Asked Dec 2, 2019

What is the Big-Oh Runtime (in terms of n) for the following segment of code?


int i;

int used[n];

for (i = 0; i < n; i++) {

    used[i] = 0;


for (i = 0; i < n; i++) {

    if (used[i] == 0) {

        used[i] = 1;

        i = -1;






Expert Answer

Step 1

Generally, we define the complexity of any code by using Big O- Notation. The complexity depends upon the kind of statements used in the code.

1)Sequence of statements-

statement 1;

statement 2;


statement k;

The total time is determined by adding the times for all statements:

total time = time(statement 1) + time(statement 2) + ... + time(statement k)

If each statement  involves basic operations, then the time for each statement is constant and the total time is also constant: O(1).

2) if-then-else statements

if (condition) {

    sequence of statements 1


else {

    sequence of statements 2


In this case, either sequence 1 will execute, or sequence 2 will execute. Therefore, the worst-case time is the slowest of the two possibilities: max(time(sequence 1), time(sequence 2)). For example, if sequence 1 is O(N) and sequence 2 is O(1) the worst-case time for the whole if-then-else statement would be O(N).

3) for loops

for (i = 0; i < N; i++) {


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