# -*- coding: utf-8 -*-
"""
Created on Thu Jun 11 13:09:04 2026

@author: student
"""

#%%
import math
print("pierwiastek z 5 (a) ", math.sqrt(5))

#%%
import math as m
print("pierwiastek z 5 (b) ", m.sqrt(5))


#%% 
from math import sqrt
print("pierwiastek z 5 (c) ", sqrt(5))

#%%
import math as m
import cmath as cm
print("pierwiastek z 5 (d) ", cm.sqrt(-5))

#%%
import sys

print(sys.builtin_module_names)
print(sys.version)

#%% 
def ciąg(n):
    if(n > 1):
        ciąg(n-1)
    print(n)
    
def ciąg2(n):
    print(n)
    if(n > 1):
        ciąg2(n-1)

ciąg2(5)

#%% 
def sum_a(n):
    if n <= 0:
        return 0
    return n + sum_a(n-1)

print("suma a", sum_a(5))

def sum_b(k, n):
    if n <= k:
        return k
    return n + sum_b(k, n-1)

print("suma b", sum_b(2, 5))

#od 1 do n co k
#niepoprawna
def sum_c_źle(n, k, c = 1):
    if n < k:
        return n
    return c + sum_c_źle(n - k, k, c + k)

print("suma c źle", sum_c_źle(8, 2))

#poprawna
def sum_c(n, k, c):
    if c <= 1:
        return 1 
    return sum_c(n, k, c - k) + c

print("suma c", sum_c(7, 2, 7))
print("suma c", sum_c(8, 2, 8))

#od 1 do n co k
def sum_d(n, k):
    if n <= k:
        return n
    return n + sum_d(n - k, k)

print("suma d", sum_d(7, 2))
print("suma d", sum_d(8, 2))
print("\n")
print("suma c", sum_c(8, 2, 8))
print("suma d", sum_d(8, 2))