Academic Year 2023

Python entry test – session 3

General note: The following code is executed as the first cell of the notebook in which all other problems’ codes are run.

import numpy as np
from scipy.integrate import solve ivp 
import scipy.stats as st
import matplotlib.pyplot as plt

1. What is the output of this code

a = np.ones((1, 3))
b = np.ones((3, 1))
c = a @ b
print(int(c))

| A  | B  | C  | D | E | F | G | H     |
|----|----|----|---|---|---|---|-------|
| -9 | -3 | -1 | 0 | 1 | 0 | 9 | Error |

2. What is the output of this code?

a = np.array(range(100)).reshape((10, -1)) 
b = np.array(range(100)).reshape((10, -1))
c = a @ b
print(c[0, 0])

| A | B  | C   | D   | E   | F    | G    | H    | K     | L     |
|---|----|-----|-----|-----|------|------|------|-------|-------|
| 1 | 10 | 100 | 285 | 385 | 2850 | 3355 | 7495 | 28500 | 29410 |

3. What is the output of this code?

import math
from sympy import *

x = Symbol('x')
y = Symbol('y')

r = diff(log(x**y), x)
r. evalf(subs={
    x: math.pi,
    y: math.pi**3
})

| A  | B  | C | D    | E    | F    | G    | H    | K    | L     |
|----|----|---|------|------|------|------|------|------|-------|
| -1 | -0 | 1 | 0.32 | 1.14 | 2.29 | 3.14 | 9.87 | 11.3 | Error |

4. What is the output of this code?

import random

a = np.array([random.gauss(mu=3., sigma=2.) 
for i in range(int(1e5))]).mean() 

b = np.array([random.random() 
for i in range(int(1e5))]).mean()

print(round(a+b, 1))

| A | B   | C | D   | E | F   | G | H   | K | L   |
|---|-----|---|-----|---|-----|---|-----|---|-----|
| 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 | 4.5 | 5 | 5.5 |

5. What is the output of this code?

s = [-1, 2]
a = np.arange(1, 5).reshape(s)
b = np.arange(6).reshape(s[::-1]) 
c = np.where(a == b[:2, :2], a, 0) 
print(sum(c[:, 0] - c[:, 1]))

| A  | B  | C  | D  | E | F | G | H | K | L     |
|----|----|----|----|---|---|---|---|---|-------|
| -6 | -5 | -2 | -1 | 0 | 1 | 2 | 5 | 6 | Error |

6. What is the output of this code?

def mystery_function(n):
    if n <= 1:
        return 1
    else:
        return n * (mystery_function(n - 1))

print(mystery_function(5))

| A    | B    | C   | D   | E   | F   | G  | H | K | L  | M  | N  | P  | U   | R   | S     |
|------|------|-----|-----|-----|-----|----|---|---|----|----|----|----|-----|-----|-------|
| -720 | -120 | -24 | -18 | -15 | -11 | -1 | 0 | 1 | 11 | 15 | 18 | 24 | 120 | 720 | Error |

7. Which of the following variables are True?

import time 
from numba import jit

def loop_mean(n): 
    lst = list()
    for i in range(n): 
        lst.append(i)
        
return sum(lst) / len(lst)

def compr_mean(n): 
    lst = [i for i in range(n)] 
    return sum(lst) / len(lst)
    
def np_mean(n): 
    arr = np.arange(n) 
    return arr.mean()
    
@jit(nopython=True) 
def numba_mean(n): 
    lst = list() 
    for i in range(n):
        lst.append(i)
return sum(lst) / len(lst)

def measure_time(fn, arg): 
    start = time.time()
    _ = fn(arg)
return time.time() - start

n = int(1e1)
e1_loop_time = measure_time(loop_mean, n)
e1_compr_time = measure_time(compr_mean, n)
e1_np_time = measure_time(np_mean, n)
e1_numba_time = measure_time(numba_mean, n)

n = int(1e6)
e6_loop_time = measure_time(loop_mean, n)
e6_compr_time = measure_time(compr_mean, n)
e6_numba_time = measure_time(numba_mean, n)
e6_np_time = measure_time(np_mean, n)

a = e6_loop_time > e6_compr_time > e6_numba_time > e6_np_time
b = e1_loop_time > e1_compr_time > e1_numba_time > e1_np_time

c = e6_loop_time > e6_compr_time > e6_np_time > e6_numba_time
d = e1_loop_time > e1_compr_time > e1_np_time > e1_numba_time

e = e6_compr_time > e6_loop_time > e6_numba_time > e6_np_time
f = e1_compr_time > e1_loop_time > e1_numba_time > e1_np_time

g = e6_compr_time > e6_loop_time > e6_np_time > e6_numba_time
h = e1_compr_time > e1_loop_time > e1_np_time > e1_numba_time

| A | B | C | D | E | F | G | H | K   | L   | M   | N   | P   | U   | R   | S   | T   | W  |
|---|---|---|---|---|---|---|---|-----|-----|-----|-----|-----|-----|-----|-----|-----|----|
| a | b | c | d | e | f | g | h | a,b | c,d | e,f | g,h | a,c | b,d | e,g | f,h | All | No |

8. What complexity does the Insertion Sort algorithm have in the worst case?

Answer must contain: (time complexity / space complexity).

A. $O(n) / O(1)$

B. $O(n) / O(n)$

C. $O(log(n)) / O(1)$

D. $O(log(n)) / O(n)$

E. $O(n \, log(n)) / O(1)$

F. $O(n \, log(n)) / O(n)$

G. $O(n \, log(n^2)) / O(1)$

H. $O(n \, log(n^2)) / O(n)$

K. $O(n^2) / O(1)$

L. $O(n^2) / O(n)$

9. What complexity does the insertion in doubly-linked list have in the worst case?

Answer must contain: (time complexity / space complexity).

A. $O(1) / O(1)$

B. $O(n) / O(n)$

C. $O(log(n)) / O(1)$

D. $O(1) / O(n \, log(n)))$

E. $O(n) / O(1)$

F. $O(log(n)) / O(n \, log(n)))$

G. $O(1) / O(n)$

H. $O(n) / O(n \, log(n)))$

K. $O(log(n))) / O(n)$

L. $O(n) / O(n)$

10. What is the output of this code?

from matplotlib import cm
plt.style.use('_mpl-gallery') 

сmар = cm.Oranges

l = 4
step = 0.2

X = np.arange(-l, l, step)
Y = np.arange(-l, l, step)

X, Y = np.meshgrid(X, Y)
Z = Y**2 + 10 * np.sin(X)

fig,ax = plt.subplots(
    subplot_kw={'projection': '3d'}, 
    figsize=(8, 8)) ax.plot_surface(X, Y, Z, vmin=Z.min() * 2, 
    cmap=cmap
)

ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')

plt.show()

A.

B.

C.

D.

E.

F.

G.

H.