Hi fellow programmers,

We are trying to create a multiple choice quiz for space and time complexity of the programs related questions. Here are a set of 20 questions we collected. Please feel free to give your answers to these questions. Any feedback about the set of questions. Please also feel propose to any more set of MCQs that you would like to add here, there might be some interesting questions that you might have encountered during the programming and would like to add here

### Q1.

Average case time complexity of quicksort?

A. \mathcal{O}(n)

B. \mathcal{O}(n \log n)

C. \mathcal{O}(n^2)

D. \mathcal{O}(n^3)

### Q2.

Worst case time complexity of quicksort?

A. \mathcal{O}(n)

B. \mathcal{O}(n \log n)

C. \mathcal{O}(n^2)

D. \mathcal{O}(n^3)

### Q3.

Time complexity of binary search?

A. \mathcal{O}(1)

B. \mathcal{O}(\log n)

C. \mathcal{O}({(\log n)}^2)

D. \mathcal{O}(n)

### Q4.

```
def f():
ans = 0
for i = 1 to n:
for j = 1 to log(i):
ans += 1
print(ans)
```

Time Complexity of this program:

A. \mathcal{O}(n)

B. \mathcal{O}(n \log n)

C. \mathcal{O}(n^2)

D. \mathcal{O}(n^3)

### Q5.

```
def f():
a = 0
for i = 1 to n:
a += i;
b = 0
for i = 1 to m:
b += i;
```

Time Complexity of this program:

A. \mathcal{O}(n)

B. \mathcal{O}(m)

C. \mathcal{O}(n + m)

D. \mathcal{O}(n * m)

### Q6.

```
def f():
a = 0
for i = 1 to n:
a += random.randint();
b = 0
for j = 1 to m:
b += random.randint();
```

Time Complexity of this program:

A. \mathcal{O}(n)

B. \mathcal{O}(m)

C. \mathcal{O}(n + m)

D. \mathcal{O}(n * m)

### Q7.

```
def f():
int a[n][n]
// Finding sum of elements of a matrix that are above or on the diagonal.
sum = 0
for i = 1 to n:
for j = i to n:
sum += a[i][j]
print(sum)
```

Time Complexity of this program:

A. \mathcal{O}(n)

B. \mathcal{O}(n \log n)

C. \mathcal{O}(n^2)

D. \mathcal{O}(n^3)

### Q8.

```
def f():
int a[n][n]
sum = 0
// Finding sum of elements of a matrix that are strictly above the diagonal.
for i = 1 to n:
for j = i to n:
sum += a[i][j]
print(sum)
for i = 1 to n:
sum -= a[i][i]
```

Time Complexity of this program:

A. \mathcal{O}(n)

B. \mathcal{O}(n \log n)

C. \mathcal{O}(n^2)

D. \mathcal{O}(n^3)

### Q9.

```
def f():
ans = 0
for i = 1 to n:
for j = n to i:
ans += (i * j)
print(ans)
```

Time Complexity of this program:

A. \mathcal{O}(n)

B. \mathcal{O}(n \log n)

C. \mathcal{O}(n^2)

D. \mathcal{O}(n^3)

### Q10.

```
def f():
int a[N + 1][M + 1][K + 1]
sum = 0
for i = 1 to N:
for j = i to M:
for k = j to K:
sum += a[i][j]
print(sum)
```

Time Complexity of this program:

A. \mathcal{O}(N + M + K)

B. \mathcal{O}(N * M * K)

C. \mathcal{O}(N * M + K)

D. \mathcal{O}(N + M * K)

### Q11.

```
def f(n):
ans = 0
while (n > 0):
ans += n
n /= 2;
print(ans)
```

Time Complexity of this program:

A. \mathcal{O}(\log n)

B. \mathcal{O}(n)

B. \mathcal{O}(n \log n)

C. \mathcal{O}(n^2)

### Q12.

```
// Find the sum of digits of a number in its decimal representation.
def f(n):
ans = 0
while (n > 0):
ans += n % 10
n /= 10;
print(ans)
```

Time Complexity of this program:

