Bit Manipulation
Leverage binary operations for elegant O(1) space solutions and XOR tricks
0/40 solved
XOR Tricks
Use XOR properties to find missing/duplicate numbers without extra space
Approach
XOR all elements together. Since duplicates cancel out (a^a=0), the result is the unique element. For two unique numbers, first XOR all to get xor_result, find any set bit to split into two groups, XOR each group separately.
How to Recognize
Find the single number in an array where all others appear twice
Find missing or duplicate number using O(1) space
XOR of a number with itself is 0; XOR with 0 gives the number
Phrases like 'appears exactly once', 'single number'
Pro Tips
a ^ a = 0, a ^ 0 = a — these two properties solve most XOR problems
To find two unique numbers: XOR all, use a set bit to divide into two groups
XOR is commutative and associative — order doesn't matter
8
Total
4
Easy
4
Medium
0
Hard
Time
O(n)
Space
O(1)