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Категория: Программир

Опубликовано: Да

Description: Some numbers have funny properties. For example:
89 --> 8¹ + 9² = 89 * 1
695 --> 6² + 9³ + 5⁴= 1390 = 695 * 2
46288 --> 4³ + 6⁴+ 2⁵ + 8⁶ + 8⁷ = 2360688 = 46288 * 51
Given a positive integer n written as abcd... (a, b, c, d... being digits) and a positive integer p
we want to find a positive integer k, if it exists, such as the sum of the digits of n taken to the successive powers of p is equal to k * n.

In other words:
Is there an integer k such as : (a ^ p + b ^ (p+1) + c ^(p+2) + d ^ (p+3) + ...) = n * k
If it is the case we will return k, if not return -1.
Note: n and p will always be given as strictly positive integers.

digPow(89, 1) should return 1 since 8¹ + 9² = 89 = 89 * 1

digPow(92, 1) should return -1 since there is no k such as 9¹ + 2² equals 92 * k

digPow(695, 2) should return 2 since 6² + 9³ + 5⁴= 1390 = 695 * 2

digPow(46288, 3) should return 51 since 4³ + 6⁴+ 2⁵ + 8⁶ + 8⁷ = 2360688 = 46288 * 51

function SpreadAndPow ($n, $p) {
    $accum = 0;
    $str = (string) $n;
    $length = strlen($str);
    for ($i = 0; $i < $length; $i++) {
        $val = (int) $str[$i];
        $accum += pow($val, $p);
        $p++;
    }
            
    if ($accum % $n == 0) {
        return $accum / $n;
    }
            
    if ($accum < PHP_INT_MAX) {
        return SpreadAndPow($n, $p++);
    }
            
    return -1;
            
}
        
echo SpreadAndPow(89, 1);

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