Lecture 18
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Data Structures Notes for Lecture 18 Introduction of Sorting By Samaher Hussein Ali 2007-2008
Sorting اﻟﺘﺮﺗﻴﺐ هﻮ ﻋﻤﻠﻴﺔ ﺗﻨﻈﻴﻢ ﻣﺠﻤﻮﻋﺔ ﻣﻦ اﻟﻌﻨﺎﺻﺮ اﻟﺒﻴﺎﻧﻴﺔ وﻓﻖ ﻗﻴﻤﺔ ﺣﻘﻞ )او ﻣﺠﻤﻮﻋﺔ ﺣﻘﻮل ( ﻳﺴﻤﻰ ﺑﺎﻟﻤﻔﺘﺎح ﺑﺼﻮرة ﺗﺼﺎﻋﺪﻳﺔ او ﺗﻨﺎزﻟﻴﺔ. واﻟﻐﺮض ﻣﻦ اﻟﺘﺮﺗﻴﺐ هﻮ-: .1ﻟﺰﻳﺎدة آﻔﺎءة ﺧﻮارزﻣﻴﺎت اﻟﺒﺤﺚ ﻋﻦ ﻋﻨﺼﺮ ﻣﺎ .2ﻟﺘﺒﺴﻴﻂ ﻣﻌﺎﻟﺠﺔ اﻟﻤﻠﻔﺎت .3ﻟﺤﻞ ﻣﺸﻜﻠﺔ ﺗﺸﺎﺑﻪ اﻟﻘﻴﻮد وﻳﻮﺟﺪ ﻋﺪة ﺗﺼﻨﻴﻔﺎت ﻟﺨﻮارزﻣﻴﺎت اﻟﺘﺮﺗﻴﺐ ﻣﻨﻬﺎ-: .1ﺧﻮارزﻣﻴﺎت ﺗﻌﺘﻤﺪ اﻟﻤﻘﺎرﻧﺎت .2ﺧﻮارزﻣﻴﺎت ﺗﻌﺘﻤﺪ اﻟﺘﻮزﻳﻊ .3ﺧﻮارزﻣﻴﺎت ﺗﻌﺘﻤﺪ ﻋﻠﻰ اﺟﻬﺰة اﻟﺨﺰن وﺗﺘﻀﻤﻦ-: أ .ﺧﻮارزﻣﻴﺎت اﻟﺘﺮﺗﻴﺐ اﻟﺪاﺧﻠﻲ
Internal Sort Algorithm
ب .ﺧﻮارزﻣﻴﺎت اﻟﺘﺮﺗﻴﺐ اﻟﺪاﺧﻠﻲ
External Sort Algorithm
*ﺧﻄﻮات ﻋﻤﻠﻴﺔ اﻟﺘﺮﺗﻴﺐ ﺧﻮارزﻣﻴﺎت اﻟﺘﺮﺗﻴﺐ ﺑﻤﺨﺘﻠﻒ اﻧﻮاﻋﻬﺎ ﺗﺘﻀﻤﻦ اﻟﺨﻄﻮات اﻟﺘﺎﻟﻴﺔ .1ﻗﺮاءة ﺣﻘﻞ اﻟﻤﻔﺘﺎح .2اﺳﺘﻨﺘﺎج ﻣﻮﻗﻊ اﻟﻌﻨﺼﺮ ﻓﻲ اﻟﺘﺮﺗﻴﺐ اﻟﺠﺪﻳﺪ .3ﻧﻘﻞ اﻟﻌﻨﺼﺮ اﻟﻰ اﻟﻤﻮﻗﻊ اﻟﺠﺪﻳﺪ
*اﺳﺲ ﻗﻴﺎس آﻔﺎءة ﺧﻮارزﻣﻴﺎت اﻟﺘﺮﺗﻴﺐ .1ﻣﻌﺪل ﻣﺎ ﺗﺤﺘﺎﺟﻪ اﻟﺨﻮارزﻣﻴﺔ ﻣﻦ ﻣﻘﺎرﻧﺎت .2ﻣﻌﺪل ﻣﺎ ﺗﺤﺘﺎﺟﻪ اﻟﺨﻮارزﻣﻴﺔ ﻣﻦ اﻟﻨﻘﻼت او اﻟﺘﺤﺮﻳﻜﺎت .3ﻣﻌﺪل ﻣﺎ ﺗﺤﺘﺎﺟﻪ اﻟﺨﻮارزﻣﻴﺔ ﻣﻦ اﻟﺘﺒﺪﻳﻼت .4ﻣﻌﺪل اﻟﺤﺠﻢ اﻟﺘﺨﺰﻳﻨﻲ
Internal Sort Algorithm ﺧﻮارزﻣﻴﺎت اﻟﺘﺮﺗﻴﺐ اﻟﺪاﺧﻠﻲ وﻧﻘ ﺼﺪ ﺑﺎﻟﺘﺮﺗﻴ ﺐ اﻟ ﺪاﺧﻠﻲ ﺑﺎﻟﺘﺮﺗﻴ ﺐ اﻟ ﺬي ﻳﺤ ﺪث ﻓ ﻲ اﻟ ﺬاآﺮة اﻟﺮﺋﻴ ﺴﻴﺔ ﻟﻠﺤﺎﺳ ﺒﺔ ﻋﻨ ﺪﻣﺎ ﻳﻜ ﻮن ﺣﺠ ﻢ اﻟﺒﻴﺎﻧ ﺎت ﻣﻨﺎﺳﺒًﺎ )ﻟﻴﺲ آﺒﻴﺮًا( وﺗﺘﻀﻤﻦ هﺬﻩ اﻟﺨﻮارزﻣﻴﺎت ﺧﻤﺲ ﻃﺮق -:
1
.1ﻃﺮق اﻟﺘﺮﺗﻴﺐ ﺑﺎﺳﺘﺨﺪام اﻟﺘﺒﺪﻳﻼت وﺗﺘﻀﻤﻦ ﻋﺪة ﺧﻮارزﻣﻴﺎت Bubble Sort (Exchange)Algorithm
* ﺧﻮارزﻣﻴﺔ اﻟﺘﺮﺗﻴﺐ اﻟﻔﻘﺎﻋﻲ
Quick Sort Algorithm
* ﺧﻮارزﻣﻴﺔ اﻟﺘﺮﺗﻴﺐ اﻟﺴﺮﻳﻊ *ﺧﻮارزﻣﻴﺔ ﺷﻴﻞ
Shell Algorithm
*ﺧﻮارزﻣﻴﺔ ﺷﻴﻜﺮ
Shaker Algorithm
* ﺧﻮارزﻣﻴﺔ اﻻزاﺣﺔ
