Constructing Shortest Path

• Want predecessor matrix $\Pi$
• Can compute $\Pi$ from final D matrix, or
• Can compute as you go
  
  $$\pi_{ij}^{(0)} \;=\; \left\{ \begin{array}{ccccc} {\rm NIL} &... ...} & i \neq j & {\rm and} & w_{ij} < \infty \end{array} \right.$$
  
  
  
  
  $$\pi_{ij}^{(k)} \;=\; \left\{ \begin{array}{ccc} \pi_{ij}^{(k-... ...rm otherwise} & (i \leadsto k \leadsto j) \end{array} \right.$$