问题描述：

研究短音节和长音节组合产生长度为n的旋律组合数，短音节标记S，占一个长度，长音节标记L，占两个长度。例如 n=4时，V4={LL , SSL, SLS, LSS, SSSS}

分析 V(n) = {"S" + V(n-1)} + {"L" + V(n-2)]

code:

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu May  3 16:49:04 2018

@author: dag
"""
def virahanka1(n):

    if n == 0:

        return [""]

    elif n == 1:

        return ["S"]

    else:

        s = ["S" + prosody for prosody in virahanka1(n-1)]
        
        l = ["L" + prosody for prosody in virahanka1(n-2)]

        return s + l

 

def virahanka2(n):

    lookup = [[""], ["S"]]

    for i in range(n-1):

       s = ["S" + prosody for prosody in lookup[i+1]]
       
       l = ["L" + prosody for prosody in lookup[i]]
       
       lookup.append(s + l)

    return lookup[n]

 

def virahanka3(n, lookup={0:[""], 1:["S"]}):

    if n not in lookup:

        s = ["S" + prosody for prosody in virahanka3(n-1)]
        
        l = ["L" + prosody for prosody in virahanka3(n-2)]
        
        lookup[n] = s + l
        
        return lookup[n]

 

from nltk import memoize

@memoize

def virahanka4(n):

    if n == 0:

        return [""]

    elif n == 1:

        return ["S"]

    else:

        s = ["S" + prosody for prosody in virahanka4(n-1)]

        l = ["L" + prosody for prosody in virahanka4(n-2)]

        return s + l

output:

virahanka4(4)
Out[11]: ['SSSS', 'SSL', 'SLS', 'LSS', 'LL']