[atAGC046E]Permutation Cover

【[atAGC046E]Permutation Cover】的更多相关文章

[atAGC046E]Permutation Cover

每一个点都在一个排列中等价于所有排列覆盖所有位置有解当且仅当满足$a_{y}\le 2a_{x}$(其中$a_{x}$为$a_{i}$的最小值,$a_{y}$为$a_{i}$的最大值) 证明:贪心选择排列覆盖,即令$r'=与[1,r]有交的排列中最大的右端点+1$(初始$r=1$,若$r=r'$则不合法),令以此法选出的排列总数为$s$,以下证明$a_{y}\le s\le 2a_{x}$ 对于每一个$p_{i}=x$,包含$i$的排列最多有两个,那么包含$x$的排列数最多为$2x$,同时一个…

Dancing Links and Exact Cover

1. Exact Cover Problem DLX是用来解决精确覆盖问题行之有效的算法. 在讲解DLX之前,我们先了解一下什么是精确覆盖问题(Exact Cover Problem)? 1.1 Polyomino 多联骨牌(Polyomino)是一种类似于七巧板的棋盘游戏: 如下图所示,除去中间$4$个方格不允许放置任何东西,这个棋盘总共有$8*8-4=60$个方格将这$12$个由$5$个方格组成的图形全部放入到棋盘中,满足每个格子都被使用,而且只被使用一次. 每个格子都被覆…

Permutation Sequence

The set [1,2,3,-,n] contains a total of n! unique permutations. By listing and labeling all of the permutations in order,We get the following sequence (ie, for n = 3): "123" "132" "213" "231" "312" "3…

[LeetCode] Palindrome Permutation II 回文全排列之二

Given a string s, return all the palindromic permutations (without duplicates) of it. Return an empty list if no palindromic permutation could be form. For example: Given s = "aabb", return ["abba", "baab"]. Given s = "a…

[LeetCode] Palindrome Permutation 回文全排列

Given a string, determine if a permutation of the string could form a palindrome. For example,"code" -> False, "aab" -> True, "carerac" -> True. Hint: Consider the palindromes of odd vs even length. What difference d…

[LeetCode] Permutation Sequence 序列排序

The set [1,2,3,…,n] contains a total of n! unique permutations. By listing and labeling all of the permutations in order,We get the following sequence (ie, for n = 3): "123" "132" "213" "231" "312" "3…

[LeetCode] Next Permutation 下一个排列

Implement next permutation, which rearranges numbers into the lexicographically next greater permutation of numbers. If such arrangement is not possible, it must rearrange it as the lowest possible order (ie, sorted in ascending order). The replaceme…