 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 simpleyes'' or
no'' answer are called decision problems. One class of decision problems, the NPcomplete 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 timeconsuming).This problem involves determining the number of routes available to an emergency vehicle operating in a city of oneway streets.
Given the intersections connected by oneway 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 oneway streets connecting two intersections.
Intersections are identified by nonnegative integers. A oneway street is specified by a pair of intersections. For example, j k indicates that there is a oneway street from intersection j to intersection k. Note that twoway streets can be modeled by specifying two oneway streets: j k and k j .
Consider a city of four intersections connected by the following oneway streets:
0 1
0 2
1 2
2 3There is one route from intersection 0 to 1, two routes from 0 to 2 (the routes are 012 and 02 ), 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 023232 is a different route than 0232 .Input
The input is a sequence of city specifications. Each specification begins with the number of oneway streets in the city followed by that many oneway streets given as pairs of intersections. Each pair j k represents a oneway 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 endoffile.There will never be a oneway 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 rowmajor 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 1Sample 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