easy way

longest_ordered.py

def longest_ordered(original):
  results = list()
  for item in original:
    for stem in tuple(results):
      if stem[-1] <= item:
        results.append(stem + [item])
    results.append([item])
    max_length = max(map(len, results))
  return [x for x in results if len(x) == max_length]

# usage: longest_ordered([1,2,5,4,6]) etc.

longest_ordered.R

longest.ordered <- function(original) {
  results <- list()
  for (item in original) {
    static_results <- results
    for (stem in static_results) {
      if (stem[length(stem)] <= item) {
        results[[length(results)+1]] <- c(stem, item)
      }
    }
    results[[length(results)+1]] <- item
  }
  return(results[which.max(sapply(results, length))])
}

# usage: longest.ordered(c(1,2,5,4,6)) etc.