square_numbers.py

import time


def is_power(c):
    m = int(c ** 0.5)
    candidate_list = range(m, 0, -1)
    for i in candidate_list:
        pos = c - i ** 2
        if pos < 0:
            continue
        other = pos ** .5
        if other.is_integer():
            return True
    return False


def is_power2(c):
    i = 0
    j = int(c ** 0.5)
    while i <= j:
        r = i*i + j*j
        if r < c:
            i += 1
        elif r > c:
            j -= 1
        else:
            return True
    return False


def is_power3(c):
    for i in range(int(c ** 0.5) + 1):
        if ((c - i ** 2) ** .5).is_integer():
            return True
    return False


if __name__ == '__main__':
    num = 88777661
    start = time.time()
    print is_power(num), time.time() - start

    start = time.time()
    print is_power2(num), time.time() - start

    start = time.time()
    print is_power3(num), time.time() - start