title: How To Check If A Given Array Represents A Binary Heap
signature: def how_to_check_if_a_given_array_represents_a_binary_heap(arr, i, n):
test_code: import array
  import bisect
  import collections
  import datetime
  import functools
  import heapq
  import itertools
  import math
  import queue
  import re
  import string
  import sys
  from typing import Any, Dict, List, Optional, Set
  
  
  # SOLUTION CODE
  # ============================================
  PLACEHOLDER_CODE_BODY
  
  # TESTING CODE 
  # ============================================
  def validate_solution(actual, expected):
      return actual == expected
  
  def driver(arr, i, n, expected):
      try:
          if validate_solution(PLACEHOLDER_FN_NAME(
              arr, i, n),
              expected
          ):
              return "PASSED"
          return "FAILED"
      except Exception as exception_obj:
          return type(exception_obj).__name__
      
  if __name__ == "__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)
      print(f"TEST-0...{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)
      print(f"TEST-1...{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)
      print(f"TEST-2...{result}")
  
      result = driver([10, 2, 1, 34, 21, 37, 49, 31, 70, 97, 87, 50, 76, 55], 0, 8, False)
      print(f"TEST-3...{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)
      print(f"TEST-4...{result}")
  
      result = driver([1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0], 12, 11, True)
      print(f"TEST-5...{result}")
  
      result = driver([5, 20, 30, 5, 10, 21, 5], 0, 7, False)
      print(f"TEST-6...{result}")
  
      result = driver([50, 20, 30, 5, 10, 21, 5], 0, 7, True)
      print(f"TEST-7...{result}")
  
      result = driver([50, 20, 30, 5, 10, 21, 5], 2, 7, True)
      print(f"TEST-8...{result}")
  
      result = driver([50, 20, 30, 5, 10, 21, 5], 4, 7, True)
      print(f"TEST-9...{result}")
  
      sys.exit(0)
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;
  }