add (solution) : interactive-search (#462)

Problem Lin : https://lightoj.com/problem/interactive-search

Author: parvez-ahammed

interactive-search/en.md

@@ -0,0 +1,88 @@
+ #  Interactive Search
+
+ ## Problem
+ This is an easy interactive problem . You will be a value `n` and you have to find the secret number which is within  `1` to `n` in `30` tries . You will be given a response `high` or `low` or `correct` . If you guess the number in `30` tries you will get `AC` otherwise `WA` .
+
+ ## Solution
+
+ The maximum value of `n` is `1e9` so we can't use linear search .
+
+ As the number of tries is `30` we can use binary search to find the number because to find a number within a range of `1` to `1e9` it will take binary search maximum `log2(1e9)` which is okay for our problem.
+
+
+ So we will use binary search to find the number . 
+ ```
+ 1. We will take the input of `n` and set the `low` as `1` and `high` as `n`. 
+ 2. Then we will find the mid value and print it as guess .
+ 3. Then we will take the response as input . 
+ 5. If the response is `high` then we will set `high` as `mid - 1` .
+ 6. If the response is `low` then we will set `low` as `mid + 1` .
+ 7. If the response is `correct` then we will return . 
+ 8. If the count is greater than `30` then we will print `too many tries` and return .
+```
+
+You can learn more about binary search from 
+1. [geeksforgeeks](https://www.geeksforgeeks.org/binary-search/)
+2. [cp-algorithms](https://cp-algorithms.com/num_methods/binary_search.html)
+
+```
+ Time Complexity : O(log(n))
+ Space Complexity : O(1)
+```
+
+
+ 
+ 
+ ## CPP
+```cpp
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+int main()
+{
+
+    int low = 1, high = 100000;
+    // Taking the value of n as input and setting it as high as it will be the maximum value
+    cin >> high;
+
+
+    // To keep track of the number of tries
+    int count = 0;
+
+    // Binary search
+    while (low <= high)
+    {
+        // Finding the mid value
+        int mid = (low + high) >> 1;
+        // Printing the guess
+        cout << "guess " << mid << endl;
+
+
+        // Taking the response as input
+        string response;
+        cin >> response;
+
+        // Checking the response
+        if (response == "correct")
+            return 0;
+        else if (response == "high")
+            high = mid - 1;
+        else if (response == "low")
+            low = mid + 1;
+
+        // Increasing the count
+        count++;
+
+        // If the count is greater than 30 then printing too many tries and returning
+        if (count >= 30)
+        {
+            cout << "too many tries" << endl;
+            return 0;
+        }
+    }
+
+    return 0;
+}
+```