Shifting Algorithm
* ﺧﻮارزﻣﻴﺔ ﺑﺎﺗﺠﺮ
Batcher Algorithm
* ﺧﻮارزﻣﻴﺔ اﻟﺘﺮﺗﻴﺐ اﻟﻔﺮدي واﻟﺰوﺟﻲ
Add-Even Sort Algorithm .2ﻃﺮق اﻟﺘﺮﺗﻴﺐ ﺑﺎﻻﺿﺎﻓﺔ وﺗﺘﻀﻤﻦ ﻋﺪة ﺧﻮارزﻣﻴﺎت * اﻟﺘﺮﺗﻴﺐ ﺑﺎﻻﺿﺎﻓﺔ اﻟﻰ اﻟﻘﺎﺋﻤﺔ * اﻟﺘﺮﺗﻴﺐ ﺑﺤﺴﺎب اﻟﻌﻨﻮان * اﻟﺘﺮﺗﻴﺐ ﺑﺎﻻﺿﺎﻓﺔ اﻟﺜﻨﺎﺋﻲ * اﻟﺘﺮﺗﻴﺐ ﺑﺎﻻﺿﺎﻓﺔ اﻟﺨﻄﻲ .3ﻃﺮق اﻟﺘﺮﺗﻴﺐ ﺑﺎﺳﺘﺨﺪام اﻟﺪﻣﺞ وﺗﺘﻀﻤﻦ ﻋﺪة ﺧﻮارزﻣﻴﺎت *ﺧﻮارزﻣﻴﺔ اﻟﺪﻣﺞ اﻟﺒﺴﻴﻂ *ﺧﻮارزﻣﻴﺔ اﻟﺪﻣﺞ اﻟﻤﺴﺘﻘﻴﻢ *ﺧﻮارزﻣﻴﺔ اﻟﺪﻣﺞ اﻟﻄﺒﻴﻌﻲ .4ﻃﺮق اﻟﺘﺮﺗﻴﺐ اﻟﺘﻮزﻳﻌﻲ وﺗﺘﻀﻤﻦ ﺧﻮارزﻣﻴﺔ واﺣﺪة ﻓﻘﻂ هﻲ-: * ﺧﻮارزﻣﻴﺔ ﺗﺮﺗﻴﺐ اﻻﺳﺎس
Radix Sort Algorithm
.5ﻃﺮق اﻟﺘﺮﺗﻴﺐ ﺑﻮاﺳﻄﺔ اﻻﺧﺘﻴﺎر وﺗﺘﻀﻤﻦ ﻋﺪة ﺧﻮارزﻣﻴﺎت-: * ﺧﻮارزﻣﻴﺔ اﻻﺧﺘﻴﺎر اﻟﺨﻄﻲ *ﺧﻮارزﻣﻴﺔ اﻻﺧﺘﻴﺎر اﻟﺘﺮﺑﻴﻌﻲ *ﺧﻮارزﻣﻴﺔ اﻟﺘﺮﺗﻴﺐ اﻟﻜﻮﻣﻲ *ﺧﻮارزﻣﻴﺔ اﻟﺘﺮﺗﻴﺐ اﻟﺸﺠﺮي *ﺧﻮارزﻣﻴﺔ اﻻﺧﺘﻴﺎر اﻟﺨﻄﻲ ﺑﺎﻟﺘﺒﺪﻳﻼت *ﺧﻮارزﻣﻴﺔ اﻻﺧﺘﻴﺎر اﻟﺨﻄﻲ ﺑﺎﻟﻌﺪ
2
External Sort Algorithm ﺧﻮارزﻣﻴﺎت اﻟﺘﺮﺗﻴﺐ اﻟﺨﺎرﺟﻲ ﻓﻜﺮﺗﻬﺎ اذا آﺎن ﻟﺪﻳﻨﺎ آﻤﻴﺔ آﺒﻴﺮة ﻣﻦ اﻟﺒﻴﺎﻧﺎت ﻻﺗﺘﺴﻌﻬﺎ اﻟﺬاآﺮة اﻟﺮﺋﻴﺴﻴﺔ ﻳﺘﻢ ﺧﺰﻧﻬﺎ ﻋﻠﻰ اﺣﺪ وﺳﺎﺋﻞ اﻟﺨﺰن اﻟﺜﺎﻧﻮﻳﺔ ﺛﻢ ﺗﻘﺴﻢ اﻟﻰ ﻣﻘﺎﻃﻊ وﻳﺘﻢ ﺗﺮﺗﻴﺒﻬﺎ وﻓﻖ اﺣﺪى ﻃﺮق اﻟﺘﺮﺗﻴﺐ اﻟﺪاﺧﻠﻲ ﺛﻢ ﻳﺘﻢ اﻟﺪﻣﺞ ﺑﻴﻦ هﺬﻩ اﻟﻤﻘﺎﻃﻊ . وﻳﺘﻀﻤﻦ اﻟﺘﺮﺗﻴﺐ اﻟﺨﺎرﺟﻲ اﻟﻄﺮق اﻟﺘﺎﻟﻴﺔ-: * اﻟﺘﺮﺗﻴﺐ ﺑﺎﻟﺪﻣﺞ ذو اﻟﻤﺴﺎرﻳﻦ
Two-Way-Merge K-Way-Merge Balanced Two-Way-Merge
* اﻟﺘﺮﺗﻴﺐ ﺑﺎﻟﺪﻣﺞ ﻣﺘﻌﺪد اﻟﻤﺴﺎرﻳﻦ * اﻟﺘﺮﺗﻴﺐ ﺑﺎﻟﺪﻣﺞ اﻟﻤﺘﻮازي ذي اﻟﻤﺴﺎرﻳﻦ
Poly phase Two-Way-Merge
* اﻟﺘﺮﺗﻴﺐ ﺑﺎﻟﺪﻣﺞ ﻣﺘﻌﺪد اﻻﻃﻮار
Bubble Sort Algorithm ﺧﻮارزﻣﻴﺔ اﻟﺘﺮﺗﻴﺐ اﻟﻔﻘﺎﻋﻲ ﻓﻜﺮﺗﻬﺎ-: هﻲ ﻣﻘﺎرﻧﺔ آﻞ ﻋﻨﺼﺮﻳﻦ ﻣﺘﺠﺎورﻳﻦ ﻓﻲ اﻟﻘﺎﺋﻤﺔ وﺗﺒﺪﻳﻞ ﻣﻮاﻗﻌﻬﻤﺎ وﺧﻼل آﻞ دورة ﻣﻦ اﻟﻤﻘﺎرﻧﺎت واﻟﺘﺒﺪﻳﻼت ﻳﺘﺤﺮك اﻟﻌﻨﺼﺮ ﺣﺘﻰ ﻳﺴﺘﻘﺮ ﻓﻲ اﻟﻤﻮﻗﻊ اﻟﻤﻨﺎﺳﺐ. ﺣﻴﺚ اﻧﻨﺎ ﻧﺤﺘﺎج اﻟﻰ ) ( N-1ﻣﻦ اﻟﺪورات ﻟﻠﺤﺼﻮل ﻋﻠﻰ ﻋﻤﻠﻴﺔ اﻟﺘﺮﺗﻴﺐ وﺣﻴﺚ ان )
( Nﻳﻤﺜﻞ ﻋﺪد اﻟﻌﻨﺎﺻﺮ.
