constraint that the total weight is smaller than $19$.

![\[fi:figure 1\] The initial state of the graph.](graph01.png)

The vertices are drawn with the squares around them, and vertices in $A$ have the labels initially set to $19$. Figure \[fi:figure 1\] contains the time and weight values for each of the edges. The time parameter is written in the square of lighter color, while the weight parameter is in the central square of each edge.

Active vertices are of blue color and edges adjacent to them are painted in blue. They are considered active and the source of water flowing through the edge is written next to the central square of each active edge. For example, the vertex $2$ is the source of the flow that goes through the edge $(2,5)$.

Notice that the smallest time component of all active edges is $2$. The first cycle of the algorithm begins by decreasing the time component of each active edge by $2$. The edge $(1,4)$ becomes [*just used*]{} because its time component is decreased to $0$. The water now flows from the vertex $1$ to the vertex $4$ and its quality decreases by $5$, since the weight of the edge $(1,4)$ is 