# Write a recurrence for the running time of this recursive version of insertion sort

The bottom level has n nodes, each contributing a cost of c, for a total cost of cn. The idea is to divide the array into two subsets — sorted subset and unsorted subset.

How should we choose k in practice? Exercises 2. We do not need the master theorem to intuitively understand why the solution to the recurrence 2. Because we are assuming that the input size is a power of 2, the next input size to consider is 2iC1. We continue expanding each node in the tree by breaking it into its constituent parts as determined by the recurrence, until the problem sizes get down to 1, each with a cost of c.

The fully expanded tree in part d has lgn C 1 levels i. Now assume as an inductive hypothesis that the number of levels of a recursion tree with 2i leaves is lg 2i C 1 D i C 1 since for any value of iwe have that lg 2i D i.

The total number of levels of the recursion tree in Figure 2.

## Recursive insertion sort javascript

Adding it to the 2T. It is also a well known online algorithm as it can sort a list as it receives it. How should we choose k in practice? A tree with n D 2iC1 leaves has one more level than a tree with 2i leaves, and so the total number of levels is. The binary search al- gorithm repeats this procedure, halving the size of the remaining portion of the sequence each time. We continue expanding each node in the tree by breaking it into its constituent parts as determined by the recurrence, until the problem sizes get down to 1, each with a cost of c. Let us rewrite recurrence 2. Because we are assuming that the input size is a power of 2, the next input size to consider is 2iC1.

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