ﺳﻤﻴﺖ ﺑﺎﻟﺘﺮﺗﻴﺐ اﻟﻔﻘﺎﻋﻲ وذﻟﻚ ﻻن اﻻرﻗﺎم اﻟﺼﻐﻴﺮة ﺗﻄﻔﻮ اﻟﻰ اﻻﻋﻠﻰ واﻻرﻗﺎم اﻟﻜﺒﻴﺮة ﺗﺴﺘﻘﺮ ﻓﻲ اﻻﺳﻔﻞ. ﻣﺜﺎل -:رﺗﺐ ﻋﻨﺎﺻﺮ اﻟﻘﺎﺋﻤﺔ اﻟﺘﺎﻟﻴﺔ ﺑﺎﺳﺘﺨﺪام اﻟﺘﺮﺗﻴﺐ اﻟﻔﻘﺎﻋﻲ 43
54
11
41
93
17
5
66
اآﺒﺮ ﻋﺪد ﻣﻦ اﻟﻤﻘﺎرﻧﺎت= ﺑﻤﺎ ان N=8ﻟﺬﻟﻚ ﻳﺠﺐ ان ﻻﻳﺰﻳﺪ ﻋﺪد اﻟﻤﻘﺎرﻧﺎت ﻋﻦ 28ﻣﻘﺎرﻧﺔ N(N-1)/2
ﺧﻄﻮات اﻟﺤﻞ-: اﻟﻤﺮﺣﻠﺔ اﻻوﻟﻰ -: ﻧﻘﺎرن اﻟﻌﻨﺼﺮ ﻓﻲ اﻟﻤﻮﻗﻊ ) ( Nﻣﻊ اﻟﻌﻨﺼﺮ ﻓﻲ اﻟﻤﻮﻗﻊ )
( N-1وﻧﺒﺪل ﻣﻮﻗﻌﻬﻤﺎ ﺑﺤﻴﺚ ﻳﻜﻮن اﻻﺻﻐﺮ ﻗﺒﻞ اﻻﺧﺮ وﻧﺴﺘﻤﺮ ﻟﺤﻴﻦ
اﻟﻮﺻﻮل اﻟﻰ ﻣﻘﺎرﻧﺔ اﻟﻌﻨﺼﺮ ﻓﻲ اﻟﻤﻮﻗﻊ اﻟﺜﺎﻧﻲ ﻣﻊ اﻟﻌﻨﺼﺮ ﻓﻲ اﻟﻤﻮﻗﻊ اﻻول اﻟﻤﺮﺣﻠﺔ اﻟﺜﺎﻧﻴﺔ -: ﻧﻘﺎرن ﺑﻨﻔﺲ اﻟﻄﺮﻳﻘﺔ اﻟﻌﻨﺼﺮ ﻓﻲ اﻟﻤﻮﻗﻊ Nاﻟﻰ اﻟﻌﻨﺼﺮ ﻓﻲ اﻟﻤﻮﻗﻊ اﻟﺜﺎﻧﻲ اﻟﻤﺮﺣﻠﺔ اﻟﺜﺎﻟﺜﺔ -: ﻧﻜﺮر اﻟﺨﻄﻮات اﻋﻼﻩ )
( N-1ﻣﻦ اﻟﺪورات
3
ﻣﻘﺎرﻧﺔ
ﻣﻘﺎرﻧﺔ
ﻣﻘﺎرﻧﺔ
ﻣﻘﺎرﻧﺔ
ﻣﻘﺎرﻧﺔ
ﻣﻘﺎرﻧﺔ
ﻣﻘﺎرﻧﺔ
اﻟﺪورة
اﻟﺪورة
اﻟﺪورة
اﻟﺪورة
اﻟﺪورة
اﻟﺪورة
اﻟﺪورة
اﻟﻘﺎﺋﻤﺔ
)(1
)(2
)(3
)(4
)(5
)(6
)(7
)(1
)(2
)(3
)(4
)(5
)(6
)(7
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)(Public sub Bubble For i=1 to n-1 For j= n to i+1 )If a(j)
Shell Sort Algorithm ﺧﻮارزﻣﻴﺔ ﺗﺮﺗﻴﺐ ﺷﻴﻞ ﻓﻜﺮﺗﻬﺎ-: ﺗﻘﺴﻴﻢ اﻟﻘﺎﺋﻤﺔ اﻟﻰ ﻣﺴﺎﻓﺎت وهﻤﻴ ﺔ وﺗﺠ ﺮي ﻣﻘﺎرﻧ ﺔ ﻟﻜ ﻞ ﻋﻨ ﺼﺮﻳﻦ او اآﺜ ﺮ ﻟﻴ ﺴﺖ ﻣﺘﺠ ﺎورة واﻧﻤ ﺎ ﻣﺘﺒﺎﻋ ﺪة ﺑﻤ ﺴﺎﻓﺔ ﻣﺤ ﺪدة ﻣﻘ ﺪارهﺎ اﻟﻤ ﺴﺎﻓﺔ اﻟﻮهﻤﻴﺔ وهﻜﺬا ﻳﺘﻢ ﺗﻐﻴﺮ اﻟﻤﺴﺎﻓﺔ اﻟﻮهﻤﻴﺔ وﺗﺠﺮى ﻋﻤﻠﻴﺔ اﻟﻤﻘﺎرﻧﺔ واﻟﺘﻐﻴﺮ ﺣﺘﻰ ﺗﺘﺮﺗﺐ اﻟﻘﺎﺋﻤﺔ ﻣﺜﺎل -:رﺗﺐ ﻋﻨﺎﺻﺮ اﻟﻘﺎﺋﻤﺔ اﻟﺘﺎﻟﻴﺔ ﺑﺎﺳﺘﺨﺪام ﺗﺮﺗﻴﺐ ﺷﻴﻞ 66
11
54
93
41
5
17
ﺧﻄﻮات اﻟﺤﻞ-: ﻻ -:ﻧﺨﺘﺎر ﻣﺴﺎﻓﺔ وهﻤﻴﺔ ﻣﻘﺪرهﺎ او ً
Gap=4
وﻧﻀﻊ اﻟﻌﻨﺎﺻﺮ اﻻآﺒﺮ ﻋﻠﻰ ﺟﻬﺔ اﻟﻴﻤﻴﻦ واﻻﺻﻐﺮ ﻋﻠﻰ اﻟﻴﺴﺎر
4
43
ﺛﺎﻧﻴ ًﺎ -: -:ﻧﺨﺘﺎر ﻣﺴﺎﻓﺔ وهﻤﻴﺔ ﻣﻘﺪرهﺎ
66
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5
17
43
66
11
54
93
41
5
17
43
66
11
54
93
41
5
17
43
66
11
54
93
41
5
17
43
Gap=2 66
11
54
93
41
5
17
43
66
93
54
43
41
11
17
5
66
93
54
43
Result
