title: How To Check If A Given Array Represents A Binary Heap
signature: function how_to_check_if_a_given_array_represents_a_binary_heap(arr, i, n)
test_code: using Printf
  
  # SOLUTION CODE
  # ============================================
  PLACEHOLDER_CODE_BODY
  
  # TESTING CODE 
  # ============================================
  function validate_solution(actual, expected)
      return actual == expected
  end
  
  function driver(arr, i, n, expected)
      try
  
          if validate_solution(PLACEHOLDER_FN_NAME(arr, i, n), expected)
              return "PASSED";
          end
          return "FAILED";
      catch exception_obj
          return string(Base.typename(typeof(exception_obj)).wrapper);
      end
  end
  
  function main()
      
      result = driver([1, 2, 3, 5, 24, 24, 25, 25, 36, 37, 37, 39, 42, 44, 46, 50, 51, 54, 56, 60, 62, 70, 71, 73, 75, 80, 80, 85, 86, 89, 91, 95, 99], 0, 18, false);
      @printf("TEST-0...%s\n",result);
      
      result = driver([-44, -58, 88, -42, 42, -14, -44, 42, 64, 94, -46, -70, 34, -10, -46, -52, -6, -78, 64, 56, 74, 98, -34, -4, -92, 6, -52, -20, 78, -72, -40], 0, 27, false);
      @printf("TEST-1...%s\n",result);
      
      result = driver([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 0, 20, false);
      @printf("TEST-2...%s\n",result);
      
      result = driver([10, 2, 1, 34, 21, 37, 49, 31, 70, 97, 87, 50, 76, 55], 0, 8, false);
      @printf("TEST-3...%s\n",result);
      
      result = driver([-94, -84, -82, -66, -64, -62, -56, -38, -24, -24, -4, 2, 4, 4, 8, 14, 16, 20, 30, 34, 34, 48, 58, 58, 70, 76, 78, 86, 88, 96, 98], 0, 26, false);
      @printf("TEST-4...%s\n",result);
      
      result = driver([1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0], 12, 11, true);
      @printf("TEST-5...%s\n",result);
      
      result = driver([5, 20, 30, 5, 10, 21, 5], 0, 7, false);
      @printf("TEST-6...%s\n",result);
      
      result = driver([50, 20, 30, 5, 10, 21, 5], 0, 7, true);
      @printf("TEST-7...%s\n",result);
      
      result = driver([50, 20, 30, 5, 10, 21, 5], 2, 7, true);
      @printf("TEST-8...%s\n",result);
      
      result = driver([50, 20, 30, 5, 10, 21, 5], 4, 7, true);
      @printf("TEST-9...%s\n",result);
      
  end
  
  main()
source_py: def how_to_check_if_a_given_array_represents_a_binary_heap(arr, i, n):
      if (i > int(((n - 2) / 2))):
          return True
      if ((arr[i] >= arr[((2 * i) + 1)]) and (arr[i] >= arr[((2 * i) + 2)]) and how_to_check_if_a_given_array_represents_a_binary_heap(arr, ((2 * i) + 1), n) and how_to_check_if_a_given_array_represents_a_binary_heap(arr, ((2 * i) + 2), n)):
          return True
      return False
source_cpp: bool how_to_check_if_a_given_array_represents_a_binary_heap(vector<int> arr, int i, int n) {
    if ( i > ( n - 2 ) / 2 ) return true;
    if ( arr [ i ] >= arr [ 2 * i + 1 ] && arr [ i ] >= arr [ 2 * i + 2 ] && how_to_check_if_a_given_array_represents_a_binary_heap ( arr, 2 * i + 1, n ) && how_to_check_if_a_given_array_represents_a_binary_heap ( arr, 2 * i + 2, n ) ) return true;
    return false;
  }