Explain the time complexity of the following code snippet in regards of the Big-O notation:1. for (i=0; i<n; i+=4) {2. for (j=1; j<n; j*=2) {3. for (k=0; k<30; k++) {4. print(“Am I still not 30?!!”);5. }6. print(“Why, God, why? We had a Deal!”);7. for (m=n; m>0; m-=2) {8. print(“Could you BE more dramatic?”);9. }10. }11. }
Question
Explain the time complexity of the following code snippet in regards of the Big-O notation:1. for (i=0; i<n; i+=4) {2. for (j=1; j<n; j*=2) {3. for (k=0; k<30; k++) {4. print(“Am I still not 30?!!”);5. }6. print(“Why, God, why? We had a Deal!”);7. for (m=n; m>0; m-=2) {8. print(“Could you BE more dramatic?”);9. }10. }11. }
Solution
The time complexity of the given code snippet can be calculated by analyzing each loop individually.
-
The outermost loop (i=0; i<n; i+=4) runs n/4 times. So, its complexity is O(n).
-
The second loop (j=1; j<n; j*=2) is a logarithmic loop and runs log(n) times. So, its complexity is O(log(n)).
-
The third loop (k=0; k<30; k++) is a constant time loop and runs 30 times regardless of the value of n. So, its complexity is O(1).
-
The innermost loop (m=n; m>0; m-=2) runs n/2 times. So, its complexity is O(n).
Now, combining all these, the total time complexity of the code is O(n) * O(log(n)) * O(1) * O(n) = O(n^2 * log(n)).
This means that the time complexity of the code increases quadratically with the size of the input and also depends on the logarithm of the input size.
Similar Questions
What is the time complexity of the following code :int i, j, k = 0;for (i = n/2; i <= n; i++) { for (j = 2; j <= n; j = j * 2) { k = k + n/2; }}
What is the time complexity of the following code? for(int i = 0; i < n; i++) { for(int j = 0; j < i; j++) { System.out.println(i * j); } } a. O(n) b. O(2^n) c. O(n^2) d. O(n log n)
What is the running time of the following code?(i.e., O(?))Sum = 0;for (i=0; i<n; i++){for (j=0; j < i; j++)++sum;}
What does O(n) represent in Big O Notation?*0/1a. Constant time complexityb. Linear time complexityQuadratic time complexity
Using big-O notation in terms of its parameter n, what is the running time of the below method in its worst case? Give the tightest and simplest bound possible, and justify your answer.public static int mystery(int n) { int total = 0; for (int i = 1; i < n; i *= 2) { for (int j = i; j < 2 * i; j++) { total += j; } } return total;}
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.