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Floor sqrt 1 0 8 x 1 2.
The inner one is redundant the outer one of course not.
Choose the greatest one which is 2 in.
Floor of square root of x cannot be more than x 2 when x 1.
Thanks to vinit for suggesting above optimization.
So which one do we choose.
2 is less than 2 31.
The floor function also known as the greatest integer function.
But 1 is also less than 2 31 and so is 0 and 1 2 3 etc.
The outer one is not redundant because the square root of a number x only results in an integer if x is a square number.
How do we define the floor of 2 31.
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The binary search can be further optimized to start with start 0 and end x 2.
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There are lots of integers less than 2 31.
Well it has to be an integer.