/**
* Determine if an array can k-sum any of its elements to equal $t. This works by iterating through each element of the
* array and then looking at the value $k. If $k is > 3 the function recursively calls itself, passing $t - $number as
* the value to look for and $k - 1 as the number of elements needed for the sum. Eventually the base case where $k = 2
* is reached and then hasTwoSum is used to determine if two elements in the array can sum to the value of $t at the
* time. The boolean value is then returned back up the stack to get the result. Obviously at very large values for $k
* this is time consuming because recursive calls are made at every level for every element in the array.
*
* @param int[] $array
* @param int $t
* @param int $k
* @return bool
*/
function hasKSumRecursive($array, $t, $k)
{
foreach ($array as $number) {
if ($k > 3) {
if (hasKSumRecursive($array, $t - $number, $k - 1)) {
return true;
}
} elseif (hasTwoSum($array, $t - $number)) {
return true;
}
}
return false;
}
/**
* Determine if an array can three sum any of its elements to equal $t. This works by going through each element and
* determining if there is a two sum that will equal $t - $number. If there is, a three sum can be achieved by adding
* $number.
*
* i.e.
* If the input array is [1, 2, 3] and t is 5
*
* <<< FOREACH LOOP BEGIN >>>
*
* Iteration 1:
* $number = 1
* Is there a two sum that equals 4? Yes, 1 + 3
*
* <<< FOREACH LOOP TERMINATION: function return >>>
*
* return true
*
* @param int[] $array
* @param int $t
* @return bool
*/
function hasThreeSum($array, $t)
{
if (empty($array)) {
throw new \InvalidArgumentException('The input $array cannot be empty');
}
if ($t > PHP_INT_MAX || $t < (PHP_INT_MAX + 1) * -1) {
throw new \InvalidArgumentException('$t must be between ' . (PHP_INT_MAX + 1) * -1 . ' and ' . PHP_INT_MAX);
}
asort($array);
foreach ($array as $number) {
if (hasTwoSum($array, $t - $number)) {
return true;
}
}
return false;
}
