# 矩阵数字的一个路径的算法，怎么利用C语言编写程序的方式实现的

Problem Description

Problems that process input and generate a simple `yes'' or`

no'' answer are called decision problems. One class of decision problems, the NP-complete problems, are not amenable to general efficient solutions. Other problems may be simple as decision problems, but enumerating all possible ``yes'' answers may be very difficult (or at least time-consuming).

This problem involves determining the number of routes available to an emergency vehicle operating in a city of one-way streets.

Given the intersections connected by one-way streets in a city, you are to write a program that determines the number of different routes between each intersection. A route is a sequence of one-way streets connecting two intersections.

Intersections are identified by non-negative integers. A one-way street is specified by a pair of intersections. For example, j k indicates that there is a one-way street from intersection j to intersection k. Note that two-way streets can be modeled by specifying two one-way streets: j k and k j .

Consider a city of four intersections connected by the following one-way streets:

0 1

0 2

1 2

2 3

There is one route from intersection 0 to 1, two routes from 0 to 2 (the routes are 0-1-2 and 0-2 ), two routes from 0 to 3, one route from 1 to 2, one route from 1 to 3, one route from 2 to 3, and no other routes.

It is possible for an infinite number of different routes to exist. For example if the intersections above are augmented by the street , there is still only one route from 0 to 1, but there are infinitely many different routes from 0 to 2. This is because the street from 2 to 3 and back to 2 can be repeated yielding a different sequence of streets and hence a different route. Thus the route 0-2-3-2-3-2 is a different route than 0-2-3-2 .

Input

The input is a sequence of city specifications. Each specification begins with the number of one-way streets in the city followed by that many one-way streets given as pairs of intersections. Each pair j k represents a one-way street from intersection j to intersection k. In all cities, intersections are numbered sequentially from 0 to the ``largest'' intersection. All integers in the input are separated by whitespace. The input is terminated by end-of-file.

There will never be a one-way street from an intersection to itself. No city will have more than 30 intersections.

Output

For each city specification, a square matrix of the number of different routes from intersection j to intersection k is printed. If the matrix is denoted M, then M[j][k] is the number of different routes from intersection j to intersection k. The matrix M should be printed in row-major order, one row per line. Each matrix should be preceded by the string ``matrix for city k'' (with k appropriately instantiated, beginning with 0).

If there are an infinite number of different paths between two intersections a -1 should be printed. DO NOT worry about justifying and aligning the output of each matrix. All entries in a row should be separated by whitespace.

Sample Input

7 0 1 0 2 0 4 2 4 2 3 3 1 4 3

5

0 2

0 1 1 5 2 5 2 1

9

0 1 0 2 0 3

0 4 1 4 2 1

2 0

3 0

3 1

Sample Output

matrix for city 0

0 4 1 3 2

0 0 0 0 0

0 2 0 2 1

0 1 0 0 0

0 1 0 1 0

matrix for city 1

0 2 1 0 0 3

0 0 0 0 0 1

0 1 0 0 0 2

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

matrix for city 2

-1 -1 -1 -1 -1

0 0 0 0 1

-1 -1 -1 -1 -1

-1 -1 -1 -1 -1

0 0 0 0 0

###### 编程介的小学生

2019/03/20 22:11- Golang
- r语言
- erlang

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