# Minimum number of guesses needed to find a specific number

**Objective**– Given the numbers 1 to 1000, what is the minimum number of guesses needed to find a specific number if you are given the hint “higher” or “lower” for each guesses you make.

**Naive Approach: Linear search**

Start guessing from 1 and then 2 then 3 …till we do not find the answer.

**Time complexity: O(N)** , N = total numbers, as per our problem it is 1000.

**Better Approach: ****Binary Search**

Start from N/2 and keep on discarding half elements after each guess based on the hint. Let’s understand from one example.

N = 1 to 1024, specific no = 378 1^{st}guess = 512, hint = lower, new N =1 to 512, discard numbers 513 to 1024. 2^{nd}guess = 256, hint = higher, new N =257 to 512, discard numbers 1 to 256 3^{rd}guess = 385, hint = lower, new N = 257 to 384, discard numbers 385 to 512 4^{th}guess = 320, hint = higher, new N = 321 to 384, discard numbers 257 to 320 5^{th}guess = 352, hint = higher, new N = 353 to 384, discard numbers 321 to 352 6^{th}guess = 368, hint = higher, new N = 369 to 384, discard numbers 353 to 368 7^{th}guess = 376, hint= higher, new N = 377 to 384, discard numbers 369 to 376 8^{th}guess = 380, hint= lower, new N = 377 to 380, discard numbers 381 to 384 9^{th}guess = 378 MATCH found Total no of guesses = 9

**Java Code**:

Output: No of guesses needed for N: 1024 and x: 378 are: 9