Ducci Sequence, R - rextester

Ducci Sequence

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ducci <- function(ntuple, sequence = data.frame(), depth = 0) {
  # Append the first value to the end of the list.
  ntupleExt <- c(ntuple, ntuple[1])
  
  # Start the result sequence with the first ntuple.
  if (nrow(sequence) == 0) {
    sequence <- rbind(sequence, ntuple)
  }

# Calculate the next sequence.
  nextSeq <- sapply(1:(length(ntupleExt) - 1), function(index) {
    abs(ntupleExt[index] - ntupleExt[index + 1])
  })

# Check if we're done.
  #if (all(nextSeq == ntuple) || all(nextSeq == 0) || depth > 100) {
  if (length(which(apply(sequence, 1, function(n) all(n == nextSeq)))) > 0 || all(nextSeq == 0)) {
    # We found a repeating sequence, we're done.
    rbind(sequence, nextSeq)
  }
  else {
    # Recurse until a duplicate or all zeroes.
    ducci(nextSeq, rbind(sequence, nextSeq), depth + 1)
  }
}

inputs <- list(
  c(0, 653, 1854, 4063),
  c(1, 5, 7, 9, 9),
  c(1, 2, 1, 2, 1, 0),
  c(10, 12, 41, 62, 31, 50),
  c(10, 12, 41, 62, 31))

x <- sapply(inputs, ducci)
print(x)

[ + ] Show input
Absolute running time: 0.33 sec, cpu time: 0.58 sec, memory peak: 31 Mb, absolute service time: 0,34 sec

[[1]] X0 X653 X1854 X4063 1 0 653 1854 4063 2 653 1201 2209 4063 3 548 1008 1854 3410 4 460 846 1556 2862 5 386 710 1306 2402 6 324 596 1096 2016 7 272 500 920 1692 8 228 420 772 1420 9 192 352 648 1192 10 160 296 544 1000 11 136 248 456 840 12 112 208 384 704 13 96 176 320 592 14 80 144 272 496 15 64 128 224 416 16 64 96 192 352 17 32 96 160 288 18 64 64 128 256 19 0 64 128 192 20 64 64 64 192 21 0 0 128 128 22 0 128 0 128 23 128 128 128 128 24 0 0 0 0 [[2]] X1 X5 X7 X9 X9.1 1 1 5 7 9 9 2 4 2 2 0 8 3 2 0 2 8 4 4 2 2 6 4 2 5 0 4 2 2 0 6 4 2 0 2 0 7 2 2 2 2 4 8 0 0 0 2 2 9 0 0 2 0 2 10 0 2 2 2 2 11 2 0 0 0 2 12 2 0 0 2 0 13 2 0 2 2 2 14 2 2 0 0 0 15 0 2 0 0 2 16 2 2 0 2 2 17 0 2 2 0 0 18 2 0 2 0 0 19 2 2 2 0 2 20 0 0 2 2 0 21 0 2 0 2 0 22 2 2 2 2 0 23 0 0 0 2 2 [[3]] X1 X2 X1.1 X2.1 X1.2 X0 1 1 2 1 2 1 0 2 1 1 1 1 1 1 3 0 0 0 0 0 0 [[4]] X10 X12 X41 X62 X31 X50 1 10 12 41 62 31 50 2 2 29 21 31 19 40 3 27 8 10 12 21 38 4 19 2 2 9 17 11 5 17 0 7 8 6 8 6 17 7 1 2 2 9 7 10 6 1 0 7 8 8 4 5 1 7 1 2 9 1 4 6 6 1 2 10 3 2 0 5 1 1 11 1 2 5 4 0 2 12 1 3 1 4 2 1 13 2 2 3 2 1 0 14 0 1 1 1 1 2 15 1 0 0 0 1 2 16 1 0 0 1 1 1 17 1 0 1 0 0 0 18 1 1 1 0 0 1 19 0 0 1 0 1 0 20 0 1 1 1 1 0 21 1 0 0 0 1 0 22 1 0 0 1 1 1 [[5]] X10 X12 X41 X62 X31 1 10 12 41 62 31 2 2 29 21 31 21 3 27 8 10 10 19 4 19 2 0 9 8 5 17 2 9 1 11 6 15 7 8 10 6 7 8 1 2 4 9 8 7 1 2 5 1 9 6 1 3 4 6 10 5 2 1 2 0 11 3 1 1 2 5 12 2 0 1 3 2 13 2 1 2 1 0 14 1 1 1 1 2 15 0 0 0 1 1 16 0 0 1 0 1 17 0 1 1 1 1 18 1 0 0 0 1 19 1 0 0 1 0 20 1 0 1 1 1 21 1 1 0 0 0 22 0 1 0 0 1 23 1 1 0 1 1 24 0 1 1 0 0 25 1 0 1 0 0 26 1 1 1 0 1 27 0 0 1 1 0 28 0 1 0 1 0 29 1 1 1 1 0 30 0 0 0 1 1