ΠΛΗ10 ΜΑΘΗΜΑ 2.7
date post
14-Jan-2017Category
Education
view
1.086download
0
Embed Size (px)
Transcript of ΠΛΗ10 ΜΑΘΗΜΑ 2.7
10 2:
2.7:
A. 1.
1. 2. (Binary Search)
2. 1. (Merge Sort)2. (Quick Sort)
. 1. Fibonacci2. 3. :
, 10, 2.7:
2
. 1.
3 , 10, 2.7:
!
( ) , ( ).
, !
: n :
! 1 2 2 1
.. 1! 1, 2! 2 1, 3! 3 2 1 6, 4! 4 3 2 1 24 ... :
! 1 ! 1 ! 1, 1
. 1. 1.
4 , 10, 2.7:
factorial
n,res: INTEGER;
factorial(n): INTEGER
n: INTEGER;
factorial: INTEGER;
y:INTEGER;
(n=1) factorial:=1;
y:=factorial(n-1);factorial:=n*y;
- -
(EOLN, " n: ");(n);
res:=factorial(n);
(n,"!=",res);
. 1. 1.
5 , 10, 2.7:
, .
factorial(3):
factorial(2):
factorial(1):
factorial(n): INTEGER
(n=1) factorial:=1;
y:=factorial(n-1);factorial:=n*y;
- -
n
fact(3)
3
y
n
fact(3)
3
y
fact(2)
n y2
n
fact(3)
3
y
fact(2)
n y2
fact(1)
n y1
. 1. 1.
6 , 10, 2.7:
H factorial(1) 1:
factorial(2) 1 y 2*1.
factorial(2) 1 y 3*2
factorial(n): INTEGER
(n=1) factorial:=1;
y:=factorial(n-1);factorial:=n*y;
- -
n
fact(3)
3
y
fact(2)
n y2
fact(1)
n y1 1
1
n
fact(3)
3
y
fact(2)
n y2
2
1
n
fact(3)
3
y
6
2
main
. 1. 1.
7 , 10, 2.7:
.
:
factorial(n): INTEGER
(n=1) factorial:=1;
y:=factorial(n-1);factorial:=n*y;
- -
factorial(3)(3=1) y:=factorial(2)
factorial(2)(2=1) y:=factorial(1)
factorial(1)(1=1) 1
y=1 2*1=2
y=2 3*2=6
. 1. 2. (Binary Search)
8 , 10, 2.7:
(Binary Search).
, .
x :
x, ! x
x
. 1. 2. (Binary Search)
9 , 10, 2.7:
( ) :
binary_search(PIN,x,start,finish): BOOLEAN
check:BOOLEAN;middle:INTEGER;
(start>finish) check:=FALSE;
middle:=(start+finish) DIV 2; (x=PIN[middle])
check:=TRUE;
(x>PIN[middle]) check:=binary_search(PIN,x,middle+1,finish);
check:=binary_search(PIN,x,start,middle-1);-
- - binary_search:=check;
-
. 1. 2. (Binary Search)
10 , 10, 2.7:
11 :
: BinarySearch(A,11,1,15): middle=(1+15) div 2=8. xA[middle]
: BinarySearch(A,11,5,7) : middle=(5+7) div 2=6 x
. 1. 2. (Binary Search)
11 , 10, 2.7:
: =[1 3 5 7 9] 7
: ( Fibonacci ) .
. 2. 1. (Merge Sort)
12 , 10, 2.7:
, (Merge Sort).
:
.
. 2. 1. (Merge Sort)
13 , 10, 2.7:
:
merge_sort(%PIN,start,finish)
PIN: ARRAY[1..MAX_N] OF INTEGER;start,finish: INTEGER;
PIN: ARRAY[1..MAX_N] OF INTEGER;
middle: INTEGER;
(startPIN[finish])
swap(%PIN[start],%PIN[finish]);-
/* 2 */middle:=(start+finish) DIV 2; merge_sort(%PIN,start,middle); merge_sort(%PIN,middle+1,finish); merge(%PIN,start,finish);
- -
-
14 , 10, 2.7:
MergeSort(,1,16)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
18 7 4 11 9 20 6 1 22 19 14 5 2 9 10 13
. 2. 1. (Merge Sort)
15 , 10, 2.7:
MergeSort(,1,16)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
18 7 4 11 9 20 6 1 22 19 14 5 2 3 10 13
1 2 3 4 5 6 7 8
18 7 4 11 9 20 6 19 10 11 12 13 14 15 16
22 19 14 5 2 3 10 13
. 2. 1. (Merge Sort)
16 , 10, 2.7:
(A,1,8)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
18 7 4 11 9 20 6 1 22 19 14 5 2 3 10 13
1 2 3 4 5 6 7 8
18 7 4 11 9 20 6 19 10 11 12 13 14 15 16
22 19 14 5 2 3 10 13
1 2 3 4
18 7 4 11
5 6 7 8
9 20 6 1
. 2. 1. (Merge Sort)
17 , 10, 2.7:
(A,1,4)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
18 7 4 11 9 20 6 1 22 19 14 5 2 3 10 13
1 2 3 4 5 6 7 8
18 7 4 11 9 20 6 19 10 11 12 13 14 15 16
22 19 14 5 2 3 10 13
1 2 3 4
18 7 4 11
5 6 7 8
9 20 6 1
1 2
18 7
3 4
4 11
. 2. 1. (Merge Sort)
18 , 10, 2.7:
(A,1,2):
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
18 7 4 11 9 20 6 1 22 19 14 5 2 3 10 13
1 2 3 4 5 6 7 8
