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Merge Sort ֲࢸݢʢKuoE0ʣ [email protected] KuoE0.ch

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Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) http://creativecommons.org/licenses/by-sa/3.0/ Latest update: Mar 6, 2013

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Traditional Merge Sort

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Algorithm ࠾༻ divide & conquer ࡦུ

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Divide ሡᙛલᏐྻሣ൒੾ׂᬇ᫮ਐߦ ௚౸ᷮႫҰݸݩૉ

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2 9 4 3 8 7 5 1 6 2 9 4 3 8 7 5 1 6 2 9 4 3 8 7 5 1 6 2 9 4 8 3 5 7 6 1 9 2

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Conquer 1. ར༻ၷݸࢦඪࢦ޲ၷݸ༗ংᏐྻ A ᢛ B 2. ൺֱࢦඪࢦ޲తᏐ值 3. ሡֱখతᏐ值์ೖ৽తᏐྻ Cɼฒሡ֘ࢦඪ ࢦ޲ԼҰᏐ值 4. ௚౸๭Ұࢦඪࢦ޲Ꮠྻ݁ඌɼሡ㠥ҰᏐྻႫ ᰨతᏐ值์౎ೖᏐྻ C

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Merge Two Sequence 9 8 7 6 5 4 3 2 1

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Merge Two Sequence 9 8 7 6 5 4 3 2 1

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Merge Two Sequence 9 8 7 6 5 4 3 2 1

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Merge Two Sequence 9 8 7 6 5 4 3 2 1

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Merge Two Sequence 9 8 7 6 5 4 3 2 1

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Merge Two Sequence 9 8 7 6 5 4 3 2 1

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Merge Two Sequence 9 8 7 6 5 4 3 2 1

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Merge Two Sequence 9 8 7 6 5 4 3 2 1

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Merge Two Sequence 9 8 7 6 5 4 3 2 1

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Merge Two Sequence 9 8 7 6 5 4 3 2 1

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1 2 3 4 5 6 7 8 9 2 3 4 8 9 1 5 6 7 2 4 9 3 8 5 7 1 6 2 9 4 8 3 5 7 6 1 9 2

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Natural Merge Sort

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Key Point ར༻Ꮠྻதత༗ংᏐྻยஈɼҎݮগ੾ׂ࣍Ꮠʂ

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༗ংᏐྻยஈ 1 3 4 2 7 9 8 0 5 1 3 4 2 7 9 8 0 5

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How to Divide 1 3 4 2 7 9 8 0 5 A B

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4 2

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4 2

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4 2 7

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4 2 7

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4 2 7 9

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4 2 7 9

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4 2 7 9 2 7 9

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4 2 7 9 2 7 9 8

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4 2 7 9 2 7 9 8

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4 2 7 9 2 7 9 8 8

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4 2 7 9 2 7 9 8 8 0

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4 2 7 9 2 7 9 8 8 0

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4 2 7 9 2 7 9 8 8 0 5

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4 2 7 9 2 7 9 8 8 0 5

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How to Divide 1 3 4 2 7 9 8 0 5 A B 1 3 4 1 3 4 2 7 9 2 7 9 8 8 0 5 0 5

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The merge operation is as same as traditional merge sort.

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