for (i=0; i<n-1; i++) { 
    for (j=0; j<n-1-i; j++) 
      if (a[j+1] < a[j]) {   
        tmp = a[j];          
        a[j] = a[j+1]; 
        a[j+1] = tmp; 
    } 
  } 
  

 
  /* Insertion sort for integers */ 
   
  void insertion( int a[], int n ) { 
  /* Pre-condition: a contains n items to be sorted */ 
      int i, j, v; 
      /* Initially, the first item is considered 'sorted' */ 
      /* i divides a into a sorted region, x<i, and an 
         unsorted one, x >= i */ 
      for(i=1;i<n;i++) { 
          /* Select the item at the beginning of the 
             as yet unsorted section */ 
          v = a[i]; 
          /* Work backwards through the array, finding where v  
             should go */ 
          j = i; 
          /* If this element is greater than v, 
                move it up one */ 
          while ( a[j-1] > v ) { 
            a[j] = a[j-1]; j = j-1; 
            if ( j <= 0 ) break; 
            } 
          /* Stopped when a[j-1] <= v, so put v at position j */ 
          a[j] = v; 
          } 
      }  
  

 
  void selectionSort(int numbers[], int array_size) 
  { 
    int i, j; 
    int min, temp; 
   
    for (i = 0; i < array_size-1; i++) 
    { 
      min = i; 
      for (j = i+1; j < array_size; j++) 
      { 
        if (numbers[j] < numbers[min]) 
          min = j; 
      } 
      temp = numbers[i]; 
      numbers[i] = numbers[min]; 
      numbers[min] = temp; 
    } 
  } 
  

 
  void quickSort(int numbers[], int array_size) 
  { 
    q_sort(numbers, 0, array_size - 1); 
  } 
   
   
  void q_sort(int numbers[], int left, int right) 
  { 
    int pivot, l_hold, r_hold; 
   
    l_hold = left; 
    r_hold = right; 
    pivot = numbers[left]; 
    while (left < right) 
    { 
      while ((numbers[right] >= pivot) && (left < right)) 
        right--; 
      if (left != right) 
      { 
        numbers[left] = numbers[right]; 
        left++; 
      } 
      while ((numbers[left] <= pivot) && (left < right)) 
        left++; 
      if (left != right) 
      { 
        numbers[right] = numbers[left]; 
        right--; 
      } 
    } 
    numbers[left] = pivot; 
    pivot = left; 
    left = l_hold; 
    right = r_hold; 
    if (left < pivot) 
      q_sort(numbers, left, pivot-1); 
    if (right > pivot) 
      q_sort(numbers, pivot+1, right); 
  }