18 7 4 11 9 20 6 19 10 11 12 13 14 15 16
22 19 14 5 2 3 10 13
1 2 3 4
18 7 4 11
5 6 7 8
9 20 6 1
1 2
7 18
3 4
4 11
. 2. 1. (Merge Sort)
19 , 10, 2.7:
(A,3,4):
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
18 7 4 11 9 20 6 1 22 19 14 5 2 3 10 13
1 2 3 4 5 6 7 8
18 7 4 11 9 20 6 19 10 11 12 13 14 15 16
22 19 14 5 2 3 10 13
1 2 3 4
18 7 4 11
5 6 7 8
9 20 6 1
1 2
7 18
3 4
4 11
. 2. 1. (Merge Sort)
20 , 10, 2.7:
(A,1,4):
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
18 7 4 11 9 20 6 1 22 19 14 5 2 3 10 13
1 2 3 4 5 6 7 8
18 7 4 11 9 20 6 19 10 11 12 13 14 15 16
22 19 14 5 2 3 10 13
1 2 3 4
4 7 11 18
5 6 7 8
9 20 6 1
1 2
7 18
3 4
4 11
. 2. 1. (Merge Sort)
21 , 10, 2.7:
(A,5,8)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
18 7 4 11 9 20 6 1 22 19 14 5 2 3 10 13
1 2 3 4 5 6 7 8
18 7 4 11 9 20 6 19 10 11 12 13 14 15 16
22 19 14 5 2 3 10 13
1 2 3 4
4 7 11 18
5 6 7 8
9 20 6 1
1 2
7 18
3 4
4 11
5 6
9 20
7 8
6 1
. 2. 1. (Merge Sort)
22 , 10, 2.7:
(A,5,6):
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
18 7 4 11 9 20 6 1 22 19 14 5 2 3 10 13
1 2 3 4 5 6 7 8
18 7 4 11 9 20 6 19 10 11 12 13 14 15 16
22 19 14 5 2 3 10 13
1 2 3 4
4 7 11 18
5 6 7 8
9 20 6 1
1 2
7 18
3 4
4 11
5 6
9 20
7 8
6 1
. 2. 1. (Merge Sort)
23 , 10, 2.7:
(A,7,8):
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
18 7 4 11 9 20 6 1 22 19 14 5 2 3 10 13
1 2 3 4 5 6 7 8
18 7 4 11 9 20 6 19 10 11 12 13 14 15 16
22 19 14 5 2 3 10 13
1 2 3 4
4 7 11 18
5 6 7 8
9 20 6 1
1 2
7 18
3 4
4 11
5 6
9 20
7 8
1 6
. 2. 1. (Merge Sort)
24 , 10, 2.7:
(A,5,8):
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
18 7 4 11 9 20 6 1 22 19 14 5 2 3 10 13
1 2 3 4 5 6 7 8
18 7 4 11 9 20 6 19 10 11 12 13 14 15 16
22 19 14 5 2 3 10 13
1 2 3 4
4 7 11 18
5 6 7 8
1 6 9 20
1 2
7 18
3 4
4 11
5 6
9 20
7 8
1 6
. 2. 1. (Merge Sort)
25 , 10, 2.7:
(A,1,8):
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
18 7 4 11 9 20 6 1 22 19 14 5 2 3 10 13
1 2 3 4 5 6 7 8
1 4 6 7 9 11 18 209 10 11 12 13 14 15 16
22 19 14 5 2 3 10 13
1 2 3 4
4 7 11 18
5 6 7 8
1 6 9 20
1 2
7 18
3 4
4 11
5 6
9 20
7 8
1 6
. 2. 1. (Merge Sort)
26 , 10, 2.7:
(9,16)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
18 7 4 11 9 20 6 1 22 19 14 5 2 3 10 13
1 2 3 4 5 6 7 8
1 4 6 7 9 11 18 209 10 11 12 13 14 15 16
2 3 5 10 13 14 19 22
1 2 3 4
4 7 11 18
5 6 7 8
1 6 9 20
1 2
7 18
3 4
4 11
5 6
9 20
7 8
1 6
9 10 11 12
5 14 19 22
13 14 15 16
2 3 10 13
9 10
19 22
11 12
5 14
13 14
2 3
15 16
10 13
. 2. 1. (Merge Sort)
27 , 10, 2.7:
(A,1,16):
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 2 3 4 5 6 7 9 10 11 13 14 18 19 20 22
1 2 3 4 5 6 7 8
1 4 6 7 9 11 18 209 10 11 12 13 14 15 16
2 3 5 10 13 14 19 22
1 2 3 4
4 7 11 18
5 6 7 8
1 6 9 20
1 2
7 18
3 4
4 11
5 6
9 20
7 8
1 6
9 10 11 12
5 14 19 22
13 14 15 16
2 3 10 13
9 10
19 22
11 12
5 14
13 14
2 3
15 16
10 13
. 2. 1. (Merge Sort)
. 2. 1. (Merge Sort)
28 , 10, 2.7:
merge : .
, .
.
29 , 10, 2.7:
. 2. 1. (Merge Sort)
30 , 10, 2.7:
merge :
merge(%PIN,start,finish)
PIN: ARRAY[1..MAX_N] OF INTEGER;start,finish: INTEGER;
PIN: ARRAY[1..MAX_N] OF INTEGER;
C: ARRAY[1..MAX_N] OF INTEGER;middle: INTEGER;i,j,k:INTEGER;n: INTEGER;m: INTEGER;
middle:=(start+finish) DIV 2;/* 1 PIN[start...middle]*/i:=start;n:=middle;/* 2 PIN[middle+1...finish]*/j:=middle+1;m:=finish;/* C: */k:=1 ; ( )
. 2. 1. (Merge Sort)
31 , 10, 2.7:
merge :
