Question

6. (8 pts) Illustrate the algorithmic operations on the maximum binary heap data sti 'perations on the maximum binary heap data structure as directed. BUILD-MAX-HEAP(A) MAX-HEAPIFY (A. i) 1 A heap-size = A.length 11 = LEFT() 2 for i = A.length/2) downto 1 2 r = RIGHT() 3 MAX-HEAPIFY (A,i) 3 if / S 4.heap-size and All > A[i] HEAP-EXTRACT-MAX (A) 4 largest = 1 5 else largest = 1 1 if A.heap-size <1 6 ifrs A heap-size and A[r] > A[largest] 2 error "heap underflow 7 largest = r 3 mar = A[D 8 if largest #1 4 A[1] = A[A.heap-size] 9 exchange A[i] with A[largest] 5 A heap-size = A.heap-size- 1 10 MAX-HEA PIFY (A. largest) 6 MAX-HEAPIFY (A, 1) 7 return max a. (4) Let Build-Max-Heap use Max-Heapify on the data in this 1-based indexing array: 1 2 3 4 5 6 7 8 9 6 2 8 3 9 4 7 5 Rewrite the array as it exists after completion of each execution of Max-Heapify (line 3 in Build- Max-Heap) in the table provided below. 1 2 3 4 5 6 7 8 9 Start 1 6 2 1 8 3 9 4 7 i=4 i=3 i= 2 i= 1 b. (2) Draw the resulting heap in tree form. ?? x 0 c. (2) Write the array after one call to Heap-Extract-Max on the heap you constructed above. Leave out the elements that do not belong to the heap: After line 5 of Heap-Extract-Max has finished executing 1 2 3 4 5 6 7 8 9 After line 6 of Heap-Extract-Max has finished executing 1 2 3 4 5 6 7 8

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Answer 1

Answer is attached in the form of images. At the top page no is written. Please see.

PAGE NO Page ① COATE 28 <elements_ At ;=4 ACJE Z E lements y=9 7 ds are not greater than 9. So Ho Change No macheanify call further i 1161218 13 914 715 1= 3 A [179 А СХЕЧ g is greater than 2 Swap Max heapi fy (2) I=to 12 8= 13 d not less than heapsize After i=3 STOP! 11213141516171819 1161983 1214715

+ 00 Backspace Num Lock II Page 2 4 index 7=2 largest = ADI 8 ... element A[r]= 3 ... element exchange 6 with 8 i-2 largest = 4 ... not equal so Max heapify (6) After above function - Langedt = 8 167 Macheopify (6) STOP. index 1/2/3/4/5/6/7/8/91 No 118917312141615

PAGE No. DATE Page (3) Macheapify (1) ACIE 8 largest = 3 ... index largest not equal to i... True Swap ① of ③ Apply Maxcheapify on Ai laynegu 5 A320 After max heapify iD 12 13 14 15 16 17 18 19 9 1814 1713121615 : Final heap

PAGE No. DATETT Page 9 Now Hepp-Ex trocke Max on the new here constructed A heapsize=9 ... Me under flow max= AC1 = 9 AC] = A.LA heapsize EAL A beqesize - A heapsize- = 9-1 = 8 After line G size updated 11213141516171819 584 171312111615 1. Mow Max heapiky CAL)= (ALS) Mew heap size- 0 0 0 0 Aca] = A[2] = 8 Al 2 ACA) = 4 i1 825. Swap largest 2

Backspace PAGE NO. Apply max heapify on A Clargest] - AC2 je on 6 Apply max beapify am A14 ] ie on ③ Fimal heap oo 0 I After line 6 1201 41 sl 61718 8171 41 6 3 2 ils