// output of ./demo/comb/dyck-rgs-demo.cc: // Description: //% Restricted growth strings (RGS) for k-ary Dyck words: //% strings s[0,...,n-1] such that s[j] <= s[j-1] + i (where i=k-1). //% Lexicographic order. //% Number of RGS is binomial(i*n,n)/((i-1)*n+1), (Catalan numbers for i=1). arg 1: 4 == n [Length of restricted growth strings] default=4 arg 2: 2 == i [Increment allowed (1==> RGS for parentheses strings)] default=2 arg 3: 0 == bw [Whether to generate in backward order.] default=0 1: [ . . . . ] 0 1..1..1..1.. [ 0 3 6 9 ] 2: [ . . . 1 ] 3 1..1..1.1... [ 0 3 6 8 ] 3: [ . . . 2 ] 3 1..1..11.... [ 0 3 6 7 ] 4: [ . . 1 . ] 2 1..1.1...1.. [ 0 3 5 9 ] 5: [ . . 1 1 ] 3 1..1.1..1... [ 0 3 5 8 ] 6: [ . . 1 2 ] 3 1..1.1.1.... [ 0 3 5 7 ] 7: [ . . 1 3 ] 3 1..1.11..... [ 0 3 5 6 ] 8: [ . . 2 . ] 2 1..11....1.. [ 0 3 4 9 ] 9: [ . . 2 1 ] 3 1..11...1... [ 0 3 4 8 ] 10: [ . . 2 2 ] 3 1..11..1.... [ 0 3 4 7 ] 11: [ . . 2 3 ] 3 1..11.1..... [ 0 3 4 6 ] 12: [ . . 2 4 ] 3 1..111...... [ 0 3 4 5 ] 13: [ . 1 . . ] 1 1.1...1..1.. [ 0 2 6 9 ] 14: [ . 1 . 1 ] 3 1.1...1.1... [ 0 2 6 8 ] 15: [ . 1 . 2 ] 3 1.1...11.... [ 0 2 6 7 ] 16: [ . 1 1 . ] 2 1.1..1...1.. [ 0 2 5 9 ] 17: [ . 1 1 1 ] 3 1.1..1..1... [ 0 2 5 8 ] 18: [ . 1 1 2 ] 3 1.1..1.1.... [ 0 2 5 7 ] 19: [ . 1 1 3 ] 3 1.1..11..... [ 0 2 5 6 ] 20: [ . 1 2 . ] 2 1.1.1....1.. [ 0 2 4 9 ] 21: [ . 1 2 1 ] 3 1.1.1...1... [ 0 2 4 8 ] 22: [ . 1 2 2 ] 3 1.1.1..1.... [ 0 2 4 7 ] 23: [ . 1 2 3 ] 3 1.1.1.1..... [ 0 2 4 6 ] 24: [ . 1 2 4 ] 3 1.1.11...... [ 0 2 4 5 ] 25: [ . 1 3 . ] 2 1.11.....1.. [ 0 2 3 9 ] 26: [ . 1 3 1 ] 3 1.11....1... [ 0 2 3 8 ] 27: [ . 1 3 2 ] 3 1.11...1.... [ 0 2 3 7 ] 28: [ . 1 3 3 ] 3 1.11..1..... [ 0 2 3 6 ] 29: [ . 1 3 4 ] 3 1.11.1...... [ 0 2 3 5 ] 30: [ . 1 3 5 ] 3 1.111....... [ 0 2 3 4 ] 31: [ . 2 . . ] 1 11....1..1.. [ 0 1 6 9 ] 32: [ . 2 . 1 ] 3 11....1.1... [ 0 1 6 8 ] 33: [ . 2 . 2 ] 3 11....11.... [ 0 1 6 7 ] 34: [ . 2 1 . ] 2 11...1...1.. [ 0 1 5 9 ] 35: [ . 2 1 1 ] 3 11...1..1... [ 0 1 5 8 ] 36: [ . 2 1 2 ] 3 11...1.1.... [ 0 1 5 7 ] 37: [ . 2 1 3 ] 3 11...11..... [ 0 1 5 6 ] 38: [ . 2 2 . ] 2 11..1....1.. [ 0 1 4 9 ] 39: [ . 2 2 1 ] 3 11..1...1... [ 0 1 4 8 ] 40: [ . 2 2 2 ] 3 11..1..1.... [ 0 1 4 7 ] 41: [ . 2 2 3 ] 3 11..1.1..... [ 0 1 4 6 ] 42: [ . 2 2 4 ] 3 11..11...... [ 0 1 4 5 ] 43: [ . 2 3 . ] 2 11.1.....1.. [ 0 1 3 9 ] 44: [ . 2 3 1 ] 3 11.1....1... [ 0 1 3 8 ] 45: [ . 2 3 2 ] 3 11.1...1.... [ 0 1 3 7 ] 46: [ . 2 3 3 ] 3 11.1..1..... [ 0 1 3 6 ] 47: [ . 2 3 4 ] 3 11.1.1...... [ 0 1 3 5 ] 48: [ . 2 3 5 ] 3 11.11....... [ 0 1 3 4 ] 49: [ . 2 4 . ] 2 111......1.. [ 0 1 2 9 ] 50: [ . 2 4 1 ] 3 111.....1... [ 0 1 2 8 ] 51: [ . 2 4 2 ] 3 111....1.... [ 0 1 2 7 ] 52: [ . 2 4 3 ] 3 111...1..... [ 0 1 2 6 ] 53: [ . 2 4 4 ] 3 111..1...... [ 0 1 2 5 ] 54: [ . 2 4 5 ] 3 111.1....... [ 0 1 2 4 ] 55: [ . 2 4 6 ] 3 1111........ [ 0 1 2 3 ] ct=55