A. \mathcal{O}(\log_2 n)

B. \mathcal{O}(\log_3 n)

C. \mathcal{O}(\log_{10} n)

D. \mathcal{O}(n)

### Q13.

```
def f():
ans = 0
for (i = n; i >= 1; i /= 2):
for j = m to i:
ans += (i * j)
print(ans)
```

Time Complexity of this program:

A. \mathcal{O}(n + m)

B. \mathcal{O}(n * m)

C. \mathcal{O}(m \log n)

D. \mathcal{O}(n \log m)

### Q14.

```
def f():
ans = 0
for (i = n; i >= 1; i /= 2):
for (j = 1; j <= m; j *= 2)
ans += (i * j)
print(ans)
```

Time Complexity of this program:

A. \mathcal{O}(n * m)

B. \mathcal{O}(\log m \log n)

C. \mathcal{O}(m \log n)

D. \mathcal{O}(n \log m)

### Q15.

```
// Finding gcd of two numbers a, b.
def gcd(a, b):
if (a < b) swap(a, b)
if (b == 0) return a;
else return gcd(b, a % b)
```

Time Complexity of this program:

Let n = \max\{a, b\}

A. \mathcal{O}(1)

B. \mathcal{O}(\log n)

C. \mathcal{O}(n)

D. \mathcal{O}(n^2

### Q16.

```
// Binary searching in sorted array for finding whether an element exists or not.
def exists(a, x):
// Check whether the number x exists in the array a.
lo = 0, hi = len(a) - 1
while (lo <= hi):
mid = (lo + hi) / 2
if (a[mid] == x): return x;
else if (a[mid] > x): hi = mid - 1;
else lo = mid + 1;
return -1; // Not found.
```

Time Complexity of this program:

Let n = len(a)

A. \mathcal{O}(1)

B. \mathcal{O}(\log n)

C. \mathcal{O}(n)

D. \mathcal{O}(n^2

### Q17.

// Given a sorted array a, find the number of occurrence of number x in the entire array.

```
def count_occurrences(a, x, lo, hi):
if lo > hi: return 0
mid = (lo + hi) / 2;
if a[mid] < x: return count_occurrences(a, x, mid + 1, hi)
if a[mid] > x: return count_occurrences(a, x, lo, mid - 1)
return 1 + count_occurrences(a, x, lo, mid - 1) + count_occurrences(a, x, mid + 1, hi)
// in the main function, we call it as
count_occurrences(a, x, 0, len(a) - 1)
```

Time Complexity of this program:

Let n = len(a)

A. \mathcal{O}(1)

B. \mathcal{O}(\log n)

C. \mathcal{O}(n)

D. \mathcal{O}(n^2

### Q18.

```
// Finding fibonacci numbers.
def f(n):
if n == 0 or n == 1: return 1
return f(n - 1) + f(n - 2)
```

Time Complexity of this program:

A. \mathcal{O}(\log n)

B. \mathcal{O}(n)

C. \mathcal{O}(n^2)

D. \mathcal{O}(2^n)

### Q19.

```
Create array memo[n + 1]
// Finding fibonacci numbers with memoization.
def f(n):
if memo[n] != -1: return memo[n]
if n == 0 or n == 1: ans = 1
else: ans = f(n - 1) + f(n - 2)
memo[n] = ans
return ans
// In the main function.
Fill the memo array with all values equal to -1.
ans = f(n)
```

Time Complexity of this program:

A. \mathcal{O}(\log n)

B. \mathcal{O}(n)

C. \mathcal{O}(n^2)

D. \mathcal{O}(2^n)

### Q20.

```
def f(a):
n = len(a)
j = 0
for i = 0 to n - 1:
while (j < n and a[i] < a[j]):
j += 1
```

Time Complexity of this program:

A. \mathcal{O}(\log n)

B. \mathcal{O}(n)

C. \mathcal{O}(n \log n)

D. \mathcal{O}(n^2)

### Q21.

```
def f():
ans = 0
for i = 1 to n:
for j = i; j <= n; j += i:
ans += 1
print(ans)
```

Time Complexity of this program:

A. \mathcal{O}(\log n)

B. \mathcal{O}(n)

C. \mathcal{O}(n \log n)

D. \mathcal{O}(n^2)