2 Exercise 2 Consider the pseudocode given for DecreaseKey on a min-heap. The two loop invariants below together lead to proving that after Decreasekey is performed the tree satisfies the min-heap property again Loop in variant 1. for all nodes u in Hexcept v and its root, key parent{u}]] Skeyful. Loop invariant 2. if u has a parent then for each child of V. keyparent[0]] key[u] do 3. swap V and its parent 3.0p a Prove maintenance of Loop invariant 1. Hint think carefully about which nodes get a new parent Also use Loop invariant 2. 100 b Prove termination: the resulting tree is indeed a min-heap