Given two integers a
and b
, return the sum of the two integers without using the operators +
and -
.
For example:
Input: a = 1, b = 2 Output: 3
Input: a = 2, b = 3 Output: 5
Can you implement a function to achieve this, considering potential edge cases and providing an explanation of the time and space complexity of your solution?
When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:
The brute force approach to finding the sum of two integers involves trying out different combinations. Think of it like manually testing every possible pair of numbers until you find the right one. We check each pair to see if it matches the desired total.
Here's how the algorithm would work step-by-step:
def two_sum_brute_force(numbers, target):
for first_number_index in range(len(numbers)):
# Consider each number as the first addend in the potential sum
for second_number_index in range(first_number_index + 1, len(numbers)):
# Consider the next number as the second addend
if numbers[first_number_index] + numbers[second_number_index] == target:
# Check to see if the sum of these two is our target
return [first_number_index, second_number_index]
#If no such pair exists, return an empty list.
return []
We'll use bitwise operations to mimic how addition works at the binary level. We will simulate the carry and sum operations separately, repeating until there's no carry left.
Here's how the algorithm would work step-by-step:
def get_sum(first_number, second_number):
mask = 0xFFFFFFFF
while (second_number & mask) > 0:
# Calculate sum without carry
sum_without_carry = (first_number ^ second_number) & mask
# Calculate carry
carry = ((first_number & second_number) << 1) & mask
first_number = sum_without_carry
second_number = carry
# Handle overflow
max_int = 0x7FFFFFFF
return first_number if first_number <= max_int else ~(first_number ^ mask)
Case | How to Handle |
---|---|
Both a and b are zero | The bitwise operations will correctly return 0. |
One of a or b is zero | Bitwise operations handle 0 correctly, simply returning the other number. |
Both a and b are positive | The bitwise operations accurately simulate addition in this common case. |
Both a and b are negative | The bitwise operations handle negative numbers represented in two's complement. |
a is positive and b is negative (a > abs(b)) | Bitwise operations correctly handle positive and negative interaction and return the correct sum. |
a is positive and b is negative (a < abs(b)) | The algorithm should compute the negative sum correctly using two's complement. |
Integer overflow (sum exceeds MAX_INT or falls below MIN_INT) | In languages like Java or Python, integer overflow wraps around, but in C/C++ it's undefined behavior; we should note this potential pitfall. |
MAX_INT and 1 or MIN_INT and -1 | Check for overflow on these edge cases after bitwise operations return the intermediate result to avoid incorrect sums. |