Question

Int sumSquares (int[] array, int first, int last) {

if {first == last}
return array [first] * array[first];
int mid = (first + last) / 2;
return sumSquares (array, first, mid) +
sumSquares (array, mid + 1, last);
}
Using the recursive method in above and assuming n is the length of the array.
a. Modify the recursion tree from the previous problem to show the amount of work on each activation and the row sums.

Answer 1

The recursion tree for the recursive function sumSquares shows the sum of squares for sub-arrays with each node's 'work' being the number of elements it processes.

Step-by-step explanation:

The recursive method provided is designed to calculate the sum of the squares of elements in an array given the start (first) and end (last) indices. When illustrating the recursion tree for this function, each activation corresponds to a recursion call that sums the squares of a sub-array of the original array. The 'amount of work' refers to the number of operations needed to calculate the sum of squares for a particular sub-array.

If we are to represent the 'work' of each activation in a recursion tree, it would be equal to the number of elements in the sub-array to which the activation corresponds since each element's square is calculated separately. The 'row sum' is the sum of all the 'work' on a given level of recursion, which, when all levels are accumulated, should equal the total amount of work done by the algorithm, n terms.

To modify the recursion tree to show the amount of work and row sums, one might label each node with the count of elements it's processing and sum these counts across each level to reflect the total work per recursion level. If there are n elements overall, the root would be labeled with 'n', and it divides down into smaller parts as we go deeper into the recursion tree. At each level, the sum of all node labels (representing the sub-array sizes) should still equal 'n', indicating that every element is counted once per level.

However, the provided example of distributing n terms to transform an expression into 2n² is not directly related to this recursive method, but instead showcases a mathematical technique to simplify an arithmetic series.