I am not trying to fit a horizontal line at every unique value of y. I am
trying fit the y values with as few horizontal lines by trading off the
number of horizontal lines with the error. The actual problem I am trying
to solve is to smooth data in a time series. Here is a realistic example of
y

y=c(134.45,141.82,143.81,141.81,145,141.61,143.72,145.71,200,175,140,200,148.77,71.64,111.57,118.15,119.15,112.8,111.64,111.64,157.26,143.8,40.19,64.99,64.99,129.98,64.99,65,64.98,64.99)

An example fit for y using multiple horizontal lines (may not be the best
fit in terms of squared error or another error metric, but I have included
the y value for concreteness)

1. A horizontal line at approximately y=140 (to fit the first 13 values -
134.45 to 148.77)
2. A horizontal line at approximately y=110 (to fit the next 7 values -
71.64 to 111.64)
3. A horizontal line at approximately y=150 (to fit the next 2 values -
157.26 to 143.8)
4. A horizontal line at approximately y=65 (to fit the last 8 values -
40.19 to 64.99)
-sashi.

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