Given an array of integers, every element appears thrice except for one, which occurs once. Find that element that does not appear thrice. NOTE: Your algorithm should have a linear runtime complexity. Can you implement it without using extra memory?Problem Constraints2 <= A <= 5*1060 <= A <= INTMAXInput FormatFirst and only argument of input contains an integer array A.Output FormatReturn a single integer.Example InputInput 1: A = [1, 2, 4, 3, 3, 2, 2, 3, 1, 1]Input 2: A = [0, 0, 0, 1]Example OutputOutput 1: 4Output 2: 1Example ExplanationExplanation 1: 4 occurs exactly once in Input 1. 1 occurs exactly once in Input 2.
Question
Given an array of integers, every element appears thrice except for one, which occurs once. Find that element that does not appear thrice. NOTE: Your algorithm should have a linear runtime complexity. Can you implement it without using extra memory?Problem Constraints2 <= A <= 5*1060 <= A <= INTMAXInput FormatFirst and only argument of input contains an integer array A.Output FormatReturn a single integer.Example InputInput 1: A = [1, 2, 4, 3, 3, 2, 2, 3, 1, 1]Input 2: A = [0, 0, 0, 1]Example OutputOutput 1: 4Output 2: 1Example ExplanationExplanation 1: 4 occurs exactly once in Input 1. 1 occurs exactly once in Input 2.
Solution
This problem can be solved using bitwise operations. Here is a Python solution:
def singleNumber(A):
result = 0
for i in range(0, 32):
sum = 0
x = (1 << i)
for j in range(0, len(A)):
if (A[j] & x):
sum += 1
if (sum % 3):
result |= x
return result
This function works by iterating over each bit position in a 32-bit integer. For each bit position, it counts how many numbers in the array have that bit set. If the count is not a multiple of 3, then the single number must have that bit set, so it sets that bit in the result.
For example, consider the array [1, 2, 4, 3, 3, 2, 2, 3, 1, 1]. The binary representations of these numbers are:
1: 0001 2: 0010 4: 0100 3: 0011
The count of set bits at each position is:
0th bit: 6 (not a multiple of 3, so the single number has this bit set) 1st bit: 6 (not a multiple of 3, so the single number has this bit set) 2nd bit: 3 (a multiple of 3, so the single number does not have this bit set) 3rd bit: 0 (a multiple of 3, so the single number does not have this bit set)
So the single number is 0011 in binary, or 3 in decimal.
This solution has a linear runtime complexity because it iterates over the array once for each bit position, and it does not use extra memory because it only uses a fixed number of variables.
Similar Questions
Given an array of integers A, every element appears twice except for one. Find that single one.NOTE: Your algorithm should have a linear runtime complexity. Could you implement it without using extra memory?Problem Constraints1 <= |A| <= 20000000 <= A[i] <= INTMAXInput FormatFirst and only argument of input contains an integer array A.Output FormatReturn a single integer denoting the single element.Example InputInput 1: A = [1, 2, 2, 3, 1]Input 2: A = [1, 2, 2]Example OutputOutput 1: 3Output 2: 1Example ExplanationExplanation 1:3 occurs once.Explanation 2:1 occurs once.
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