/*  Dutch Flag Algo: To separate three different entities
    e.g :- Sort 0s,1s and 2s in an array without using sorting algo
    Complexity : O(n)  
*/

#include <iostream>
using namespace std;

/*  0 0 0 1 1 1 ? ? ? ? 2 2 2
          |     |     |
          v     v     v  
         Low   Mid   High
   
   > In this algo, we tend to shrink this '?' region 
   whose ends are pointed by Mid and High indexes.

   > Low points to the region where the 1s start

*/

void dutch_flag(int arr[],int size){
    //mid to high is the region we are about to shrink
    int low = 0, mid = 0, high = size-1;
    while(mid <= high){
        if(arr[mid] == 0){
            swap(arr[low],arr[mid]);
            low++; mid++;
        }
        else if(arr[mid] == 1){
            mid++;
        }
        else if(arr[mid] == 2){
            swap(arr[high],arr[mid]);
            high--;
        }
    }
}

//Utility function to print the array
void printArray(int arr[], int arr_size) 
{  
    for (int i = 0; i < arr_size; i++) 
        cout << arr[i] << " "; 
} 


int main(){
    int a[] = {0, 1, 1, 0, 1, 2, 1, 2, 0, 0, 0, 1};
    int n = sizeof(a)/sizeof(a[0]);
    dutch_flag(a,n);
    printArray(a,n);
    return 0;
}