Answered Essay: void func3 (float] data) int m = data.length; int t = m; while (t>1) t=t/2; for (int j=0; j

Determine the worst-case running time of the following functions, using big-O notation.

Notes:

Make your bound as tight as possible and Define any variables you use in your expression

Need some thought and process on this two functions

void func3 (float] data) int m = data.length; int t = m; while (t>1) t=t/2; for (int j=0; j < m; j += t) { data[j]++ int func4(int[] A, int target) int bound = 1000, n A. length; if (n < bound) bound n; for (int i-0; i < bound; i++) f if (A[i] target) return i; return -1;

void func3 (float] data) int m = data.length; int t = m; while (t>1) t=t/2; for (int j=0; j

Expert Answer

 

Solution:

func3 time complexity is explained below line by line.

int m= data.length; here the length of the array is fetched from data and it is assigned to m; which will take constant time which is O(1)

int t=m; O(1)

Now comes the loop which will decide what the time complexity of this function is going to be

So the loop is running until t becomes 1

let’s see how the t is decremented (what is the logic which is changing it), and based on that time complexity will be decided.

t= t/2; is the statement

suppose the value of t was 1024

so the value of t will change as

1024

512

256

128

64

32

16

8

4

2

If we observe the pattern here then we can say it is operating log t times.

there is an inner loop as well so whatever time the inner loop consume will be multiplied by log t, since the inner loop will be executed log t times

since the loop is controlled by the value of t, this loop will also run log t times.

So, over all time complexity for func3 is O(log^2 t) or we can say O(log^2 length), where length is the number of elements present in array data. Because t is assigned by m which is assigned by the value of the length of array data.

func4()

Since I have explained above how the time complexity will be calculated, here I will go through only the effective statements which drive the time complexity

so, here is only one loop and it is controlled by the value of variable bound which is assigned to the length of the array named data.

so the time complexity of func4 will be O(length), where length is the number of elements present in array data.

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