# Integer to Roman

MathString

## # Solution

All following three solutions take linear time.

### # Many if/else Statements

A verbose but straightforward solution is done with `while` and `if/else` statements.

``````def intToRoman(self, num: int) -> str:
res = ""
while num>0:
if num>=1000:
num -= 1000
res += "M"
elif num>=900:
num -= 900
res += "CM"
elif num>=500:
num -= 500
res += "D"
elif num>=400:
num -= 400
res += "CD"
elif num>=100:
num -= 100
res += "C"
elif num>=90:
num -= 90
res += "XC"
elif num>=50:
num -= 50
res += "L"
elif num>=40:
num -= 40
res += "XL"
elif num>=10:
num -= 10
res += "X"
elif num>=9:
num -= 9
res += "IX"
elif num>=5:
num -= 5
res += "V"
elif num>=4:
num -= 4
res += "IV"
else:
num -= 1
res += "I"
return res
``````
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### # Cache into Arrays

There are 2 ways to store the mappings from number to symbol.

#### # Cache Corresponding `nums` and `symbols`

``````def intToRoman(self, num: int) -> str:
nums = [1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1]
symbols = ["M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"]
digit = 0
res = ''
while num>0:
times, num = divmod(num, nums[digit])
for _ in range(times):
res += symbols[digit]
digit += 1
return res
``````
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#### # Cache Remainders of Divisions

``````def intToRoman(self, num: int) -> str:
M = ["", "M", "MM", "MMM"]
C = ["", "C", "CC", "CCC", "CD", "D", "DC", "DCC", "DCCC", "CM"]
X = ["", "X", "XX", "XXX", "XL", "L", "LX", "LXX", "LXXX", "XC"]
I = ["", "I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX"]
return M[num//1000] + C[(num%1000)//100] + X[(num%100)//10] + I[num%10]
``````
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