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']