I came across a post How to find a duplicate element in an array of shuffled consecutive integers? but later realized that this fails for many input.
For ex:
a
Remember these two properties of XOR operator :
(1) If you take xor of a number with 0 ( zero ) , it would return the same number again.
Means , n ^ 0 = n
(2) If you take xor of a number with itself , it would return 0 ( zero ).
Means , n ^ n = 0
Now , Coming to the problem :
Let Input_arr = { 23 , 21 , 24 , 27 , 22 , 27 , 26 , 25 }
Output should be 27 ( because 27 is the duplicate element in the Input_arr ).
Solution :
Step 1 : Find “min” and “max” value in the given array. It will take O(n).
Step 2 : Find XOR of all integers from range “min” to “max” ( inclusive ).
Step 3 : Find XOR of all elements of the given array.
Step 4 : XOR of Step 2 and Step 3 will give the required duplicate number.
Description :
Step1 : min = 21 , max = 27
Step 2 : Step2_result = 21 ^ 22 ^ 23 ^ 24 ^ 25 ^ 26 ^ 27 = 20
Step 3 : Step3_result = 23 ^ 21 ^ 24 ^ 27 ^ 22 ^ 27 ^ 26 ^ 25 = 15
Step 4 : Final_Result = Step2_result ^ Step3_result = 20 ^ 15 = 27
But , How Final_Result calculated the duplicate number ?
Final_Result = ( 21 ^ 22 ^ 23 ^ 24 ^ 25 ^ 26 ^ 27 ) ^ ( 23 ^ 21 ^ 24 ^ 27 ^ 22 ^ 27 ^ 26 ^ 25 )
Now , Remember above two properties : n ^ n = 0 AND n ^ 0 = n
So , here ,
Final_Result = ( 21 ^ 21 ) ^ ( 22 ^ 22 ) ^ ( 23 ^ 23 ) ^ ( 24 ^ 24 ) ^ ( 25 ^ 25 ) ^ ( 26 ^ 26 ) ^ ( 27 ^ 27 ^ 27 )
= 0 ^ 0 ^ 0 ^ 0 ^ 0 ^ 0 ^ ( 27 ^ 0 ) ( property applied )
= 0 ^ 27 ( because we know 0 ^ 0 = 0 )
= 27 ( Required Result )