Question

For each of the below code snippets, identify the bounding function (the big O) of the number of times the indicated line is run (justify your answer briefly): int i = 1: while (i < n) { printf ("Insert difficult work here!") i = i + i: } for(i = 0: i < n: i++) { for (j = 0: j < n: j++) { for (k = 0: k < n: k++) { if(i==j && j==k) arr[i] [j] [k] = 1: } } }

Answer 1

int i = 1;
while (i < n) {

    printf("Insert difficult work here!"); (This Line)
    i = i +1;
}

The complexity is of O(n). The loop is running for n times as i starting with 1 and going up to n.

for(i=0; i<n; i++) {
   for(j=0; j<n; i++) {
       for(k=0; k<n; i++) {
           if (i==j && j==k)
                arr[i][j][k] = 1; (This Line)
          
       }
   }
}

This is again O(n) . For i = 1 the statement will be executed only once (i.e j = 1 && k = 1). So it means that for each value of i, the statement will be executed once and i is going from 1 to n so it is of order(n)