ﺛﺎﻟﺜ ًﺎ -: -:ﻧﺨﺘﺎر ﻣﺴﺎﻓﺔ وهﻤﻴﺔ ﻣﻘﺪرهﺎ
41
11
17
5
Gap=1 93
66
54
41
43
17
11
5
Quick Sort Algorithm ﺧﻮارزﻣﻴﺔ اﻟﺘﺮﺗﻴﺐ اﻟﺴﺮﻳﻊ ﻓﻜﺮﺗﻬﺎ-: اﺧﺘﻴﺎر ﻋﻨﺼﺮ ﻣﻦ ﻋﻨﺎﺻﺮ اﻟﻘﺎﺋﻤﺔ اﻟﻤﻌﻄﺎة ﻣﺜﻞ ) Xاﻻﻓﻀﻞ ان ﻳﻜﻮن اﻟﻌﻨﺼﺮ اﻟﻮﺳﻄﻲ( ﺛﻢ ﻧﺠﻌﻞ اﻟﻌﻨﺎﺻﺮ اﻟﺘﻲ ﻗﻴﻤﺘﻬﺎ اﻗ ﻞ ﻣ ﻦ xﻗﺒﻠ ﻪ ﻓ ﻲ اﻟﻘﺎﺋﻤﺔ اﻣﺎ اﻟﻌﻨﺎﺻﺮ اﻟﺘﻲ ﺗﻜﻮن ﻗﻴﻤﺘﻬﺎ اآﺒﺮ ﻣﻦ xﺑﻌﺪﻩ ﺛﻢ ﺗﺘﻢ ﻋﻤﻠﻴﺔ اﻟﻤﺴﺢ اﻟﺘﺼﺎﻋﺪي ﻟﻌﻨﺎﺻﺮ اﻟﻘﺎﺋﻤﺔ اﻟﺘﻲ ﺗﻘ ﻊ ﻗﺒ ﻞ اﻟﻌﻨ ﺼﺮ xﻓ ﺎذا وﺟ ﺪﻧﺎ ﻋﻨﺼﺮ اآﺒﺮ ﻣﻨﻪ ﻧﺤﺪدﻩ )أي ﻧﻀﻊ اﺷﺎرة( ﺛﻢ ﻧﻤﺴﺢ ﺗﻨﺎزﻟﻴًﺎ ﻋﻨﺎﺻﺮ اﻟﻘﺎﺋﻤﺔ اﻟﻮاﻗﻌﺔ ﺑﻌﺪ xﻓﺎن وﺟﺪﻧﺎ ﻋﻨﺼﺮ اﻗﻞ ﻣﻨﻪ ﻧﺤ ﺪدﻩ اﻳ ﻀًﺎ ﺛ ﻢ ﻧﺠ ﺮي ﻋﻤﻠﻴﺔ اﻟﺘﺒﺪﻳﻞ ﺑﻴﻨﻬﻤﺎ وﻧﺴﺘﻤﺮ ﺣﺘﻰ ﺗﺘﺮﺗﺐ اﻟﻘﺎﺋﻤﺔ. ﻣﺜﺎل -:رﺗﺐ ﻋﻨﺎﺻﺮ اﻟﻘﺎﺋﻤﺔ اﻟﺘﺎﻟﻴﺔ ﺑﺎﺳﺘﺨﺪام اﻟﺘﺮﺗﻴﺐ اﻟﺴﺮﻳﻊ 66
5
17
اﻻآﺒ ﺮ
41
93 X
5
11
54 اﻻﺻ ﻐﺮ
43
ﺧﻄﻮات اﻟﺤﻞ-: اﻟﻤﺮﺣﻠﺔ اﻻوﻟﻰ: X= 41
ﻻ -:ﻧﺨﺘﺎر او ً 41<66
اذن ﺗﺒﻘﻰ ﻣﻜﺎﻧﻬﺎ
41 rel="nofollow">5
اذن ﻧﻀﻊ اﺷﺎرة ﻋﻠﻰ اﻟـ 5
41<43اذن ﻧﻀﻊ اﺷﺎرة ﻋﻠﻰ اﻟـ 43 ﻧﺠﺮي ﻋﻤﻠﻴﺔ اﻟﺘﺒﺪﻳﻞ ﻓﺘﺼﺒﺢ اﻟﻘﺎﺋﻤﺔ هﻲ-: 66 41>17
اذن ﻧﻀﻊ اﺷﺎرة ﻋﻠﻰ اﻟـ 17
41<54
اذن ﻧﻀﻊ اﺷﺎرة ﻋﻠﻰ اﻟـ 54
43
17
93
11
41
5
54
ﻧﺠﺮي ﻋﻤﻠﻴﺔ اﻟﺘﺒﺪﻳﻞ ﻓﺘﺼﺒﺢ اﻟﻘﺎﺋﻤﺔ هﻲ-: 66 41<93
اذن ﺗﺒﻘﻰ ﻣﻜﺎﻧﻬﺎ
41>11
اذن ﺗﺒﻘﻰ ﻣﻜﺎﻧﻬﺎ
43
54
93
11
41
5
17
اﻟﻤﺮﺣﻠﺔ اﻟﺜﺎﻧﻴﺔ: ﻻ -:ﻧﺄﺧﺬ ﻗﺎﺋﻤﺔ اﻻﻋﺪاد اﻟﺘﻲ هﻲ اآﺒﺮ ﻣﻦ او ً
X
43
66
93
54
ا .ﻧﺨﺘﺎر ﻟﻬﺎ X=54
54<66
اذن ﺗﺒﻘﻰ ﻣﻜﺎﻧﻬﺎ
54>43
اذن ﻧﻀﻊ اﺷﺎرة ﻋﻠﻰ اﻟـ 43
54<93
اذن ﻧﻀﻊ اﺷﺎرة ﻋﻠﻰ اﻟـ 93 66
ﻧﺠﺮي ﻋﻤﻠﻴﺔ اﻟﺘﺒﺪﻳﻞ ﻓﺘﺼﺒﺢ اﻟﻘﺎﺋﻤﺔ هﻲ-: ب .ﻧﺨﺘﺎر
X=93
93
43
54
ﺑﺎﻟﻨﺴﺒﺔ اﻟﻰ اﻟﻘﺎﺋﻤﺔ 93
66 ﻓﺘﺼﺒﺢ اﻟﻘﻠﺌﻤﺔ -: 93
66
43
54
ﻧﻄﺒﻖ ﻧﻔﺲ اﻟﺨﻄﻮات ﺑﺎﻟﻨﺴﺒﺔ اﻟﻰ اﻟﻘﺎﺋﻤﺔ 11
6
17
5
-:ﻣﻼﺣﻈﺎت ﻋﺎﻣﺔ ﻋﻨﺪﻣﺎ ﻧﻀﻊ اﺷﺎرة ﻋﻠﻰ ﻋﻨﺼﺮ ﻓﺎﻧﻪ ﻳﻨﺘﻘﻞ اﻟﻰ اﻟﺠﻬﺔ اﻻﺧﺮى ﻣﻦ اﻟﻘﺎﺋﻤﺔ.1 ( 2N*Ln N
) ﻳﻜﻮن اآﺒﺮ ﻋﺪد ﻣﻦ اﻟﻤﻘﺎرﻧﺎت اﻟﻰ هﺬﻩ اﻟﻄﺮﻳﻘﺔ هﻮ.2
