jeseHainsij
2021-11-18
Stephanie Mann
Beginner2021-11-19Added 25 answers
Assume that there are n elements in our array. This indicates that the possible arrangements for an array are n! permutations. Although all of the leaves in a decision tree must be the same height, they are not always.
For example take consider an array of numbers: 7, 10, 1, 12, 14
When algorithm starts comparing it compares 7 and 10. Obviously, 10is larger than 7. Next, we compare 11 and 10. 11 is larger than 10. We don't need to compare 11 and 7 because transitive properties hold: if and then . This means that we will perform only n-1 comparisons which yields depth of n.
When an array isnt
Gloria Lusk
Beginner2021-11-20Added 18 answers
n-1 for an input array of length n.
In a decision tree, each internal node is annotated by for some i and j in the range , where n is the no of elements in the input sequence.
The absolute best case happens for a path in decision tree, in which, for each node there is no other node or in the path for some k in .
The length of the path, thus, will be n-1.
Example :- decision tree for insertion sort being implemented on a sorted array.
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