#
#
### Can you have groups of different sizes *and* they have the same Sums-of-Squares?
#

sos <- function(x){sum((x - mean(x))^2)}
pop <- seq(-5, 5, by = 1)
pop <- sort(c(pop, rep(0, 21))); pop
hist(pop)
summary(pop)
sos(pop)
length(pop)

result <- 1
all.results <- as.vector(0)
b.out <- 0
z <- 0
best.so.far <- as.vector(0)
g.id <- c(rep("x1",10),rep("x2",15))
data.results <- as.list(0)
system.time(
while(result != 0){
  b.out <- b.out + 1
  x1 <- sort(sample(pop, 10, replace = F))
  x2 <- sort(sample(pop, 15, replace = F))
  dat <- data.frame(g.id, c(x1,x2))
  data.results[[b.out]] <- dat; rm(dat)
  result <- abs(sos(x1) - sos(x2))
  print(rep(b.out,10))
  print(x1); print(x2)
  print("abs(sos(x1) - sos(x2))"); print(result)
  print(rep("#", 10))
  all.results[b.out] <- result
  plot(sort(all.results, decreasing = T))
  if(b.out > 3){z <- z + 1; best.so.far[z] <- min(all.results)}
  if(b.out == 10000){break}
  }
)

min(best.so.far)
plot(sort(all.results, decreasing = T))
best <- which(all.results == min(all.results)); best
data.results[best]


ls()
rm(g.id, data.results, best, all.results, b.out, best.so.far,
   pop, result, sos, x1, x2, z)
ls()

# End; last updated Feb. 5, 2013.