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Check whether the given number is a perfect square

Objec­tive:  Given an inte­ger check whether it is a per­fect square.

Exam­ple:

number = 37
Output: false

number = 49
Output: true

This is fun puz­zle which is asked in the inter­view.
Approach:

  1. Say num­ber is n.
  2. Start a loop from 1 to n/2.
  3. Dur­ing iter­a­tion, for every inte­ger ‘i’, cal­cu­late x = i*i.
  4. Now with this ‘x’ there are 3 possibilities.
    1. If x == n then n is a per­fect square, return true
    2. If x > n then x has crossed the n, n is not per­fect square. Return false
    3. If above step a or b are not true then continue.

Time Com­plex­ity: O(sqrt(n))

Code:

Out­put:

37 is square: false
49 is square: true

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  • lipsa patel

    How about num­ber 1? 1 is a per­fect square. The above imple­men­ta­tion will return false.