Question

Run the time complexity.cpp, which you can find at directory Code/Chapter 1. For different input n, i.e., n = 1, n = 10, n = 20, write down the final value of counter for function1, function2, and function3. Explain the counter result through math calculation.

#include <iostream>  

using namespace std;

void function1(int n){
    int count = 0;
    for(int x = 0; x < 12; x++){
        cout<<"counter:"<< count++<<endl;
    }
}

void function2(int n){
    int count = 0;
    for(int x = 0; x < n; x++){
        cout<<"--- x="<<x<<"------"<<endl;
        for(int i =0; i < n; i++){
            cout<<"counter:"<< count++<<endl;
        }
    }
}

void function3(int n){
    int count = 0;
    for(int x = 0; x < n; x++){
        cout<<"--- x ="<<x<<"------"<<endl;
        for(int i = 0; i < x; i++){
            cout<<"counter:"<< count++<<endl;
        }
    }
}


int main()
{   
    int input = 10;
    cout<<"********function 1*********"<<endl;
    function1(input);
    cout<<"********function 2*********"<<endl;
    function2(input);
    cout<<"********function 3*********"<<endl;
    function3(input);

    return 0;
}

Answer 1

OUTPUT:

********function 1*********
counter:0
counter:1
counter:2
counter:3
counter:4
counter:5
counter:6
counter:7
counter:8
counter:9
counter:10
counter:11

Explanation:

count value assigned to 0. In for loop, the condition is x<12 and is initialized to 0 .so the counter is printed 12 times. count++ is a post increment operator it will count after the current count value printed
********function 2*********
--- x=0------
counter:0
counter:1
counter:2
counter:3
counter:4
counter:5
counter:6
counter:7
counter:8
counter:9

Explanation:

The first for loop variable x initialized to 0 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<n the loops prints count value upto n.

--- x=1------
counter:10
counter:11
counter:12
counter:13
counter:14
counter:15
counter:16
counter:17
counter:18
counter:19

Explanation:

The first for loop variable x initialized to 1 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<n. the loops prints count value upto n.

--- x=2------
counter:20
counter:21
counter:22
counter:23
counter:24
counter:25
counter:26
counter:27
counter:28
counter:29

Explanation:

The first for loop variable x initialized to 2 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<n. the loops prints count value upto n.

--- x=3------
counter:30
counter:31
counter:32
counter:33
counter:34
counter:35
counter:36
counter:37
counter:38
counter:39

Explanation:

The first for loop variable x initialized to 3 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<n. the loops prints count value upto n.

--- x=4------
counter:40
counter:41
counter:42
counter:43
counter:44
counter:45
counter:46
counter:47
counter:48
counter:49

Explanation:

The first for loop variable x initialized to 4 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<n. the loops prints count value upto n.

--- x=5------
counter:50
counter:51
counter:52
counter:53
counter:54
counter:55
counter:56
counter:57
counter:58
counter:59

Explanation:

The first for loop variable x initialized to 5  and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<n. the loops prints count value upto n.

--- x=6------
counter:60
counter:61
counter:62
counter:63
counter:64
counter:65
counter:66
counter:67
counter:68
counter:69

Explanation:

The first for loop variable x initialized to 6 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<n. the loops prints count value upto n.

--- x=7------
counter:70
counter:71
counter:72
counter:73
counter:74
counter:75
counter:76
counter:77
counter:78
counter:79

Explanation:

The first for loop variable x initialized to 7 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<n. the loops prints count value upto n.

--- x=8------
counter:80
counter:81
counter:82
counter:83
counter:84
counter:85
counter:86
counter:87
counter:88
counter:89

Explanation:

The first for loop variable x initialized to 8 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<n. the loops prints count value upto n.

--- x=9------
counter:90
counter:91
counter:92
counter:93
counter:94
counter:95
counter:96
counter:97
counter:98
counter:99

Explanation:

The first for loop variable x initialized to 9 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<n. the loops prints count value upto n.

********function 3*********
--- x =0------

Explanation:

The first for loop variable x initialized to 0 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<x(0<0)  the condition FALSE and the inside loop will never executed.

--- x =1------
counter:0

Explanation:

The first for loop variable x initialized to 1 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<x(0<1) the condition TRUE and the inside loop will executes upto x.
--- x =2------
counter:1
counter:2

Explanation:

The first for loop variable x initialized to 2 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<x(0<2) the condition TRUE and the inside loop will executes upto x.

--- x =3------
counter:3
counter:4
counter:5

Explanation:

The first for loop variable x initialized to 3 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<x(0<3) the condition TRUE and the inside loop will executes upto x.

--- x =4------
counter:6
counter:7
counter:8
counter:9

Explanation:

The first for loop variable x initialized to 4 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<x(0<4) the condition TRUE and the inside loop will executes upto x.

--- x =5------
counter:10
counter:11
counter:12
counter:13
counter:14

Explanation:

The first for loop variable x initialized to 5 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<x(0<5) the condition TRUE and the inside loop will executes upto x.

--- x =6------
counter:15
counter:16
counter:17
counter:18
counter:19
counter:20

Explanation:

The first for loop variable x initialized to 6 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<x(0<6) the condition TRUE and the inside loop will executes upto x.

--- x =7------
counter:21
counter:22
counter:23
counter:24
counter:25
counter:26
counter:27

Explanation:

The first for loop variable x initialized to 7 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<x(0<7) the condition TRUE and the inside loop will executes upto x.

--- x =8------
counter:28
counter:29
counter:30
counter:31
counter:32
counter:33
counter:34
counter:35

Explanation:

The first for loop variable x initialized to 8 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<x(0<8) the condition TRUE and the inside loop will executes upto x.

--- x =9------
counter:36
counter:37
counter:38
counter:39
counter:40
counter:41
counter:42
counter:43
counter:44

Explanation:

The first for loop variable x initialized to 9 and the condition x<n .inside the loop there is another  loop  has variable i initialized to 0  and the condition i<x(0<9) the condition TRUE and the inside loop will executes upto x and finally the loop terminates.