Interactive Problems are those problems in which our solution or code interacts with the judge in real time. When we develop a solution for an Interactive Problem then the input data given to our solution may not be predetermined but is built for that problem specifically. The solution performs a series of exchange of data with the judge and at the end of the conversation the judge decides whether our solution was correct or not.

## Guessing the Number (An Interactive Problem)

In this problem the user has to guess the number during a communication with the judge. The user is provided with the upper and lower bound and he/she can ask the judge whether a number is the number to be guessed. The judge replies with -1 if the number is smaller than the number to be guessed or 1 if number is greater than the number to be guessed or 0 if it is equal to the number to be guessed.

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Approach 1 : Linear Guessing

The user can query the judge for all the numbers between lower limit and upper limit to find the solution.

`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` `; ` ` ` `} ` ` ` `} ` ` ` `} ` `} ` |

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**Time Complexity:** O(n)

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Approach 2 : Applying Binary Search

We can also apply binary search interactively to find the solution. This solution is efficient as compared to the previous approach.

`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` `; ` ` ` `} ` ` ` `} ` ` ` `} ` `} ` |

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**Time Complexity:** O(logn)

**Algorithm Paradigm:** Divide and Conquer

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