Q:

# Sort an array of zeros, ones and twos in linear time complexity

Sort an array of zeros, ones and twos in linear time complexity

Given an array consisting only 0's, 1's and 2's. Give an algorithm for sorting the array in O(n) time complexity ( in the sorted array, 0's will be at starting ,then the 1's & then the 2's).

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Algorithm

1. Set three variables low=0,mid=0, high=n-1 where n=length of input array
2. While (mid<=high), consider three cases on basis of the value of array [mid].
3. If array[mid] is 0
Swap (array [low], array [mid]) since 0's should be at starting
Increment low
Increment mid
Break statement
4. If array[mid] is 1
Keep as it is since 1's should be at middle after being sorted
Increment mid
Break statement
5. If array[mid] is 2
Swap (array [mid], array [high])
Decrement high
Break statement
6. Resulting array is sorted.

### C++ program to sort an array of 0's, 1's and 2's in linear time complexity

``````#include<stdio.h>
#include<stdlib.h>

//function to swap by reference
void swap(int*a,int*b){
int temp;
temp=*b;
*b=*a;
*a=temp;
return;
}
int* asort(int *a,int n){
int low=0,mid=0,high=n-1;   //variables are set

while(mid<=high){
switch(a[mid]){
case 0:     //if a[mid]==0
//swap a[low] & a[mid], swapping by reference
swap(&a[low],&a[mid]);
low++;      //increment low
mid++;      //increment mid
break;
case 1:     //if a[mid]==1
mid++;      //increment mid
break;
case 2:     //if a[mid]==2
//swap a[mid] & a[high], swapping by reference
swap(&a[mid],&a[high]);
high--;     //decrement high
break;
}
}
//returning adress of array(sorted)
return a;
}

int main() {
int n;

printf("enter no of array elements\n");
//input array length
scanf("%d",&n);

int* a=(int*)malloc(sizeof(int)*n);

printf("enter array elements\n");
//input array elements
for(int j=0;j<n;j++)
scanf("%d",&a[j]);
//array is modified
a=asort(a,n);
printf("after being sorted..............\n");
//printing the sorted array
for(int j=0;j<n-1;j++)
printf("%d ",a[j]);

printf("%d\n",a[n-1]);

return 0;
}
``````

Output

```First run:
enter no of array elements
10
enter array elements
0
2
2
1
1
1
2
1
2
1
after being sorted..............
0 1 1 1 1 1 2 2 2 2

Second run:
enter no of array elements
10
enter array elements
2
2
2
2
0
0
0
0
1
1
after being sorted..............
0 0 0 0 1 1 2 2 2 2```

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