هﺬﻩ اﻟﻄﺮﻳﻘﺔ ﺗﻜﻮن ﻣﻔﻴﺪة اﻟﻰ ﻟﻠﻘﻮاﺋﻢ اﻟﺘﻲ ﺗﻜﻮن ﻏﻴﺮ ﻣﺮﺗﺒﺔ اﻟﻰ ﺣﺪ آﺒﻴﺮ وﻏﻴﺮ ﻋﻤﻠﻴﺔ ﻟﻠﻘﻮاﺋﻢ ﺷﺒﻪ اﻟﻤﺮﺗﺒﺔ.3 Public sub Quicksort(byref list as string, byref F as integer, byref L as integer ) Dim I as integer Dim j as integer Dim x as integer{or any other type} I=f J=L X=list((i+j) / 2) Repeat While list(i)<x do i=i+1 While x< list(j) do j=j+1 If i<=j then Swap(list(i),list(j)) I=i+1 J=j+1 End if Loop untie i<j If f<j then Quicksort(list,f,j) End if If i
7
Sorting اﻟﺘﺮﺗﻴﺐ هﻮ ﻋﻤﻠﻴﺔ ﺗﻨﻈﻴﻢ ﻣﺠﻤﻮﻋﺔ ﻣﻦ اﻟﻌﻨﺎﺻﺮ اﻟﺒﻴﺎﻧﻴﺔ وﻓﻖ ﻗﻴﻤﺔ ﺣﻘﻞ )او ﻣﺠﻤﻮﻋﺔ ﺣﻘﻮل ( ﻳﺴﻤﻰ ﺑﺎﻟﻤﻔﺘﺎح ﺑﺼﻮرة ﺗﺼﺎﻋﺪﻳﺔ او ﺗﻨﺎزﻟﻴﺔ. واﻟﻐﺮض ﻣﻦ اﻟﺘﺮﺗﻴﺐ هﻮ-: .1ﻟﺰﻳﺎدة آﻔﺎءة ﺧﻮارزﻣﻴﺎت اﻟﺒﺤﺚ ﻋﻦ ﻋﻨﺼﺮ ﻣﺎ .2ﻟﺘﺒﺴﻴﻂ ﻣﻌﺎﻟﺠﺔ اﻟﻤﻠﻔﺎت .3ﻟﺤﻞ ﻣﺸﻜﻠﺔ ﺗﺸﺎﺑﻪ اﻟﻘﻴﻮد وﻳﻮﺟﺪ ﻋﺪة ﺗﺼﻨﻴﻔﺎت ﻟﺨﻮارزﻣﻴﺎت اﻟﺘﺮﺗﻴﺐ ﻣﻨﻬﺎ-: .1ﺧﻮارزﻣﻴﺎت ﺗﻌﺘﻤﺪ اﻟﻤﻘﺎرﻧﺎت .2ﺧﻮارزﻣﻴﺎت ﺗﻌﺘﻤﺪ اﻟﺘﻮزﻳﻊ .3ﺧﻮارزﻣﻴﺎت ﺗﻌﺘﻤﺪ ﻋﻠﻰ اﺟﻬﺰة اﻟﺨﺰن وﺗﺘﻀﻤﻦ-: أ .ﺧﻮارزﻣﻴﺎت اﻟﺘﺮﺗﻴﺐ اﻟﺪاﺧﻠﻲ
Internal Sort Algorithm
ب .ﺧﻮارزﻣﻴﺎت اﻟﺘﺮﺗﻴﺐ اﻟﺪاﺧﻠﻲ
External Sort Algorithm
*ﺧﻄﻮات ﻋﻤﻠﻴﺔ اﻟﺘﺮﺗﻴﺐ ﺧﻮارزﻣﻴﺎت اﻟﺘﺮﺗﻴﺐ ﺑﻤﺨﺘﻠﻒ اﻧﻮاﻋﻬﺎ ﺗﺘﻀﻤﻦ اﻟﺨﻄﻮات اﻟﺘﺎﻟﻴﺔ .1ﻗﺮاءة ﺣﻘﻞ اﻟﻤﻔﺘﺎح .2اﺳﺘﻨﺘﺎج ﻣﻮﻗﻊ اﻟﻌﻨﺼﺮ ﻓﻲ اﻟﺘﺮﺗﻴﺐ اﻟﺠﺪﻳﺪ .3ﻧﻘﻞ اﻟﻌﻨﺼﺮ اﻟﻰ اﻟﻤﻮﻗﻊ اﻟﺠﺪﻳﺪ
*اﺳﺲ ﻗﻴﺎس آﻔﺎءة ﺧﻮارزﻣﻴﺎت اﻟﺘﺮﺗﻴﺐ .1ﻣﻌﺪل ﻣﺎ ﺗﺤﺘﺎﺟﻪ اﻟﺨﻮارزﻣﻴﺔ ﻣﻦ ﻣﻘﺎرﻧﺎت .2ﻣﻌﺪل ﻣﺎ ﺗﺤﺘﺎﺟﻪ اﻟﺨﻮارزﻣﻴﺔ ﻣﻦ اﻟﻨﻘﻼت او اﻟﺘﺤﺮﻳﻜﺎت .3ﻣﻌﺪل ﻣﺎ ﺗﺤﺘﺎﺟﻪ اﻟﺨﻮارزﻣﻴﺔ ﻣﻦ اﻟﺘﺒﺪﻳﻼت .4ﻣﻌﺪل اﻟﺤﺠﻢ اﻟﺘﺨﺰﻳﻨﻲ
Internal Sort Algorithm ﺧﻮارزﻣﻴﺎت اﻟﺘﺮﺗﻴﺐ اﻟﺪاﺧﻠﻲ وﻧﻘ ﺼﺪ ﺑﺎﻟﺘﺮﺗﻴ ﺐ اﻟ ﺪاﺧﻠﻲ ﺑﺎﻟﺘﺮﺗﻴ ﺐ اﻟ ﺬي ﻳﺤ ﺪث ﻓ ﻲ اﻟ ﺬاآﺮة اﻟﺮﺋﻴ ﺴﻴﺔ ﻟﻠﺤﺎﺳ ﺒﺔ ﻋﻨ ﺪﻣﺎ ﻳﻜ ﻮن ﺣﺠ ﻢ اﻟﺒﻴﺎﻧ ﺎت ﻣﻨﺎﺳﺒًﺎ )ﻟﻴﺲ آﺒﻴﺮًا( وﺗﺘﻀﻤﻦ هﺬﻩ اﻟﺨﻮارزﻣﻴﺎت ﺧﻤﺲ ﻃﺮق -:
1
.1ﻃﺮق اﻟﺘﺮﺗﻴﺐ ﺑﺎﺳﺘﺨﺪام اﻟﺘﺒﺪﻳﻼت وﺗﺘﻀﻤﻦ ﻋﺪة ﺧﻮارزﻣﻴﺎت Bubble Sort (Exchange)Algorithm
* ﺧﻮارزﻣﻴﺔ اﻟﺘﺮﺗﻴﺐ اﻟﻔﻘﺎﻋﻲ
Quick Sort Algorithm
