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最新推荐文章于 2024-10-23 23:04:28 发布

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最新推荐文章于 2024-10-23 23:04:28 发布

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本文探讨了如何使用Python编程实现寻找特定数值位数的Armstrong数，并详细解释了算法背后的逻辑，包括预处理阶段、查找过程以及验证方法。

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http://bbs.youkuaiyun.com/topics/360188055#r_73147548

# -*- coding:utf-8 -*-
#! /usr/bin/env python
'''
Created on 2014年7月24日

@author: dWX232085
'''
#存放10的0~N次方
powerOfTen = [1]
#存放0~9的数i的N次方乘以出现次数j的结果（j*i^N）
preTable = []
#记录离PreTable中对应数最近的10的k次方
preTable3 = []
#记录0到9中每个数出现的次数
selected = []
#记录armstrong数的长度（位数）
length = 0
#记录已经找到的armstrong数的个数
count = 0
#记录进制
numberSystem = 10

def armstrongNum(n):
    global length,preTable,preTable3,powerOfTen
    length = n
    for i in range(1,n+1):
        powerOfTen.append(powerOfTen[i-1]*10)
    preTable3 = [[None]*(n+1)]*numberSystem
    for i in range(numberSystem):
        preTable.append([])
        for j in range(n+1):
            preTable[i].append((i**n)*j)
            for k in range(n, -1, -1):
                if powerOfTen[k]<preTable[i][j]:
                    preTable3[i][j]=k
#                     print preTable3[i][j]
                    break
#     print preTable[3][39]

def show():
    search(numberSystem-1, 0, length)

# currentIndex 当前正在选择的数字
# sum当前已选数字N次方之和
# remainCount还可以选择多少个数字
def search(currentIndex, sum, remainCount):
    global count,selected
    selected = [None]*10
    if sum >= powerOfTen[length]:return  #第1个结束条件
    if remainCount==0:
        if sum > powerOfTen[length-1] and check(sum):
            count+=1
            print count+'.',sum
        return
    if not preCheck(currentIndex, sum, remainCount):return #结束条件3,4
    if (sum+preTable[currentIndex][remainCount])<powerOfTen[length-1]:return  #结束条件2
    if currentIndex == 0:  #选到0时的处理
        selected[0]=remainCount
        search(-1, sum, 0)
    else:
        for i in range(remainCount+1):  #穷举所有可能的情况
            selected[currentIndex] = i
            search(currentIndex-1, sum+(preTable[currentIndex][i]), remainCount-i)
    selected[currentIndex] = 0

def preCheck(currentIndex, sum, remainCount):
    if sum < preTable[currentIndex][remainCount]:return True
    max = sum+preTable[currentIndex][remainCount]  #当前情况的最大值
    max /= powerOfTen[preTable3[currentIndex][remainCount]]  #取当前sum和max的前面部分进行比较
    sum /= powerOfTen[preTable3[currentIndex][remainCount]]
    #检验sum和max首部是否有相同的部分
    while max!=sum:
        max/=10
        sum/=10
    if max==0:return True  #无相同部分
    counter = getCounter(max)
    for i in range(9, currentIndex, -1):
        if counter[i]>selected[i]:return False  #结束条件3
    for i in range(currentIndex+1):remainCount -= counter[i]
    return remainCount >= 0  #结束条件4
        
def check(sum):
    counter = getCounter(sum)
    for i in range(numberSystem):
        if selected[i]!=counter[i]:return False
    return True

def getCounter(value):
    counter = [0]*numberSystem
    sumChar = list(str(value))
    for i in range(len(sumChar)):
        counter[ord(sumChar[i])-ord('0')]+=1
    return counter