首页 > ACM题库 > HDU-杭电 > hdu 4795 Easy Problem Once More待解决[解题报告]C++
2015
09-18

hdu 4795 Easy Problem Once More待解决[解题报告]C++

Easy Problem Once More

问题描述 :

Define matrix Arnold , if for every m(1 ≤ m ≤ n),
Arnold
then matrix A can be called as partially negative matrix. Here matrix
Arnold, and {i1,..,im} is a sub set of {1,..,n}.If you are not familiar with determinant of a matrix, please read the Note part of this problem.
For example, matrix Arnold is a partially negative matrix because |-2|, |-6| andArnoldare negative.
A symmetric matrix is a square matrix that equals to its transpose. Formally, matrix A is symmetric if A = AT. For example, Arnold is a symmetric matrix.
Given two N-dimensional vector x and b, and we guarantee that there will be at least
one 0 value in vector b. You task is to judge if there exists a symmetric partially
negative matrix A, which fulfills Ax = b.

输入:

There are several test cases. Proceed to the end of file.
Each test case is described in three lines.
The first line contains one integer N (2 ≤ N ≤ 100000) .
The second line contains N integers xi (-1000000 < xi < 1000000, 1 ≤ i ≤ N), which is vector x.
The third line contains N integers bi (-1000000 < bi < 1000000, 1 ≤ i ≤ N), which is vector b. There will be at least one bi which equals to zero.

输出:

There are several test cases. Proceed to the end of file.
Each test case is described in three lines.
The first line contains one integer N (2 ≤ N ≤ 100000) .
The second line contains N integers xi (-1000000 < xi < 1000000, 1 ≤ i ≤ N), which is vector x.
The third line contains N integers bi (-1000000 < bi < 1000000, 1 ≤ i ≤ N), which is vector b. There will be at least one bi which equals to zero.

样例输入:

2
2 1
0 6

样例输出:

Yes
Hint
There exists a symmetric partially negative matrix Arnold Arnold Note Determinant of an n × n matrix A is defined as below: Arnold Here the sum is computed over all permutations σ of the set {1, 2, ..., n}. A permutation is a function that reorders this set of integers. The value in the ith position after the reordering σ is denoted σi. For example, for n = 3, the original sequence 1, 2, 3 might be reordered to σ = [2, 3, 1],with σ[sub]1[/sub] = 2, σ[sub]2[/sub] = 3, and σ[sub]3[/sub] = 1. The set of all such permutations (also known as the symmetric group on n elements) is denoted Sn. For each permutation σ, sgn(σ) denotes the signature of σ, a value that is +1 whenever the reordering given by σ can be achieved by successively interchanging two entries an even number of times, and −1 whenever it can be achieved by an odd number of such interchanges.