Which of the following approaches guarantees a correct and efficient solution for all integer inputs, including negatives?
easy🔍 Pattern Recognition Q11 of Q15
Bit Manipulation - Sum of Two Integers Without + Operator
You need to compute the sum of two integers without using any arithmetic operators like + or -. Which of the following approaches guarantees a correct and efficient solution for all integer inputs, including negatives?
AUse bitwise XOR to add bits without carry and bitwise AND shifted left to compute carry, repeating until carry is zero.
BUse dynamic programming to store partial sums and build up the final sum iteratively.
CUse a greedy approach that adds bits from least significant to most significant, carrying over when needed.
DUse brute force by incrementing one number by 1 repeatedly until the other number is added.
Step-by-Step Solution
Solution:
Step 1: Understand bitwise sum without +
Bitwise XOR adds bits without carry, while bitwise AND identifies carry bits.
Step 2: Repeat until no carry remains
Carry bits are shifted left and added recursively or iteratively until carry is zero, ensuring all bits are summed correctly.
Final Answer:
Option A -> Option A
Quick Check:
Bitwise XOR and AND with carry loop is the classic sum without + [OK]
Quick Trick:Sum without + uses XOR for sum and AND for carry [OK]
Common Mistakes:
MISTAKES
Thinking greedy bit-by-bit addition works without carry handling
Using DP unnecessarily
Brute force increment is inefficient
Trap Explanation:
PITFALL
Greedy bit addition seems intuitive but fails to handle carry properly, making it incorrect for some inputs.
Interviewer Note:
CONTEXT
Tests if candidate recognizes bitwise sum pattern beyond naive addition.
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