int root = low;

while( (root * 2 + 1) <= high ) {

int left_child = root * 2 + 1;

int right_child = left_child + 1;

int swpIdx = root;

//if root is less than left child.

if ( list[root] < list[left_child] ) {

swpIdx = left_child;

}

// if right child exists and bigger

if ( (right_child <= high) && list[swpIdx] < list[right_child] ) {

swpIdx = right_child;

}

if ( swpIdx != root ) {

algo::swap( list[swpIdx], list[root] );

} else {

break;

}

//keep going down

swpIdx = root;

}

int mid = (high - low - 1)/2;

while( mid >=0 ) {

__sift_down(list, mid, high);

--mid;

}

assert(list);

assert(size > 0);

//heapify the list

__heapify(list, 0, size-1);

int high = size - 1;

while ( high > 0 ) {

algo::swap(list[high], list[0]);

--high;

__heapify(list, 0, high);

}