Divide Integers Without Division | Dataford Interview Questions

Your question is Divide Integers Without Division. Start with the requirements on the right.

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Problem

The Fannie Mae Desktop Underwriter (DU) calculation layer needs integer division for bounded values, but the arithmetic primitive cannot use division, modulo, or multiplication operators. Implement a function that returns the quotient and remainder of two integers.

The quotient must truncate toward zero. The remainder must have the same sign as the dividend, satisfying dividend = divisor * quotient + remainder mathematically. You may use addition, subtraction, comparisons, bit shifts, bitwise operations, and unary negation. The divisor is guaranteed to be nonzero.

Formal Specification

Implement divide_integers(dividend, divisor).

Input: Two integers, dividend and divisor.
Output: A two-element list [quotient, remainder].
Do not use /, //, %, or multiplication in the implementation.
The result should support signed 32-bit input values and mathematical integer output.

Constraints

-2^31 <= dividend <= 2^31 - 1
-2^31 <= divisor <= 2^31 - 1
divisor != 0
Do not use /, //, %, or multiplication
Return mathematical integer results without fixed-width overflow

Function Signature

def divide_integers(dividend, divisor):