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算法练习(51): 栈的可生成性问题中禁止出现的排列(1.3.46)

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kyson老师
2017.11.18 00:21* 字数 379

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算法(第4版)

知识点

  • 栈的可生成性问题中禁止出现的排列

题目

1.3.46 栈的可生成性问题中禁止出现的排列。若三元组 (a, b, c) 中 a<b<c 且 c 最先被弹出,a 第二,b 第三(c 和 a 以及 a 和 b 之间可以间隔其他整数),那么当且仅当排列中不含这样的三元组时(如上题所述的)栈才可能生成它。


1.3.46 Forbidden triple for stack generability. Prove that a permutation can be gener- ated by a stack (as in the previous question) if and only if it has no forbidden triple (a, b, c) such that a < b < c with c first, a second, and b third (possibly with other intervening integers between c and a and between a and b).
Partial solution: Suppose that there is a forbidden triple (a, b, c). Item c is popped before a and b, but a and b are pushed before c. Thus, when c is pushed, both a and b are on the stack. Therefore, a cannot be popped before b.

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