R - discrete colours for continuous data in ggplot

I'm trying to plot some time-continuous data. I have applied a simple algorithm that assigns a discrete number (state) to each row of the data. It looks something like this.

time   flow    pre    state
0.0    0.0     3      1
0.2    0.01    4      1
0.4    0.10    10     2
0.6   -0.11    -2     0      # Set as NA in the example below

Now, I want to plot for instance flow (using ggplot) and have state determine the colour. Problem is, if I do

ggplot(data) +
  geom_line(aes(x = time, y = flow, color = state))

The plot has too little contrast in the colours to easily differentiate state. But if I do

ggplot(data) +
  geom_line(aes(x = time, y = flow, color = factor(state))) +
  scale_color_manual(values = c("red", "green", "blue"))

it splits the lines and they appear as three different lines. What I would like to is to use the continuous scale, but add one or several intermediate colours for contrast. Current solution is this

ggplot(data = alg1) +
  geom_line(aes(x = time, y = flow, colour = state)) +
  scale_color_gradient(low = "#0000FF", high = "#FF0000",
                       na.value = "#00FF00", guide = "legend")

But this 1) only works for three states, and one of them has to be NA, 2) excludes one state (NA) from legend and 3) displays not-used values in legend.

Image produced by current code: