Suppose you have a max heap in which each node stores a distinct integer. Consider the following algorithm which claims to implement the 'pop' operation, i.e. remove the node of largest value from the heap. Maintain a pointer to the node of largest value, initially at the top of the heap, and recurse downwards. At each stage: - if the node has two children, swap it with the child of larger value; - if the node has only one child, swap it with that child; - if the node has no children, delete it. 2.1 Demonstrate the execution of the algorithm on a nontrivial example in which it correctly removes the node of largest value from the heap. 2.2 Does this algorithm correctly implement the 'pop' operation? Justify your