Python Program to Find the Number Occurring Odd Number of Times
Write a Python program for a given array of positive integers. All numbers occur an even number of times except one number which occurs an odd number of times. Find the number in O(n) time & constant space.
Examples :
Input: arr = {1, 2, 3, 2, 3, 1, 3}
Output : 3
Input: arr = {5, 7, 2, 7, 5, 2, 5}
Output: 5
Python Program to Find the Number Occurring Odd Number of Times using Nested Loop:
A Simple Solution is to run two nested loops. The outer loop picks all elements one by one and the inner loop counts the number of occurrences of the element picked by the outer loop.
Below is the implementation of the brute force approach :
Python3
def getOddOccurrence(arr, arr_size):
for i in range ( 0 ,arr_size):
count = 0
for j in range ( 0 , arr_size):
if arr[i] = = arr[j]:
count + = 1
if (count % 2 ! = 0 ):
return arr[i]
return - 1
arr = [ 2 , 3 , 5 , 4 , 5 , 2 , 4 , 3 , 5 , 2 , 4 , 4 , 2 ]
n = len (arr)
print (getOddOccurrence(arr, n))
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Time Complexity: O(n^2)
Auxiliary Space: O(1)
Python Program to Find the Number Occurring Odd Number of Times using Hashing:
A Better Solution is to use Hashing. Use array elements as a key and their counts as values. Create an empty hash table. One by one traverse the given array elements and store counts.
Below is the implementation of the above approach:
Python3
def getOddOccurrence(arr,size):
Hash = dict ()
for i in range (size):
Hash [arr[i]] = Hash .get(arr[i], 0 ) + 1 ;
for i in Hash :
if ( Hash [i] % 2 ! = 0 ):
return i
return - 1
arr = [ 2 , 3 , 5 , 4 , 5 , 2 , 4 , 3 , 5 , 2 , 4 , 4 , 2 ]
n = len (arr)
print (getOddOccurrence(arr, n))
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Time Complexity: O(n)
Auxiliary Space: O(n)
Python Program to Find the Number Occurring Odd Number of Times using Bit Manipulation:
The Best Solution is to do bitwise XOR of all the elements. XOR of all elements gives us odd occurring elements.
Here ^ is the XOR operators;
Note :
x^0 = x
x^y=y^x (Commutative property holds)
(x^y)^z = x^(y^z) (Distributive property holds)
x^x=0
Below is the implementation of the above approach.
Python3
def getOddOccurrence(arr):
res = 0
for element in arr:
res = res ^ element
return res
arr = [ 2 , 3 , 5 , 4 , 5 , 2 , 4 , 3 , 5 , 2 , 4 , 4 , 2 ]
print ( "%d" % getOddOccurrence(arr))
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Time Complexity: O(n)
Auxiliary Space: O(1)
Please refer complete article on Find the Number Occurring Odd Number of Times for more details!
Last Updated :
24 Oct, 2023
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