Shortest way to check perfect Square?

Question

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What's a good algorithm to determine if an input is a perfect square?

I want Shortest and Simplest way to Check a number is perfect square in C#

Some of Perfect Squares:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, ......

@dogbane That question is closed as dup :D – Dr. belisarius Feb 03 '11 at 12:24 — Dr. belisarius, Feb 03 '11 at 12:24

score 53 · Accepted Answer · answered Feb 03 '11 at 12:10

53

Probably checking if the square root of the number has any decimal part, or if it is a whole number.

Implementationwise, I would consider something like this:

double result = Math.Sqrt(numberToCheck);
bool isSquare = result%1 == 0;

isSquare should now be true for all squares, and false for all others.

answered Feb 03 '11 at 12:10

Øyvind Bråthen

10

+1: I was surprised that the % operator works on doubles – Binary Worrier Feb 03 '11 at 12:17
14

The above answer is not always correct with large number. Try with this: double result = Math.Sqrt ( 3999680306388005621 ); bool isSquare = result % 1 == 0; long x = ( long ) result; long y = x * x; // y is not 3999680306388005621 – Setyo N Oct 26 '12 at 07:56
I'm not sure but that might be when the number starts to lose precision / floating point? – Luke Aug 02 '17 at 12:16

Daren Thomas · Answer 2 · 2014-03-10T10:33:35.053

7

This is a variant on checking if the square root is integral:

bool IsPerfectSquare(double input)
{
    var sqrt = Math.Sqrt(input);
    return Math.Abs(Math.Ceiling(sqrt) - Math.Floor(sqrt)) < Double.Epsilon;
}

Math.Ceiling will round up to the next integer, whereas Math.Floor will round down. If they are the same, well, then you have an integer!

This can also be written as a oneliner:

if (int(Math.Ceiling(Math.Sqrt(n))) == int(Math.Floor(Math.Sqrt(n)))) /* do something */;

edited Mar 10 '14 at 10:33

answered Feb 03 '11 at 12:14

Daren Thomas

2

`Math.Ceiling()` and `Math.Floor()` return a double value, so you'll run into possible issues here. Instead, do a floating point comparison: `if (Math.Abs(val1 - valu2) < Double.Epsilon) { ... }` – michael Mar 09 '14 at 19:53
@michael, thank you, that is a very good point! I have updated my answer to reflect this! – Daren Thomas Mar 10 '14 at 10:32
Any reason to do `< Double.Epsilon` instead of `> 0`? – j.i.h. Sep 17 '14 at 13:17

score 5 · Answer 3 · answered Feb 03 '11 at 12:26

5

    public bool IsPerferctSquare(uint number)
    {
        return (Math.Sqrt(number) % 1 == 0);
    }

answered Feb 03 '11 at 12:26

rajesh

score 2 · Answer 4 · edited Jun 16 '12 at 02:18

2

public bool IsPerfectSquare(int num)
{
   int root = (int)Math.Sqrt(num);
   return (int) Math.Pow(root,2) == num;
}

edited Jun 16 '12 at 02:18

Sebazzz

answered Feb 03 '11 at 12:12

Itay Karo

4 Answers4