ggplot2 legend to bottom and horizontal

How can I move a ggplot2 legend to the bottom of the plot and turn it horizontally?

Sample code:

library(reshape2) # for melt
df <- melt(outer(1:4, 1:4), varnames = c("X1", "X2"))
p1 <- ggplot(df, aes(X1, X2)) + geom_tile(aes(fill = value))
p1 + scale_fill_continuous(guide = guide_legend())

Desired (approximate) outcome:

If you want to move the position of the legend please use the following code:

library(reshape2) # for melt
df <- melt(outer(1:4, 1:4), varnames = c("X1", "X2"))
p1 <- ggplot(df, aes(X1, X2)) + geom_tile(aes(fill = value))
p1 + scale_fill_continuous(guide = guide_legend()) +
    theme(legend.position="bottom")

This should give you the desired result.

Here is how to create the desired outcome:

library(reshape2); library(tidyverse)
melt(outer(1:4, 1:4), varnames = c("X1", "X2")) %>%
ggplot() + 
  geom_tile(aes(X1, X2, fill = value)) + 
  scale_fill_continuous(guide = guide_legend()) +
  theme(legend.position="bottom",
        legend.spacing.x = unit(0, 'cm'))+
  guides(fill = guide_legend(label.position = "bottom"))

^{Created on 2019-12-07 by the reprex package (v0.3.0)}

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Edit: no need for these imperfect options anymore, but I'm leaving them here for reference.

Two imperfect options that don't give you exactly what you were asking for, but pretty close (will at least put the colours together).

library(reshape2); library(tidyverse)
df <- melt(outer(1:4, 1:4), varnames = c("X1", "X2"))
p1 <- ggplot(df, aes(X1, X2)) + geom_tile(aes(fill = value))
p1 + scale_fill_continuous(guide = guide_legend()) +
 theme(legend.position="bottom", legend.direction="vertical")

p1 + scale_fill_continuous(guide = "colorbar") + theme(legend.position="bottom")

^{Created on 2019-02-28 by the reprex package (v0.2.1)}