Question

For the following parts, try to get the best Big-O estimate that you can and briefly justify your
answers (3-4 sentences per part). You should also consider running times for all the operations
contained within the loop body (but ignore the running times for initializer, entry condition and
increment).
Part a
int i, j;
int n = 100 ;
for (i = 1 ; i <= n; i++) {
for ( j = 3 *i ; j <= n; j++) {
printf( "programming is
fun\n" ) ;
}
}

Part b
int i, j;
int n = 1000000 ;
for (i = 1 ; i <= n; i++) {
for (j = 1 ; j <= 10000 ; j++)
{
printf ( "%d %d\n" , i, j);
}
}

Part c
int i = 0 ;
int n = 10 ;
int j;
while (i < n) {
i++ ;
j = i ;
while (i < n) {
printf( "hello %d\n" ,
i) ;
i++ ;
}
i = j;
}

Part d
int i = 0 ;
int n = 10 ;
int j;
while (i < n) {
i++ ;
j = i ;
while (i < n) {
printf( "hello %d\n" ,
i) ;
i++ ;
break;
}
i = j;
}
Page

Answer 1

As the question contains more than 1 question and all the questions are independent so I would be solving only the 1st question(following the guidelines of Chegg).

a) As the loops are nested(one loop is inside the other) ,so the overall complexity involved would be the multiplication of the individual complexities of the loops.

As the outer loop runs from 1 to n with increment of 1 so,the complexity of the outer loop would be O(n).

As the inner loop runs from 1 to n with increment of 1 and just the initialization is from i*3 which doesn't make any difference when the n value would be large ,so its complexity would be O(n).

As discussed above ,the overall complexity would be the multiplication of the individual complexities,so overall complexity is O(n)*O(n) that given complexity as O(n²).