Most optimized algorithm for incrementing squares [closed]

Question

Write the "fastest" program to print an incrementing series of squares from a given input to a given input.

Example input:

-2
7

Example output:

4, 1, 0, 1, 4, 9, 16, 25, 36, 49

When using a "cryptic" language, please post the pseudocode, in addition to your program.

The entries will be judged on the most efficient algorithm.

Answer 1

The tag says "code-challenge", but I don't see any challenge. Just some mathematics we studied when I was about 12.

import java.util.*;

public class IncSquares
{
    public static void main(String[] args)
    {
        Scanner in = new Scanner(System.in);
        int min = in.nextInt();
        int max = in.nextInt();

        int sq = min * min;
        System.out.print(sq);
        while (min < max) {
            sq += (min << 1) + 1;
            min++;
            System.out.print(", " + sq);
        }
        System.out.println();
    }
}

Answer 2

Python

print ", ".join(`x*x` for x in range(int(raw_input()), int(raw_input())+1))

Answer 3

C

Since my usual language interpreter has a one-second startup time already, I chose not to use it here.

#include <stdio.h>

int main(void) {
    int start, end, i;
    scanf("%d\n%d", &start, &end);
    for (i = start; i <= end; i++) {
        printf("%d", i*i);
        if (i != end)
            printf(", ");
    }
    return 0;
}

Answer 4

Ruby

a,b=*$<.map(&:to_i)
p (a+1..b).reduce([a**2]){|m,x|m<<m[-1]+x+x-1;m}*?,

Answer 5

Jelly 12 bytes

+³’µ²
_N‘RÇ€

---

Explanation

+³’µ²
 ³’    -Decrement the first argument
+      -Sum it
   µ   -Groups the functions prior to this
    ²  -Square the result

_N‘RÇ€
_      -Subtract the two arguments
 N     -Negate the difference
  ‘    -Increment the difference
   R   -Generate Range from Difference
    ǀ -Map range with above function

Try it online!

Answer 6

(z + 1)^2 = z^2 + (2z + 1)

We already know z^2, and 2z is simply z<<1.

(z + 1)^2 = (z^2) + (z << 2 + 1)

---

Now just memorize this trick if you want to list squares in your head.

If you've got an arbitrary [two-digit] square (to do in your head), z^2, do this:

z^2 = (z-n)*(z+n) + n^2

Or:

23^2 = (23-3)*(23+3) + 3^2
23^2 = 20*26 + 9
23^2 = 520 + 9
23^2 = 529

Works even "faster" with larger numbers, relative to you doing 97*97 in your head. Have fun showing off.