Find the element that appears once in sorted array
PROBLEM :
Given a sorted array of integers, every element appears twice except for one. Find that single one in linear time complexity and without using extra memory.
Input:
The first line of input consists number of the test cases. The description of T test cases is as follows:
The first line of each test case contains the size of the array, and the second line has the elements of the array.
Output:
In each separate line print the number that appears only once in the array.
Constraints:
1 = T = 70
1 = N = 100
0 = A[i] = 100000
Example:
Input:
1
11
1 1 2 2 3 3 4 50 50 65 65
Output:
4
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SIMPLE c++ IMPLEMENTATION :( O(n) Solution using Bitwise)
--------------------------------------------------------------------------------
#include<iostream>
using namespace std;
int main()
{
int t ;
cin>>t ;
while(t--)
{
int no ;
cin>>no ;
int arr[no] ;
for(int i=0;i<no;i++)
cin>>arr[i] ;
int XOR=0 ;
for(int i=0;i<no;i++)
XOR=XOR^arr[i] ;
cout<<XOR<<endl ;
}
return 0;
}
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SIMPLE c++ IMPLEMENTATION :( O(Logn) Solution using Binary Search)
--------------------------------------------------------------------------------
#include<iostream>
using namespace std;
int FindElement(int [],int ,int ) ;
int main()
{
int t ;
cin>>t ;
while(t--)
{
int no ;
cin>>no ;
int arr[no] ;
for(int i=0;i<no;i++)
cin>>arr[i] ;
cout<<FindElement(arr,0,no-1)<<endl ;
}
return 0;
}
int FindElement(int arr[],int start,int end)
{
if(start>end)
return -1 ;
if(start==end)
return arr[start] ;
int mid=(start+end)/2 ;
if(mid%2==0)
{
if(arr[mid]==arr[mid+1])
return FindElement(arr,mid+2,end) ;
else
return FindElement(arr,start,mid) ;
}
else
{
if(arr[mid]==arr[mid-1])
return FindElement(arr,mid+1,end) ;
else
return FindElement(arr,start,mid-1) ;
}
}
--------------------------------------------------------------------------------
Given a sorted array of integers, every element appears twice except for one. Find that single one in linear time complexity and without using extra memory.
Input:
The first line of input consists number of the test cases. The description of T test cases is as follows:
The first line of each test case contains the size of the array, and the second line has the elements of the array.
Output:
In each separate line print the number that appears only once in the array.
Constraints:
1 = T = 70
1 = N = 100
0 = A[i] = 100000
Example:
Input:
1
11
1 1 2 2 3 3 4 50 50 65 65
Output:
4
--------------------------------------------------------------------------------
SIMPLE c++ IMPLEMENTATION :( O(n) Solution using Bitwise)
--------------------------------------------------------------------------------
#include<iostream>
using namespace std;
int main()
{
int t ;
cin>>t ;
while(t--)
{
int no ;
cin>>no ;
int arr[no] ;
for(int i=0;i<no;i++)
cin>>arr[i] ;
int XOR=0 ;
for(int i=0;i<no;i++)
XOR=XOR^arr[i] ;
cout<<XOR<<endl ;
}
return 0;
}
--------------------------------------------------------------------------------
SIMPLE c++ IMPLEMENTATION :( O(Logn) Solution using Binary Search)
--------------------------------------------------------------------------------
#include<iostream>
using namespace std;
int FindElement(int [],int ,int ) ;
int main()
{
int t ;
cin>>t ;
while(t--)
{
int no ;
cin>>no ;
int arr[no] ;
for(int i=0;i<no;i++)
cin>>arr[i] ;
cout<<FindElement(arr,0,no-1)<<endl ;
}
return 0;
}
int FindElement(int arr[],int start,int end)
{
if(start>end)
return -1 ;
if(start==end)
return arr[start] ;
int mid=(start+end)/2 ;
if(mid%2==0)
{
if(arr[mid]==arr[mid+1])
return FindElement(arr,mid+2,end) ;
else
return FindElement(arr,start,mid) ;
}
else
{
if(arr[mid]==arr[mid-1])
return FindElement(arr,mid+1,end) ;
else
return FindElement(arr,start,mid-1) ;
}
}
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