Problem 5 (14 points) In this problem, we use a Union-Find d…
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Prоblem 5 (14 pоints) In this prоblem, we use а Union-Find dаtа structure. However, instead of using the standard link-by-size algorithm discussed in class, this implementation uses a modified linking rule. Assume the elements are initially: {1,2,3,4,5,6,7,8} Initially, every element is in its own set. Therefore, every element is the root of a tree with height 0. The modified algorithm uses link-by-height. In other words, when performing union(x,y): 1. Use find to determine the roots of the two sets.2. Compare the heights of the two root trees.3. The root of the shorter tree becomes a child of the root of the taller tree.4. In order to ensure we end up with the same answer, if the two trees being combined have the same height, the root with the smaller label becomes the parent. Task After each union operation, report the height of every tree currently in the Union-Find data structure. For this problem, you should only report the height of trees using their root nodes. Do not report heights for nodes that are no longer roots. For example, initially every element is in its own tree, so every element is a root with height 0: 1:0,2:0,3:0,4:0,5:0,6:0,7:0,8:0 Now consider the operation: union(1,2) Both trees have height 0, so the tie-breaking rule is used. Since 1
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