there is path from vi to vk and path from vk to vj where all the nodes use vk- thereforepk- [ ][ and pk- [ ][ hencethe path matrix pn can be calculated with the formula given aspk[ ][jpk- [ ][jv (pk- [ ][kl pk- [ ][ ]where indicates logical or operation and indicates logical and operation figure shows the warshall' algorithm to find the path matrix using the adjacency matrix step [initialize the path matrixrepeat step for to - where is the number of nodes in the graph step repeat step for to - step if [ ][jthen set [ ][jelse [ ][ [end of loop[end of loopstep [calculate the path matrix prepeat step for to - step repeat step for to - step repeat step for jto - step set pk[ ][jpk- [ ][jv (pk- [ ][kl pk- [ ][ ]step exit figure warshall' algorithm example consider the graph in fig and its adjacency matrix we can straightaway calculate the path matrix using the warshall' algorithm the path matrix can be given in single step asa ae ~ bcd figure graph and its path matrix thuswe see that calculating aa to calculate is very slow and inefficient technique as compared to the warshall' technique programming exam write program to implement warshall' algorithm to find the path matrix #include #include void read (int mat[ ][ ]int )void display (int mat[ ][ ]int )void mul(int mat[ ][ ]int )int main(int adj[ ][ ] [ ][ ]nijkclrscr()