CODEWITHSUNDEEP
pythondecimal
Anshul
Anshul

Reputation: 23

Run time error when Decimal() is not used

I am trying to solve this question. My solution (as written) gives Runtime error

    import math
    from decimal import Decimal

    for i in range(int(input())):
        v,r=map(int,input().split())
        x=9.8

        ans=math.degrees(math.asin(r*x/(v*v))/2)
        format_float = "{:.7f}".format(ans)
        print("Case #"+str(i+1)+":",format_float)

but when I use x = Decimal(9.8) instead - it is accepted.

What is happening here? Also when or when not to use Decimal.

Time limit: 60 seconds. Memory limit: 1 GB. 1 ≤ T ≤ 4500 , 1 ≤ V ≤ 300 , 1 ≤ D ≤ 10000 , It is guaranteed that each test case will be solvable.

Upvotes: 0

Views: 115

Answers (1)

Kelly Bundy
Kelly Bundy

Reputation: 27588

You can just solve all three million allowed cases with both Decimal and float and show where and how they differ:

import math
from decimal import Decimal

def f(v, r):
    try:
        x=9.8
        ans=math.degrees(math.asin(r*x/(v*v))/2)
        format_float = "{:.7f}".format(ans)
        return format_float
    except:
        return 'error'
        
def d(v, r):
    try:
        x=Decimal(9.8)
        ans=math.degrees(math.asin(r*x/(v*v))/2)
        format_float = "{:.7f}".format(ans)
        return format_float
    except:
        return 'error'
        
for v in range(1, 301):
    for r in range(1, 10001):
        expect = d(v, r)
        result = f(v, r)
        if result != expect:
            print(f'{v=}  {r=}  Decimal:{expect}  float:{result}')

Output:

v=21  r=45  Decimal:45.0000000  float:error
v=42  r=180  Decimal:45.0000000  float:error
v=63  r=405  Decimal:45.0000000  float:error
v=84  r=720  Decimal:45.0000000  float:error
v=119  r=1445  Decimal:45.0000000  float:error
v=126  r=1620  Decimal:45.0000000  float:error
v=161  r=2645  Decimal:45.0000000  float:error
v=168  r=2880  Decimal:45.0000000  float:error
v=175  r=3125  Decimal:45.0000000  float:error
v=231  r=5445  Decimal:45.0000000  float:error
v=238  r=5780  Decimal:45.0000000  float:error
v=245  r=6125  Decimal:45.0000000  float:error
v=252  r=6480  Decimal:45.0000000  float:error

Let's look at the smallest one v=21 r=45 more closely:

x = 9.8
v = 21
r = 45
print(r*x/(v*v))

Output:

1.0000000000000002

So, due to float imprecision, you happen to produce a number larger than 1, which asin then crashes on.

One way to avoid that in this case is to stay in integerland until the final division:

r*98/(10*v*v)

Using this, you get the same results as with Decimal in all allowed cases.

Upvotes: 1

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