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# Time complexity Choose the correct answer and say why. a) Given the following program with n as parameter:

Time complexity

Choose the correct answer and say why.

a)     Given the following program with n as parameter:

0                                i = 0; j =0;

1                                for(int k=0; k<=n; k++)

2                                     for( int i = 0; i <= n; i++ )

3                                    {

4                                        i=i+k;

5                                               for( int k = 0; k < i; k++ )

6                                                      j++;

7                                     }

1. How many times is statement 4 executed?

a. O( N )

b. O( N2 )

c. O( N3 )

d. O( N4 )

e. none of the above

2. How many times is statement 6 executed?

a. O( N )

b. O( N2 )

c. O( N3 )

d. O( N4 )

e. none of the above

3. What is the time complexity of the above program?

a. O( N4 )

b. O( N5 )

c. O( N6 )

d. O( N7 )

e. none of the above

b) Given the following program with n as parameter:

0 i = 0; j =0;

1 while(i<1000)

2 for( int k = i; k <= n; k++ ){

3 i++;

4 j++;}

5 for( int p = 0; p < n*n; p++ )

6 for( int q = 0; q < p; q++ )

7 j--;

1. How many times is the instruction 3 executed?

a. O( N )

b. O( N2 )

c. O( N3 )

d. O( N4 )

e. none of the above

2. How many times is statement 7 executed?

a. O( N )

b. O( N2 )

c. O( N3 )

d. O( N4 )

e. none of the above

3. What is the time complexity of the above program?

a. O( N4 )

b. O( N5 )

c. O( N6 )

d. O( N7 )

e. none of the above

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