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