Codeforces Round #245 (Div. 2)D（树的性质+状压+dfs）_html/css_WEB-ITnose

E. Guess the Tree

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

iahub and iahubina went to a picnic in a forest full of trees. less than 5 minutes passed before iahub remembered of trees from programming. moreover, he invented a new problem and iahubina has to solve it, otherwise iahub won't give her the food.

Iahub asks Iahubina: can you build a rooted tree, such that

each internal node (a node with at least one son) has at least two sons;

node i has ci nodes in its subtree?

Iahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.

Input

The first line of the input contains integer n (1?≤?n?≤?24). Next line contains n positive integers: the i-th number represents ci (1?≤?ci?≤?n).

DALL·E 2

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Output

Output on the first line "YES" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output "NO" (without quotes).

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Sample test(s)

input

41 1 1 4

output

YES

input

51 1 5 2 1

output

NO

题意：RT

思路：首先注意，根据每个点至少有两个孩子这个性质可以知道，为1的点的数量一定会>=n/2

            所以24个点的状态就减少为12个点的状态，敲好可以状压

            只考虑不为1的点，先按降序排序，然后一个一个选孩子，如果已经轮到i来选孩子，先检查它自己有没有被前面的点选为孩子，

            如果没有选，则不需要继续了，因为它不可能有父亲了

           如果选了，则继续为i选2个或以上的孩子，选过的点标记一下就可以了

           整个过程用递归算就可以了

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