower_bound = 2;
    upper_bound = 10;
 
    # Number to be guessed is 6
 
    # Iterating from lower_bound to upper_bound
    for i in range(lower_bound, upper_bound + 1):
        print(i)
 
        # Input the response from the judge
        response = int(input())
 
        if (response == 0):
            print("Number guessed is :", i, end = '')
            break;
 
            # This code is contributed by rutvik_56

C#

using System;
class GFG
{
    public static void Main(string[] args)
    {      
        int lower_bound = 2;
        int upper_bound = 10;
  
        // Number to be guessed is 6
  
        // Iterating from lower_bound to upper_bound
        for (int i = lower_bound; i <= upper_bound; i++)
        {
            Console.WriteLine(i);
  
            // Input the response from the judge
            int response = int.Parse(Console.ReadLine());
  
            if (response == 0) {
                Console.WriteLine("Number guessed is :" + i);
                break;
            }
        }
    }
}
 
// This code is contributed by Pratham76

时间复杂度： O(n)

方法 2：应用二分搜索

我们还可以交互式地应用二分搜索来找到解决方案。与先前的方法相比，该解决方案是有效的。

Java

import java.util.*;
class GFG {
    public static void main(String[] args)
    {
        Scanner sc1 = new Scanner(System.in);
        int lower_bound = 2;
        int upper_bound = 10;
 
        // Number to be guessed is 9
 
        // Applying Binary Search interactively
        while (lower_bound <= upper_bound) {
            int mid = (lower_bound + upper_bound) / 2;
 
            // Print the guessed number
            System.out.println(mid);
 
            // Input the response from the judge
            int response = sc1.nextInt();
 
            if (response == -1) {
                lower_bound = mid + 1;
            }
            else if (response == 1) {
                upper_bound = mid - 1;
            }
            else if (response == 0) {
                System.out.println("Number guessed is :" + mid);
                break;
            }
        }
    }
}

C＃

using System;
class GFG {
  static void Main() {
    int lower_bound = 2;
    int upper_bound = 10;
 
    // Number to be guessed is 9
 
    // Applying Binary Search interactively
    while (lower_bound <= upper_bound) {
        int mid = (lower_bound + upper_bound) / 2;
 
        // Print the guessed number
        Console.WriteLine(mid);
 
        // Input the response from the judge
        int response = Convert.ToInt32(Console.ReadLine());
 
        if (response == -1) {
            lower_bound = mid + 1;
        }
        else if (response == 1) {
            upper_bound = mid - 1;
        }
        else if (response == 0) {
            Console.WriteLine("Number guessed is :" + mid);
            break;
        }
    }
  }
}
 
// This code is contributed by divyesh072019

时间复杂度： O(logn)
算法范式：分而治之

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