* ﺧﻮارزﻣﻴﺔ اﻟﺘﺮﺗﻴﺐ اﻟﺴﺮﻳﻊ *ﺧﻮارزﻣﻴﺔ ﺷﻴﻞ
Shell Algorithm
*ﺧﻮارزﻣﻴﺔ ﺷﻴﻜﺮ
Shaker Algorithm
* ﺧﻮارزﻣﻴﺔ اﻻزاﺣﺔ
Shifting Algorithm
* ﺧﻮارزﻣﻴﺔ ﺑﺎﺗﺠﺮ
Batcher Algorithm
* ﺧﻮارزﻣﻴﺔ اﻟﺘﺮﺗﻴﺐ اﻟﻔﺮدي واﻟﺰوﺟﻲ
Add-Even Sort Algorithm .2ﻃﺮق اﻟﺘﺮﺗﻴﺐ ﺑﺎﻻﺿﺎﻓﺔ وﺗﺘﻀﻤﻦ ﻋﺪة ﺧﻮارزﻣﻴﺎت * اﻟﺘﺮﺗﻴﺐ ﺑﺎﻻﺿﺎﻓﺔ اﻟﻰ اﻟﻘﺎﺋﻤﺔ * اﻟﺘﺮﺗﻴﺐ ﺑﺤﺴﺎب اﻟﻌﻨﻮان * اﻟﺘﺮﺗﻴﺐ ﺑﺎﻻﺿﺎﻓﺔ اﻟﺜﻨﺎﺋﻲ * اﻟﺘﺮﺗﻴﺐ ﺑﺎﻻﺿﺎﻓﺔ اﻟﺨﻄﻲ .3ﻃﺮق اﻟﺘﺮﺗﻴﺐ ﺑﺎﺳﺘﺨﺪام اﻟﺪﻣﺞ وﺗﺘﻀﻤﻦ ﻋﺪة ﺧﻮارزﻣﻴﺎت *ﺧﻮارزﻣﻴﺔ اﻟﺪﻣﺞ اﻟﺒﺴﻴﻂ *ﺧﻮارزﻣﻴﺔ اﻟﺪﻣﺞ اﻟﻤﺴﺘﻘﻴﻢ *ﺧﻮارزﻣﻴﺔ اﻟﺪﻣﺞ اﻟﻄﺒﻴﻌﻲ .4ﻃﺮق اﻟﺘﺮﺗﻴﺐ اﻟﺘﻮزﻳﻌﻲ وﺗﺘﻀﻤﻦ ﺧﻮارزﻣﻴﺔ واﺣﺪة ﻓﻘﻂ هﻲ-: * ﺧﻮارزﻣﻴﺔ ﺗﺮﺗﻴﺐ اﻻﺳﺎس
Radix Sort Algorithm
.5ﻃﺮق اﻟﺘﺮﺗﻴﺐ ﺑﻮاﺳﻄﺔ اﻻﺧﺘﻴﺎر وﺗﺘﻀﻤﻦ ﻋﺪة ﺧﻮارزﻣﻴﺎت-: * ﺧﻮارزﻣﻴﺔ اﻻﺧﺘﻴﺎر اﻟﺨﻄﻲ *ﺧﻮارزﻣﻴﺔ اﻻﺧﺘﻴﺎر اﻟﺘﺮﺑﻴﻌﻲ *ﺧﻮارزﻣﻴﺔ اﻟﺘﺮﺗﻴﺐ اﻟﻜﻮﻣﻲ *ﺧﻮارزﻣﻴﺔ اﻟﺘﺮﺗﻴﺐ اﻟﺸﺠﺮي *ﺧﻮارزﻣﻴﺔ اﻻﺧﺘﻴﺎر اﻟﺨﻄﻲ ﺑﺎﻟﺘﺒﺪﻳﻼت *ﺧﻮارزﻣﻴﺔ اﻻﺧﺘﻴﺎر اﻟﺨﻄﻲ ﺑﺎﻟﻌﺪ
2
External Sort Algorithm ﺧﻮارزﻣﻴﺎت اﻟﺘﺮﺗﻴﺐ اﻟﺨﺎرﺟﻲ ﻓﻜﺮﺗﻬﺎ اذا آﺎن ﻟﺪﻳﻨﺎ آﻤﻴﺔ آﺒﻴﺮة ﻣﻦ اﻟﺒﻴﺎﻧﺎت ﻻﺗﺘﺴﻌﻬﺎ اﻟﺬاآﺮة اﻟﺮﺋﻴﺴﻴﺔ ﻳﺘﻢ ﺧﺰﻧﻬﺎ ﻋﻠﻰ اﺣﺪ وﺳﺎﺋﻞ اﻟﺨﺰن اﻟﺜﺎﻧﻮﻳﺔ ﺛﻢ ﺗﻘﺴﻢ اﻟﻰ ﻣﻘﺎﻃﻊ وﻳﺘﻢ ﺗﺮﺗﻴﺒﻬﺎ وﻓﻖ اﺣﺪى ﻃﺮق اﻟﺘﺮﺗﻴﺐ اﻟﺪاﺧﻠﻲ ﺛﻢ ﻳﺘﻢ اﻟﺪﻣﺞ ﺑﻴﻦ هﺬﻩ اﻟﻤﻘﺎﻃﻊ . وﻳﺘﻀﻤﻦ اﻟﺘﺮﺗﻴﺐ اﻟﺨﺎرﺟﻲ اﻟﻄﺮق اﻟﺘﺎﻟﻴﺔ-: * اﻟﺘﺮﺗﻴﺐ ﺑﺎﻟﺪﻣﺞ ذو اﻟﻤﺴﺎرﻳﻦ
Two-Way-Merge K-Way-Merge Balanced Two-Way-Merge
* اﻟﺘﺮﺗﻴﺐ ﺑﺎﻟﺪﻣﺞ ﻣﺘﻌﺪد اﻟﻤﺴﺎرﻳﻦ * اﻟﺘﺮﺗﻴﺐ ﺑﺎﻟﺪﻣﺞ اﻟﻤﺘﻮازي ذي اﻟﻤﺴﺎرﻳﻦ
Poly phase Two-Way-Merge
* اﻟﺘﺮﺗﻴﺐ ﺑﺎﻟﺪﻣﺞ ﻣﺘﻌﺪد اﻻﻃﻮار
Bubble Sort Algorithm ﺧﻮارزﻣﻴﺔ اﻟﺘﺮﺗﻴﺐ اﻟﻔﻘﺎﻋﻲ ﻓﻜﺮﺗﻬﺎ-: هﻲ ﻣﻘﺎرﻧﺔ آﻞ ﻋﻨﺼﺮﻳﻦ ﻣﺘﺠﺎورﻳﻦ ﻓﻲ اﻟﻘﺎﺋﻤﺔ وﺗﺒﺪﻳﻞ ﻣﻮاﻗﻌﻬﻤﺎ وﺧﻼل آﻞ دورة ﻣﻦ اﻟﻤﻘﺎرﻧﺎت واﻟﺘﺒﺪﻳﻼت ﻳﺘﺤﺮك اﻟﻌﻨﺼﺮ ﺣﺘﻰ ﻳﺴﺘﻘﺮ ﻓﻲ اﻟﻤﻮﻗﻊ اﻟﻤﻨﺎﺳﺐ. ﺣﻴﺚ اﻧﻨﺎ ﻧﺤﺘﺎج اﻟﻰ ) ( N-1ﻣﻦ اﻟﺪورات ﻟﻠﺤﺼﻮل ﻋﻠﻰ ﻋﻤﻠﻴﺔ اﻟﺘﺮﺗﻴﺐ وﺣﻴﺚ ان )
( Nﻳﻤﺜﻞ ﻋﺪد اﻟﻌﻨﺎﺻﺮ.
