(Heap Sort)

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?????

• (Heap Sort)

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• ????????,?????????(0?)?????????????????
• ?????????,????????????????????????,
• ???????,?????????????????????,??????????
• ????????,????????(Heap Sort)??

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??

• ???????????????????,??John Williams???
• ????????,???????????,????logn??,??????????????????
  ?O(nlogn),??????????????,??????????????
• ????????????????????(heap tree)

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??????

• ?????????
• ?????????????????????

??a ???12,55,618,40,60,47,25,1,30,6,66?????????
???
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?????  
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• ????????,??????
• ???i??????????N?????
• i N / 2 -1
• ??j???i??????????
• if ( a 2i 1 gt a 2 i 2 )
• j 2 i 1
• else
• j 2 i 2
• ????i???????j????,???i?j??,???i ???j?
• if ( a i gt a j )
• swap ( a i , a j )
• i j
• ????i????????step 2
• ??i??0,?i i 1,??step 2

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(a) 60?66??
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(b)55?66???,??60??
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(c) 12?618???,??47??
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????

• ????????????

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(a) 618?55??
a 0 1 2 3 4 5 6 7 8 9 10
? 55 66 47 40 60 12 25 1 30 6 618
???? ???? ???? ???? ???? ???? ???? ???? ???? ???? ???? ????
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(b)??55
a 0 1 2 3 4 5 6 7 8 9
? 66 60 47 40 55 12 25 1 30 6
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(c) 66?6??,??6
a 0 1 2 3 4 5 6 7 8 9
? 60 55 47 40 6 12 25 1 30 66
???? ???? ???? ???? ???? ???? ???? ???? ???? ???? ????
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(d)66?30??,??30
a 0 1 2 3 4 5 6 7 8
? 55 40 47 30 6 12 25 1 60
???? ???? ???? ???? ???? ???? ???? ???? ???? ????
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(e) 55?1??,??1
a 0 1 2 3 4 5 6 7
? 47 40 25 30 6 12 1 55
????  ????  ????  ????  ????  ????  ????  ????  ???? 
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(f)47?1??,??1
a 0 1 2 3 4 5 6
? 40 30 25 1 6 12 47
???? ???? ???? ???? ???? ???? ???? ????
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(g) 40?12??,??12
a 0 1 2 3 4  5
? 30 12 25 1 6  40
???? ???? ???? ???? ???? ???? ????
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(h)6?30??,??6
a 0 1 2 3 4
? 25 12 6 1 30
???? ???? ???? ???? ???? ????
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(i) 25?1??,??1
a 0 1 2 3
? 12 1 6 25
???? ???? ???? ???? ????
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(j)12?6??
a 0 1 2
? 6 1 6
???? ???? ???? ????
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???

• gtC?????
• move_down(int a , int from, int to)
• int i, j, t
• i from
• while ( i lt to /2 )
• j i 2 1
• if ( j 1 lt to a j lt a j 1 )
• j
• if (a i lt a j )

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• t a i
• a i a j
• a j t
• i j

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• heap_sort(int a , int n )
• int i, t
• for ( i n /2 1 i gt 0 i - -)
• move_down(a, i, n)
• for ( i n 1 i gt 0 i - -)
• t a 0
• a 0 a i
• a i t
• move_down ( a, 0, i )

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• gt???????
• ???????????,
• ??????????????O(nlogn)?
• ??????????

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????-????

• include ltstudio.hgt
• void adjust ( int , int )
• int data 11 0, 75, 23, 98, 44, 57, 12, 29,
  64, 38, 82
• void main ( )
• int i , k , temp
• printf ( \n ltlt Heap sort gtgt\n )
• printf ( Number )
• for ( k 1 k lt 10 k )
• printf ( d , data k )
• puts ( )for ( k 0 k lt 60 k ) printf (
  - )

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• for ( i 10 / 2 i gt 0 i --)
• adjust ( i, 10 )
• printf ( \nHeap )
• for ( k 1 k lt 10 k )
• printf ( d , data k )
• for ( i 9 i gt 0 i --)
• temp data i1
• data i1 data 1

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• data 1 temp
• adjust (1, i )
• printf ( \nAccess )
• for ( k 1 k lt 60 k )
• printf ( d , data k )
• puts ( )
• for ( k 0 k lt 60 k ) printf ( - )
• printf ( \nSorting )
• for ( k 1 k lt 60 k )

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• void adjust ( int i, int n )
• int j, k, dome 0
• k data i
• j 2 i
• while (( j lt n ) ( done 0 ))
• if (( j lt n ) ( data j lt data j 1
  )) j
• if (( j lt n ) done 1

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• else
• data j / 2 data j
• j 2
• data j / 2 k