===== Cvičení 2 =====

==== 02a ====
[[ https://youtu.be/FHiWnjyLZgw | While cyklus ]]

while1.py:
<code>
print("for")
for i in range(10,40,5):
    print(i)
print("while")
i=10
while i<40:
    print(i)
    i+=5
</code>
while2.py:
<code>
print("for")
for i in range(20,-20,-5):
    print(i)
print("while")
i=20
while True:
    print(i)
    i-=5
    if i<=-20:
        break
</code>
while-continue.py
<code>
for i in range(15):
    if i%2==0:
        continue
    if i%3==0:
        continue
    print(i)

print("while")
i=0
while i<15:
    if i%2==0:
        i+=1
        continue
    if i%3==0:
        i+=1
        continue
    print(i)
    i+=1
</code>        
problem.py:
<code>
i=int(input())
while i>1:
    print(i)
    if i%2==0:
        i//=2 # i = i//2
    else:
        i=i*3+1
</code>

==== 02b ====
[[ https://youtu.be/43m8Z5g1LbM | Počítání s reálnými čísly ]]

presnost.py:
<code>
suma=0
step=0.1
for i in range(1,11):
    suma+=step
    if suma==i/10:
        print("Plati", suma, "rovno", i/10)
    else:
        print("Neplati", suma, "nerovno", i/10)
</code>
rovnost.py:
<code>
x=2.1
epsilon=1e-10
print(abs(x+0.2-2.3))
if abs(x+0.2-2.3)>epsilon:
    y=10./(x-2.1)
    print(y)
else:
    print("Nelze delit nulou")
</code>
odmocnina.py:
<code>
y=2
x=0
step=1
k=0
for i in range(100):
    limit=10
    while (x+step)**2<=y and (i==0 or limit>=0):
        x+=step
        print("Krok",k,x,x**2,y)
        k+=1
        limit-=1
    if i>0 and limit<0:
        break
    step/=10
    print(x)
print("Vysledek", x, x**2, y)
</code>

==== 02c ====
[[ https://youtu.be/M2so_7F-Et4 | Metoda půlení intervalu ]]

puleni.py:
<code>
c=float(input())
if c>=0:
    x1=0
    if c<=1:
        x2=1
    else:
        x2=c
    #zacneme pulit interval
    k=0
    while (x2-x1)>1e-10:
        x_s = (x1+x2)/2
        f_x_s = x_s**2-c
        f_x1 = x1**2-c
        if ((f_x1<0) == (f_x_s<0)):
            x1 = x_s
        else:
            x2 = x_s
        print("Krok",k,x1,x2, x_s**2, c)
        k+=1
    x_r = (x1+x2)/2
    print(x_r, x_r**2, c)
else:
    print("Odmocnina ze zaporneho cisle neni realna")
</code>

        
newton.py:
<code>
c=float(input())
if c>=0:
    x_n=1
    x_n_1 = x_n/2+c/(2*x_n)
    while abs(x_n_1-x_n)>1e-10:
        x_n = x_n_1
        x_n_1 = x_n/2+c/(2*x_n)
        print(x_n_1, x_n_1**2, c)
    print(x_n_1, x_n_1**2, c)
else:
    print("Odmocnina ze zaporneho cisle neni realna")
</code>