ﺳﻤﻴﺖ ﺑﺎﻟﺘﺮﺗﻴﺐ اﻟﻔﻘﺎﻋﻲ وذﻟﻚ ﻻن اﻻرﻗﺎم اﻟﺼﻐﻴﺮة ﺗﻄﻔﻮ اﻟﻰ اﻻﻋﻠﻰ واﻻرﻗﺎم اﻟﻜﺒﻴﺮة ﺗﺴﺘﻘﺮ ﻓﻲ اﻻﺳﻔﻞ. ﻣﺜﺎل -:رﺗﺐ ﻋﻨﺎﺻﺮ اﻟﻘﺎﺋﻤﺔ اﻟﺘﺎﻟﻴﺔ ﺑﺎﺳﺘﺨﺪام اﻟﺘﺮﺗﻴﺐ اﻟﻔﻘﺎﻋﻲ 43
54
11
41
93
17
5
66
اآﺒﺮ ﻋﺪد ﻣﻦ اﻟﻤﻘﺎرﻧﺎت= ﺑﻤﺎ ان N=8ﻟﺬﻟﻚ ﻳﺠﺐ ان ﻻﻳﺰﻳﺪ ﻋﺪد اﻟﻤﻘﺎرﻧﺎت ﻋﻦ 28ﻣﻘﺎرﻧﺔ N(N-1)/2
ﺧﻄﻮات اﻟﺤﻞ-: اﻟﻤﺮﺣﻠﺔ اﻻوﻟﻰ -: ﻧﻘﺎرن اﻟﻌﻨﺼﺮ ﻓﻲ اﻟﻤﻮﻗﻊ ) ( Nﻣﻊ اﻟﻌﻨﺼﺮ ﻓﻲ اﻟﻤﻮﻗﻊ )
( N-1وﻧﺒﺪل ﻣﻮﻗﻌﻬﻤﺎ ﺑﺤﻴﺚ ﻳﻜﻮن اﻻﺻﻐﺮ ﻗﺒﻞ اﻻﺧﺮ وﻧﺴﺘﻤﺮ ﻟﺤﻴﻦ
اﻟﻮﺻﻮل اﻟﻰ ﻣﻘﺎرﻧﺔ اﻟﻌﻨﺼﺮ ﻓﻲ اﻟﻤﻮﻗﻊ اﻟﺜﺎﻧﻲ ﻣﻊ اﻟﻌﻨﺼﺮ ﻓﻲ اﻟﻤﻮﻗﻊ اﻻول اﻟﻤﺮﺣﻠﺔ اﻟﺜﺎﻧﻴﺔ -: ﻧﻘﺎرن ﺑﻨﻔﺲ اﻟﻄﺮﻳﻘﺔ اﻟﻌﻨﺼﺮ ﻓﻲ اﻟﻤﻮﻗﻊ Nاﻟﻰ اﻟﻌﻨﺼﺮ ﻓﻲ اﻟﻤﻮﻗﻊ اﻟﺜﺎﻧﻲ اﻟﻤﺮﺣﻠﺔ اﻟﺜﺎﻟﺜﺔ -: ﻧﻜﺮر اﻟﺨﻄﻮات اﻋﻼﻩ )
( N-1ﻣﻦ اﻟﺪورات
3
ﻣﻘﺎرﻧﺔ
ﻣﻘﺎرﻧﺔ
ﻣﻘﺎرﻧﺔ
ﻣﻘﺎرﻧﺔ
ﻣﻘﺎرﻧﺔ
ﻣﻘﺎرﻧﺔ
ﻣﻘﺎرﻧﺔ
اﻟﺪورة
اﻟﺪورة
اﻟﺪورة
اﻟﺪورة
اﻟﺪورة
اﻟﺪورة
اﻟﺪورة
اﻟﻘﺎﺋﻤﺔ
)(1
)(2
)(3
)(4
)(5
)(6
)(7
)(1
)(2
)(3
)(4
)(5
)(6
)(7
43
43
43
43
43
43
43
5
5
5
5
5
5
5
5
54
54
54
54
54
54
5
43
43
11
11
11
11
11
11
11
11
11
11
11
5
54
54
54
43
17
17
17
17
17
41
41
41
41
5
11
11
11
11
54
43
41
41
41
41
93
93
93
5
41
41
41
41
41
17
54
43
43
43
43
17
17
5
93
93
93
93
93
93
41
41
54
54
54
54
5
5
17
17
17
17
17
17
17
93
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
93
93
93
93
93
)(Public sub Bubble For i=1 to n-1 For j= n to i+1 )If a(j)
Shell Sort Algorithm ﺧﻮارزﻣﻴﺔ ﺗﺮﺗﻴﺐ ﺷﻴﻞ ﻓﻜﺮﺗﻬﺎ-: ﺗﻘﺴﻴﻢ اﻟﻘﺎﺋﻤﺔ اﻟﻰ ﻣﺴﺎﻓﺎت وهﻤﻴ ﺔ وﺗﺠ ﺮي ﻣﻘﺎرﻧ ﺔ ﻟﻜ ﻞ ﻋﻨ ﺼﺮﻳﻦ او اآﺜ ﺮ ﻟﻴ ﺴﺖ ﻣﺘﺠ ﺎورة واﻧﻤ ﺎ ﻣﺘﺒﺎﻋ ﺪة ﺑﻤ ﺴﺎﻓﺔ ﻣﺤ ﺪدة ﻣﻘ ﺪارهﺎ اﻟﻤ ﺴﺎﻓﺔ اﻟﻮهﻤﻴﺔ وهﻜﺬا ﻳﺘﻢ ﺗﻐﻴﺮ اﻟﻤﺴﺎﻓﺔ اﻟﻮهﻤﻴﺔ وﺗﺠﺮى ﻋﻤﻠﻴﺔ اﻟﻤﻘﺎرﻧﺔ واﻟﺘﻐﻴﺮ ﺣﺘﻰ ﺗﺘﺮﺗﺐ اﻟﻘﺎﺋﻤﺔ ﻣﺜﺎل -:رﺗﺐ ﻋﻨﺎﺻﺮ اﻟﻘﺎﺋﻤﺔ اﻟﺘﺎﻟﻴﺔ ﺑﺎﺳﺘﺨﺪام ﺗﺮﺗﻴﺐ ﺷﻴﻞ 66
11
54
93
41
5
17
ﺧﻄﻮات اﻟﺤﻞ-: ﻻ -:ﻧﺨﺘﺎر ﻣﺴﺎﻓﺔ وهﻤﻴﺔ ﻣﻘﺪرهﺎ او ً
Gap=4
وﻧﻀﻊ اﻟﻌﻨﺎﺻﺮ اﻻآﺒﺮ ﻋﻠﻰ ﺟﻬﺔ اﻟﻴﻤﻴﻦ واﻻﺻﻐﺮ ﻋﻠﻰ اﻟﻴﺴﺎر
4
43
ﺛﺎﻧﻴ ًﺎ -: -:ﻧﺨﺘﺎر ﻣﺴﺎﻓﺔ وهﻤﻴﺔ ﻣﻘﺪرهﺎ
66
11
54
93
41
5
17
43
66
11
54
93
41
5
17
43
66
11
54
93
41
5
17
43
66
11
54
93
41
5
17
43
Gap=2 66
11
54
93
41
5
17
43
66
93
54
43
41
11
17
5
66
93
54
43
Result
ﺛﺎﻟﺜ ًﺎ -: -:ﻧﺨﺘﺎر ﻣﺴﺎﻓﺔ وهﻤﻴﺔ ﻣﻘﺪرهﺎ
41
11
17
5
Gap=1 93
66
54
41
43
17
11
5
