a
À¡ ‘÷‚“
(40-354) ‘ûݵþ¤Úó ۃܽ— ø üŸÂÏ
Design and Analysis of Algorithms
—ƒ³õ‘î ü¨À€úõ ýùÀØÈ÷¢
ü¨Àì ÀÞ½õ :§¤Àõ
‘ûݵþ¤Úó ü÷‘±õ ø ‘û¤‘µ¡‘¨ù¢¢ :¥‘ƒ÷ǃ•
3 :ÀŸø ¢Àã—
§¤¢ ¢õ þ¤
–‘ƒÜî
1
.À÷ªüõ ‚µÔð Óܵ¿õ Ûþ‘Æõ ۟ ýÂ“ ¤‘î ø âþ¨ ý‘ûݵþ¤Úó ۃܽ— ø üŸÂÏ Óܵ¿õ ý‘û©ø¤ §¤¢ ßþ ¤¢
.¢ªüõ Àƒî‘— ‘ûݵþ¤Úó ۃܽ— ø üµ¨¤¢ –‘±™ ø °¨‘€õ ý‘û¤‘µ¡‘¨ù¢¢ ¥ ù¢‘Ôµ¨ “ °ó‘Îõ ý‚Ž¤ ¤¢
⛐Âõ
2
1. T. Cormen, C. Leiserson, R. Riverst, and C. Stein (CLRS) Introduction to Algorithms, MIT Press,
Sept. 3rd Edition, 2009.
(üܬ â›Âõ)
2. Jon Kleinberg, Eva Tardos, Algorithm Design, Addison Wesley, 2005. (üØÞî
’‘µî)
3. Udi Manber, Introduction to Algorithms: A Creative Approach, Addison Wesley, 1989.
(üØÞî ’‘µî)
¢õ þ¤
3
–‘õÀÖõ (1
amortized analysis ü€ØªÂ¨
ۃܽ— (2
‘ûݵþ¤Úó üŸÂÏ ý‘û©ø¤ (3
(ü΃½õ ýùÂþ¢ ßþ—םî ,¤Æ÷‘¨ ,¤úÈõ ýù¤‘µ¨ ,ýÂð Àî) ǑÂÖµ¨ §‘¨ “
⊳
‘ûÅþ—‘õ ’® ,‘ûý‚ÜޛÀ€ ’® ,¯‘Ö÷ ßþ—×þ¢÷ ,‘û©Â¡ö‘Þ¨ ,‘ûý¥‘“ ´€Þ÷¤—) ۟ ø ݃Æ֗
⊳
(¥‘¨°—Âõ ý‘û‚رª ,âþ¨ ý‚þ¤ê ÛþÀ±— ,(ߨÂµ¨)
(‚€ƒÞî ý›ø´Æ› üþø¢ø¢ ´¡¤¢ ,üµÈ•‚óî ,ýÀ€“éÂ𐤑• ,LCS Ûþ‘Æõ ,‘ûÅþ—‘õ ’®) ‘þ•
⊳
(ßÞê‘û Àî ,ñ• ö¢Âî¢Â¡ ,ýÀ€“ö‘õ¥ Ûþ‘Æõ) ‚÷‘ÊþŸ
⊳
À Ÿø’‘ ã È ÷ ,α-β §Â Ÿ ,ý¥‘ “ ´ ¡¤¢ ,(backtracking) ¢Â ðÅ • ©ø¤ :Û õ‘ î ý ›ø´ Æ ›
⊳
.(¢Âðù¤ø¢ ýùÀ€ªøÂê ý‚ÜÿÆõ) (Branch-and-Bound)
éÂð ý‘ûݵþ¤Úó (4
ñø-¼Î¨ ,ñø-ÕÞä –¤¬‚“ éÂð ý›ø´Æ›
⊳
À€±Þûø¢ ý› ,À€±Þû ý› ,¤ø¢ ßµê‘þ ,(topological) üîó•— ý¥‘¨°—Âõ
⊳
1
(Kruskal ø
Prim ý‘ûݵþ¤Úó)
Floyd ø Dijkstra ,Bellman-Ford ý‘ûݵþ¤Úó
(Edmond-Karp ø
‚€ƒÞî ƒðÂê ´¡¤¢
⊳
:éÂ𠤢 ‘ûƒÆõ ßþ—ù‘—î
⊳
Ford-Fulkerson ý‘ûݵþ¤Úó)
(string
¤‘ª ý‘û‚رª
matching)
⊳
‘û‚µª¤ Փ‘Η (5
‘Þ—-ü•ö Ûþ‘Æõ (6
,ü ÷ µ Ü ƒ Þ û ¤ø¢ ,Clique ,Vertex-Cover ,3D-matching ,3-Sat) ü Ü ¬ Û þ‘ Æ õ ,‘ Þ —-ü •ö ý‚ þÂ Ñ ÷ ,–‘ õÀ Ö õ
.‘ûݵþ¤Úó ۃܽ— ýÂ“ ၮõ ßþ ¥ ù¢‘Ôµ¨ ,‚ÜÿÆõ ×þ ö¢“ ‘Þ—-ü•ö –‘±™ ý‘û©ø¤ (,¥Âê
ùø• ,öõ¥ ,ßþÂޗ
Àþ‘“ ‘Þª .¢ªüõ ù¢¢ üÆþ÷‚õ‘÷“ ßþÂޗ ×þ ‚µÔû‚¨ Âû ø ü±µî ßþÂޗ ×þ ‚µÔû ø¢ Âû ‘f ±þÂ֗ §¤¢ ßþ ¤¢
ßþ ý‘û‚ÜÿÆõ ¥ ý¢À㗠,‘û×÷õ¥ ¤¢ .´Æƒ÷ ý¤ø® ‘ûö ý‚Þû Ûþ½— üóø Àƒ€î ۟ ¤ ü±µî ý‘ûßþÂޗ
.Àƒ€î ۟ ‚î À÷ªüõ ’‘¿µ÷ ‘ûßþÂޗ
ùÂÞ÷ 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Àƒû¢ Ûþ½— Àþ‘“ ‚î ü±µî ßþÂޗ 2
•
ùÂÞ÷ 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ‘ûßþÂޗ ¤¢ ùÀª ù¢¢ ێ‘Æõ ¥ ×÷õ¥ 3
•
ùÂÞ÷ 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . üÆþ÷‚õ‘÷“ ßþÂޗ 4
•
(‚ê‘® ùÂÞ÷ 1 ·îÀŸ ,‚±—¤ ‚“ ‚µÆ“) ùÂÞ÷ 2 ‘— 1
ü¨ý ×±¨ ‚“ üÆþ÷‚õ‘÷“ ‚Ö“‘Æõ ×þ
•
(ùÂÞ÷ 4 —‚“ öõ¥) ùÂÞ÷ 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . —ö‘ƒõ öõ¥ ¢Àä 2
•
ùÂÞ÷ 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . üþ‘ú÷ öõ¥
•
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ß þ ùÂ Þ ÷ 16 ¥ ùÂ Þ ÷ 8 Û ìÀ Ÿ ° Æ î ü ó ± ì ¯Â ª .´ ¨‘ ûö õ¥ ý‘ ûùÂ Þ ÷ §¤¢ ß þ ¤¢ ü ó ± ì í… õ :‚ › —
.´¨‘ûöõ¥
2