. All algorithms are in pseudocode Acknowledge (add a note and/or hyperlink and/or comment) any help or resource you used Problem 1. (15p) Heap properties 1.1 (5p) Consider a heap with n elements. Prove that the number of leaves in the implicit binary tree is 1.2 (op) Consider a heap AI nl. Prove that by filling its implicit binary tree from top to bottom, left to right order (first all nodes in a layer, then their children) makes A 2j] as the left child and A2j 1 as the right child of A j] Note: Consider induction for both above proofs 1.3 (5p) What is the result of Build-Max-Heap on the input A- 16,4, 2,9, 1, 44, 30? Illustrate all intermediate steps. What is the result of increasing the key #1 to 34 once the max-heap is built