Assume n is a positive integer Count the number of

Last updated: 11/13/2023

Assume n is a positive integer Count the number of operations in the loop below x 0 for i 1 to n for j 1 to i for k 1 to j x i j k next k next j next i 1 Start by counting the number of operations performed in the innermost loop the k loop This total will depend on j In each iteration of the innermost loop The inner loop runs operations are performed times so the total number of operations performed in this loop is 2 Now we want to count the number of operations the middle loop the j loop performs in a complete run of it In the ith iteration of the middle loop The middle loop runs a total of times To get the total number of operations we need to add up the number of operations performed for each value of j That is the total number of operations performed in the middle operations are performed This total depends on the value of j start adding from the smallest value of j 3 Finally we compute the total number of operations this algorithm performs In the ith iteration of the outer loop The outer loop runs a total of times To get the total number of operations we need to add up the number of operations performed for each value of i That is the total number of operations performed in the algorith operations are performed This total depends on the value of i