A Simple Interview Question
August 14, 2018
Today’s interview question comes from Apple:
Write a program to add two integers. You may not use the
+(addition) operator, but may use the++(increment by 1) or--(decrement by 1) operators. Be sure your solution works for both positive and negative inputs.
Your task is to write a program to add two integers. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.
Programming Praxis 
Here is my take with Julia (v. 1.0). Optimizing for number of iterations:
function add(x::Int64, y::Int64)
if x == 0
return y
elseif y == 0
return x
else
x_ = abs(x)
y_ = abs(y)
ind = argmin([x_, y_])
end
The expression (- x (- y)), equivalently x – -y for infix programmers, seems to meet the conditions of the problem.
Haskell.
decr :: Integral a => a -> a decr = subtract 1 incr :: Integral a => a -> a incr = (+1) add :: Integral a => a -> a -> a add x y | y < 0 = add (decr x) (incr y) | y == 0 = x | y > 0 = add (incr x) (decr y) main = do print $ add (-4) (-5) print $ add (-4) 5 print $ add 4 (-5) print $ add 4 5Here’s a solution in C.
#include <stdio.h> #include <stdlib.h> int add(int a, int b) { while (a > 0) { --a; ++b; } while (a < 0) { ++a; --b; } return b; } int main(int argc, char* argv[]) { if (argc != 3) { fprintf(stderr, "Usage: %s INT INT\n", argv[0]); return EXIT_FAILURE; } int a = atoi(argv[1]); int b = atoi(argv[2]); int result = add(a, b); printf("%d\n", result); return EXIT_SUCCESS; }Examples:
function sum(a, b) {
return a – (-b);
}
Instead of the add instruction, let’s use <<, >>, &, ==, ++, and — to implement a classical binary adder. Because Python automatically promotes ints to bignums, we special case -1 to prevent infinite regress.
def add(a, b, carry=0): if a == -1: carry -= 1 a = 0 if b == -1: carry -= 1 b = 0 if a == b == 0: return carry if a & 1: carry += 1 if b & 1: carry += 1 r = add(a >> 1, b >> 1, carry >> 1) << 1 if carry & 1: r += 1 return rAnother approach in Python.
def add(a, b): return 2*a if a == b else (a*a - b*b) // (a - b)