29. Divide Two Integers
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Given two integers dividend and divisor, divide two integers without using multiplication, division, and mod operator.
The integer division should truncate toward zero, which means losing its fractional part. For example, 8.345 would be truncated to 8, and -2.7335 would be truncated to -2.
Return the quotient after dividing dividend by divisor.
Note: Assume we are dealing with an environment that could only store integers within the 32-bit signed integer range: [−231, 231 − 1]. For this problem, if the quotient is strictly greater than 231 - 1, then return 231 - 1, and if the quotient is strictly less than -231, then return -231.
Example 1:
Input: dividend = 10, divisor = 3 Output: 3 Explanation: 10/3 = 3.33333.. which is truncated to 3.
Example 2:
Input: dividend = 7, divisor = -3 Output: -2 Explanation: 7/-3 = -2.33333.. which is truncated to -2.
Code
Idea:
- Remove decimals from both
divisoranddivident - Remember the result sign (
positiveor< 0) - Subtract
divisorfromdividentuntil result is less or equal to zero.
Works but is too slow in case small number divisor (1) and greater number dividend (-2147483648):
class Solution:
def divide(self, dividend: int, divisor: int) -> int:
res = 0
dd = abs(dividend)
ds = abs(divisor)
sign = -1 if (dividend > 0 and divisor < 0) or (dividend < 0 and divisor > 0) else 1
while dd >= ds:
dd -= ds
res += 1
return sign * res
Improve idea:
- Sum
divisorafter “success” subtract until result of subtract is> 0 - Subtract
divisorback until we can subtract it fromdividend
class Solution:
def divide(self, dividend: int, divisor: int) -> int:
res = 0
dd = abs(dividend)
ds = abs(divisor)
sign = -1 if (dividend > 0 and divisor <
0) or (dividend < 0 and divisor > 0) else 1
if divisor == -1 and dividend == -2147483648:
return 2147483647
elif divisor == 1:
return sign * dd
while dd >= ds:
tmp = ds
multiples = 1 # count of subtracts
while dd >= tmp: ## sum divisor
dd -= tmp
res += multiples # hense sum count of subtracts
tmp += tmp
multiples += multiples
else:
if dd >= ds:
dd -= ds
res += 1
return sign * res
Better idea
Idea: Bit manipulation
class Solution:
def divide(self, dividend, divisor):
positive = (dividend < 0) is (divisor < 0)
dividend, divisor = abs(dividend), abs(divisor)
res = 0
while dividend >= divisor:
curr_divisor, num_divisors = divisor, 1
while dividend >= curr_divisor:
dividend -= curr_divisor
res += num_divisors
curr_divisor = curr_divisor << 1
num_divisors = num_divisors << 1
if not positive:
res = -res
return min(max(-2147483648, res), 2147483647)
Explanation:
Another:
Time: $O(\log^2 n)$ Space: $O(1)$
class Solution:
def divide(self, dividend: int, divisor: int) -> int:
if dividend == -2**31 and divisor == -1:
return 2**31 - 1
sign = -1 if (dividend > 0) ^ (divisor > 0) else 1
res = 0
dvd = abs(dividend)
dvs = abs(divisor)
while dvd >= dvs:
k = 1
while k * 2 * dvs <= dvd:
k <<= 1
dvd -= k * dvs
res += k
return sign * res