Quick Sort Algorithm ﺧﻮارزﻣﻴﺔ اﻟﺘﺮﺗﻴﺐ اﻟﺴﺮﻳﻊ ﻓﻜﺮﺗﻬﺎ-: اﺧﺘﻴﺎر ﻋﻨﺼﺮ ﻣﻦ ﻋﻨﺎﺻﺮ اﻟﻘﺎﺋﻤﺔ اﻟﻤﻌﻄﺎة ﻣﺜﻞ ) Xاﻻﻓﻀﻞ ان ﻳﻜﻮن اﻟﻌﻨﺼﺮ اﻟﻮﺳﻄﻲ( ﺛﻢ ﻧﺠﻌﻞ اﻟﻌﻨﺎﺻﺮ اﻟﺘﻲ ﻗﻴﻤﺘﻬﺎ اﻗ ﻞ ﻣ ﻦ xﻗﺒﻠ ﻪ ﻓ ﻲ اﻟﻘﺎﺋﻤﺔ اﻣﺎ اﻟﻌﻨﺎﺻﺮ اﻟﺘﻲ ﺗﻜﻮن ﻗﻴﻤﺘﻬﺎ اآﺒﺮ ﻣﻦ xﺑﻌﺪﻩ ﺛﻢ ﺗﺘﻢ ﻋﻤﻠﻴﺔ اﻟﻤﺴﺢ اﻟﺘﺼﺎﻋﺪي ﻟﻌﻨﺎﺻﺮ اﻟﻘﺎﺋﻤﺔ اﻟﺘﻲ ﺗﻘ ﻊ ﻗﺒ ﻞ اﻟﻌﻨ ﺼﺮ xﻓ ﺎذا وﺟ ﺪﻧﺎ ﻋﻨﺼﺮ اآﺒﺮ ﻣﻨﻪ ﻧﺤﺪدﻩ )أي ﻧﻀﻊ اﺷﺎرة( ﺛﻢ ﻧﻤﺴﺢ ﺗﻨﺎزﻟﻴًﺎ ﻋﻨﺎﺻﺮ اﻟﻘﺎﺋﻤﺔ اﻟﻮاﻗﻌﺔ ﺑﻌﺪ xﻓﺎن وﺟﺪﻧﺎ ﻋﻨﺼﺮ اﻗﻞ ﻣﻨﻪ ﻧﺤ ﺪدﻩ اﻳ ﻀًﺎ ﺛ ﻢ ﻧﺠ ﺮي ﻋﻤﻠﻴﺔ اﻟﺘﺒﺪﻳﻞ ﺑﻴﻨﻬﻤﺎ وﻧﺴﺘﻤﺮ ﺣﺘﻰ ﺗﺘﺮﺗﺐ اﻟﻘﺎﺋﻤﺔ. ﻣﺜﺎل -:رﺗﺐ ﻋﻨﺎﺻﺮ اﻟﻘﺎﺋﻤﺔ اﻟﺘﺎﻟﻴﺔ ﺑﺎﺳﺘﺨﺪام اﻟﺘﺮﺗﻴﺐ اﻟﺴﺮﻳﻊ 66
5
17
اﻻآﺒ ﺮ
41
93 X
5
11
54 اﻻﺻ ﻐﺮ
43
ﺧﻄﻮات اﻟﺤﻞ-: اﻟﻤﺮﺣﻠﺔ اﻻوﻟﻰ: X= 41
ﻻ -:ﻧﺨﺘﺎر او ً 41<66
اذن ﺗﺒﻘﻰ ﻣﻜﺎﻧﻬﺎ
41 rel="nofollow">5
اذن ﻧﻀﻊ اﺷﺎرة ﻋﻠﻰ اﻟـ 5
41<43اذن ﻧﻀﻊ اﺷﺎرة ﻋﻠﻰ اﻟـ 43 ﻧﺠﺮي ﻋﻤﻠﻴﺔ اﻟﺘﺒﺪﻳﻞ ﻓﺘﺼﺒﺢ اﻟﻘﺎﺋﻤﺔ هﻲ-: 66 41>17
اذن ﻧﻀﻊ اﺷﺎرة ﻋﻠﻰ اﻟـ 17
41<54
اذن ﻧﻀﻊ اﺷﺎرة ﻋﻠﻰ اﻟـ 54
43
17
93
11
41
5
54
ﻧﺠﺮي ﻋﻤﻠﻴﺔ اﻟﺘﺒﺪﻳﻞ ﻓﺘﺼﺒﺢ اﻟﻘﺎﺋﻤﺔ هﻲ-: 66 41<93
اذن ﺗﺒﻘﻰ ﻣﻜﺎﻧﻬﺎ
41>11
اذن ﺗﺒﻘﻰ ﻣﻜﺎﻧﻬﺎ
43
54
93
11
41
5
17
اﻟﻤﺮﺣﻠﺔ اﻟﺜﺎﻧﻴﺔ: ﻻ -:ﻧﺄﺧﺬ ﻗﺎﺋﻤﺔ اﻻﻋﺪاد اﻟﺘﻲ هﻲ اآﺒﺮ ﻣﻦ او ً
X
43
66
93
54
ا .ﻧﺨﺘﺎر ﻟﻬﺎ X=54
54<66
اذن ﺗﺒﻘﻰ ﻣﻜﺎﻧﻬﺎ
54>43
اذن ﻧﻀﻊ اﺷﺎرة ﻋﻠﻰ اﻟـ 43
54<93
اذن ﻧﻀﻊ اﺷﺎرة ﻋﻠﻰ اﻟـ 93 66
ﻧﺠﺮي ﻋﻤﻠﻴﺔ اﻟﺘﺒﺪﻳﻞ ﻓﺘﺼﺒﺢ اﻟﻘﺎﺋﻤﺔ هﻲ-: ب .ﻧﺨﺘﺎر
X=93
93
43
54
ﺑﺎﻟﻨﺴﺒﺔ اﻟﻰ اﻟﻘﺎﺋﻤﺔ 93
66 ﻓﺘﺼﺒﺢ اﻟﻘﻠﺌﻤﺔ -: 93
66
43
54
ﻧﻄﺒﻖ ﻧﻔﺲ اﻟﺨﻄﻮات ﺑﺎﻟﻨﺴﺒﺔ اﻟﻰ اﻟﻘﺎﺋﻤﺔ 11
6
17
5
-:ﻣﻼﺣﻈﺎت ﻋﺎﻣﺔ ﻋﻨﺪﻣﺎ ﻧﻀﻊ اﺷﺎرة ﻋﻠﻰ ﻋﻨﺼﺮ ﻓﺎﻧﻪ ﻳﻨﺘﻘﻞ اﻟﻰ اﻟﺠﻬﺔ اﻻﺧﺮى ﻣﻦ اﻟﻘﺎﺋﻤﺔ.1 ( 2N*Ln N
) ﻳﻜﻮن اآﺒﺮ ﻋﺪد ﻣﻦ اﻟﻤﻘﺎرﻧﺎت اﻟﻰ هﺬﻩ اﻟﻄﺮﻳﻘﺔ هﻮ.2
هﺬﻩ اﻟﻄﺮﻳﻘﺔ ﺗﻜﻮن ﻣﻔﻴﺪة اﻟﻰ ﻟﻠﻘﻮاﺋﻢ اﻟﺘﻲ ﺗﻜﻮن ﻏﻴﺮ ﻣﺮﺗﺒﺔ اﻟﻰ ﺣﺪ آﺒﻴﺮ وﻏﻴﺮ ﻋﻤﻠﻴﺔ ﻟﻠﻘﻮاﺋﻢ ﺷﺒﻪ اﻟﻤﺮﺗﺒﺔ.3 Public sub Quicksort(byref list as string, byref F as integer, byref L as integer ) Dim I as integer Dim j as integer Dim x as integer{or any other type} I=f J=L X=list((i+j) / 2) Repeat While list(i)<x do i=i+1 While x< list(j) do j=j+1 If i<=j then Swap(list(i),list(j)) I=i+1 J=j+1 End if Loop untie i<j If f<j then Quicksort(list,f,j) End if If i
7
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