A9300. Fox and Minimal path
编程题
普及/提高-
知识点
题目描述
Fox Ciel wants to write a task for a programming contest. The task is: "You are given a simple undirected graph with $n$ vertexes. Each its edge has unit length. You should calculate the number of shortest paths between vertex 1 and vertex 2."
Same with some writers, she wants to make an example with some certain output: for example, her birthday or the number of her boyfriend. Can you help her to make a test case with answer equal exactly to $k$ ?
Same with some writers, she wants to make an example with some certain output: for example, her birthday or the number of her boyfriend. Can you help her to make a test case with answer equal exactly to $k$ ?
输入格式
The first line contains a single integer $k$ ( $1<=k<=10^{9}$ ).
输出格式
You should output a graph $G$ with $n$ vertexes ( $2<=n<=1000$ ). There must be exactly $k$ shortest paths between vertex 1 and vertex 2 of the graph.
The first line must contain an integer $n$ . Then adjacency matrix $G$ with $n$ rows and $n$ columns must follow. Each element of the matrix must be 'N' or 'Y'. If $G_{ij}$ is 'Y', then graph $G$ has a edge connecting vertex $i$ and vertex $j$ . Consider the graph vertexes are numbered from 1 to $n$ .
The graph must be undirected and simple: $G_{ii}$ = 'N' and $G_{ij}=G_{ji}$ must hold. And there must be at least one path between vertex 1 and vertex 2. It's guaranteed that the answer exists. If there multiple correct answers, you can output any of them.
The first line must contain an integer $n$ . Then adjacency matrix $G$ with $n$ rows and $n$ columns must follow. Each element of the matrix must be 'N' or 'Y'. If $G_{ij}$ is 'Y', then graph $G$ has a edge connecting vertex $i$ and vertex $j$ . Consider the graph vertexes are numbered from 1 to $n$ .
The graph must be undirected and simple: $G_{ii}$ = 'N' and $G_{ij}=G_{ji}$ must hold. And there must be at least one path between vertex 1 and vertex 2. It's guaranteed that the answer exists. If there multiple correct answers, you can output any of them.
输入输出样例
输入 #1
2
输出 #1
4 NNYY NNYY YYNN YYNN
输入 #2
9
输出 #2
8 NNYYYNNN NNNNNYYY YNNNNYYY YNNNNYYY YNNNNYYY NYYYYNNN NYYYYNNN NYYYYNNN
输入 #3
1
输出 #3
2 NY YN
说明/提示
In first example, there are 2 shortest paths: 1-3-2 and 1-4-2.
In second example, there are 9 shortest paths: 1-3-6-2, 1-3-7-2, 1-3-8-2, 1-4-6-2, 1-4-7-2, 1-4-8-2, 1-5-6-2, 1-5-7-2, 1-5-8-2.
In second example, there are 9 shortest paths: 1-3-6-2, 1-3-7-2, 1-3-8-2, 1-4-6-2, 1-4-7-2, 1-4-8-2, 1-5-6-2, 1-5-7-2, 1-5-8-2.