Backtracking

陳鵬宇 (float)<float.tw@gmail.com>

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Backtracking● 概念

– 枚舉所有可能性

● 排列、組合

Example● 1, 2, 3 的所有排列

Example● 第一格目前可以選 : 1, 2, 3

Example● 第二格目前可以選 : 2, 3

1

1

Example● 第三格目前可以選 : 3

1

1 2

1 2

Example● 找到第一個組合 :1-2-3

1

1 2

1 2 3

Example● 往回走，第三格可以選 : 3

1

1 2

1 2 3

Example● 3 已經選過，再往回，第二格可以選 :2, 3

1

1 2

1 2 3

Example● 3 已經選過，再往回，第二格可以選 :2, 3

1

1 2

1 2 3

Example● 2 已經選過，選 3

1

1 2

1 2 3

1 3

Example● 後略 ...

1

1 2

1 2 3

1 3

1 3 2

Example

1

1 2

1 2 3

1 3

1 3 2

Example● 1, 2, 3 的所有組合

1 2 3

Example

1 2 3

1 2 3

1 2 3

Example

1 2 3

1 2 3

1 2 3 1 2 3

Example

1 2 3

1 2 3

1 2 3 1 2 3

1 2 3

1 2 3 1 2 3

Practice

UVa - 441

8 Queen Problem● 問題：在 8x8 的西洋棋棋盤上擺放八隻皇后，

讓他們恰好無法互相攻擊對方。● 組合

● Uva - 750

Sudoku● 數獨：行、列、方格內不可重復● 排列

● UVa - 989

剪支● 在完成遞迴條件前檢查是否可能為答案

– Ex. 組合遞增數列

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Thank You for Your Listening.