Kuntal Majumder - 6 months ago 43

C++ Question

Recently I came across this problem in the Iarcs website. Here is the problem statement:

It is well known that the routing algorithm used on the Internet is

highly non-optimal. A "hop", in Internet jargon, is a pair of nodes

that are directly connected - by a cable or a microwave link or

whatever. The number of hops that a packet may take in going from one

node to another may be far more than the minimum required.

But the routing algorithm used by the Siruseri Network company is

worse. Here, a packet sent from one node to another could even go

through the same node twice or even traverse the same hop twice before

it eventually finds its way to its destination. Sometimes a packet

even goes through the destination more than once before it is

considered "delivered". Suppose the network in Siruseri consisted of

the following nodes and cables: Figure

There are 5 nodes and 8 cable links. Note that a pair of nodes may be

connected by more than one link. These are considered to be different

hops. All links are bidirectional. A packet from node 1 to node 5 may,

for example, travel as follows: 1 to 2, 2 to 1, 1 to 3, 3 to 2, 2 to

1, 1 to 4, 4 to 5, 5 to 4, 4 to 5. This routing is of length 9 (the

number of hops is the length of a given routing). We are interested in

counting the number of different routings from a given source to a

target that are of a given length.

For example, the number of routings from 1 to 2 of length 3 are 7.

They are as follows (separated by ;): 1 to 2, 2 to 1 and 1 to 2; 1 to

3, 3 to 1 and 1 to 2; 1 to 4, 4 to 1 and 1 to 2; 1 to 5, 5 to 1 and 1

to 2; 1 to 4, 4 to 3 (via the left cable) and 3 to 2; 1 to 4, 4 to 3

(via the right cable) and 3 to 2; 1 to 2, 2 to 3 and 3 to 2.

You will be given a description of the network at Siruseri as well as

a source, a target and the number of hops, and your task is to

determine the number of routings from the source to the target which

have the given number of hops. The answer is to be reported modulo

42373.

So as discussed on this thread , the solution is to calculate the given matrix to the power k where k is the number of routes given.

Here I did the same:

`#include <iostream>`

#include <vector>

std::vector<std::vector<int> >MatrixMultiplication(std::vector<std::vector<int> >matrix1,std::vector<std::vector<int> >matrix2,int n){

std::vector<std::vector<int> >retMatrix(n,std::vector<int>(n));

for(int i=0;i<n;i++){

for(int j=0;j<n;j++){

for(int k=0;k<n;k++){

retMatrix[i][j] = retMatrix[i][j] + matrix1[i][k] * matrix2[k][j];

}

}

}

return retMatrix;

}

std::vector<std::vector<int> >MatrixExponentiation(std::vector<std::vector<int> >matrix,int n,int power){

if(power == 0 || power == 1){

return matrix;

}

if(power%2 == 0){

return MatrixExponentiation(MatrixMultiplication(matrix,matrix,n),n,power/2);

}else{

return MatrixMultiplication(matrix,MatrixExponentiation(MatrixMultiplication(matrix,matrix,n),n,(power-1)/2),n);

}

}

int main (int argc, char const* argv[])

{

int n;

std::cin >> n;

std::vector<std::vector<int> >matrix(n,std::vector<int>(n));

for(int i=0;i<n;i++){

for(int j=0;j<n;j++){

std::cin >> matrix[i][j];

}

}

int i ,j ,power;

std::cin >> i >> j >> power;

std::vector<std::vector<int> >retMax(n,std::vector<int>(n));

retMax = MatrixExponentiation(matrix,n,power);

std::cout << matrix[i-1][j-1] << std::endl;

return 0;

}

But the output doesnt matches even for the example case , am I missing something here , or I have to try another approach for this problem?

`if(power == 0){`

std::vector<std::vector<int> >retMatrix(n,std::vector<int>(n));

for(int i=0;i<n;i++){

retMatrix[i][i] = 1;

}

return retMatrix;

}

Answer

I think you are just printing out the wrong value, change:

```
std::cout << matrix[i-1][j-1] << std::endl;
```

to

```
std::cout << retMax [i-1][j-1] << std::endl;
```