素数环 python递归求解

作者在 2012-05-12 06:41:56 发布以下内容
#-*- coding: gbk -*-

#素数环

def IsPrimeNum(num):
    for i in range(2, num):
        if num % i == 0:
            return False
    return True
    
def GetPrimeDic(n):
    Dic = {}
    for i in range(1, n+1):
        Dic[i] = []
        
    for i in range(1, n+1, 2):
        #even number
        for j in range(2, n+1, 2):
            #odd number
            if IsPrimeNum(i + j):
                assert(j not in Dic[i])
                #{1:[2, 4, ...]}
                Dic[i] += [j]
                
                assert(i not in Dic[j])
                #{2:[1, 5, ...]}
                Dic[j] += [i]
    return Dic

def EnumPrimeRing(Dic, ringParts):
    #print ringParts
    tail = ringParts[-1]
    ringLen = len(ringParts)
    
    assert(ringLen <= len(Dic))
    
    if ringLen == len(Dic):
        head = ringParts[0]
        if tail in Dic[head]:
            print ringParts
        ringParts.pop()
        return
        
    for i in Dic[tail]:
        if i in ringParts:
            continue
        ringParts += [i]
        
        EnumPrimeRing(Dic, ringParts)
        if len(ringParts) > ringLen:
            ringParts.pop()
        assert(len(ringParts))
    return ringParts
    
if __name__ == "__main__":
    n = int(raw_input('input:'))
    primeDic = GetPrimeDic(n)
    primeRing = EnumPrimeRing(primeDic, [1])
    
 
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