《算法图解》代码实现和改进

请随意观看表演

• 二分查找
• 数组和链表
• 递归
• 递归条件和基线条件
• 快速排序
• 散列表
• 广度优先搜索
• 狄克斯特拉算法
• 贪婪算法

二分查找

def bin_search(list,item):    low = 0    high = len(list) - 1        while low<=high:        mid = (low+high)//2 #得到中间值         guess = list[mid]        if guess==item:            return mid        elif guess>item:            high = mid-1        else:            low = mid+1        return Nonefunc = lambda x:x%2!=0my_list = list(filter(func,range(0,10)))print(my_list)print(bin_search(my_list,2))print(bin_search(my_list,5))

[1, 3, 5, 7, 9]None2

数组和链表

选择排序

def findSmall(arr):#找到最小    small = arr[0]    small_index = 0    for i in range(1,len(arr)):        if arr[i]<small:            small = arr[i]            small_index = i    return (small_index,small)def selectionSelect(arr):#选择排序,升序    newArr = []    for i in range(len(arr)):        small_index = findSmall(arr)[0]        newArr.append(arr.pop(small_index))    return newArrprint(selectionSelect([i for i in range(10,0,-1)]))

[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

递归

盒子查找

迭代写法

def lookForKey(mainBox):    pile = mainBox.makePileToLook()    while len(pile):        box = pile.grabBox()        for item in box:            if item.isBox():                pile.append(item)            elif item.isKey():                print("found the key!")

递归写法

def lookForKey(box):    for item in box:        if item.isBox():            lookForKey(item)        elif item.isKey():            print('Found the key at ',item)

基线条件和递归条件

def countdown(i):    print(i)    if i-1:        countdown(i-1)    else : returncountdown(5)

54321

快速排序

分而治之

def Sum(arr):    if len(arr):        return arr[0] + Sum(arr[1:])    else:        return 0Sum([i for i in range(1,101)])

5050

找到最大值

'''错误的写法，out of rangedef getMax(arr,index=0):    if len(arr)>1:        new_index = index + 1        print(new_index,len(arr))        return arr[index] if arr[index]>getMax(arr[new_index:],new_index) else getMax(arr[new_index:],new_index)    else:        return arr[index]        '''    def getMax(arr):    if arr and len(arr)>1:        return arr[0] if arr[0] > getMax(arr[1:]) else getMax(arr[1:])    else:        return arr[0]import randomList = [i for i in range(6)]random.shuffle(List)print(List)getMax(List)

[1, 4, 5, 2, 3, 0]5

快速排序

def quickSort(arr):    if len(arr)<2:        return arr #基线条件，为空或者只含有一个元素的数组    else:        pivot = arr[0] # 递归条件，这里可以随机选取的        small= [i for i in arr[1:] if i<=pivot] #小于基准值组成的子数组        big  = [i for i in arr[1:] if i>pivot]        return quickSort(small) +[pivot] + quickSort(big)print(quickSort([10,5,3]))

[3, 5, 10]

快速排序改进（个人代码，可能有bug）

from random import randrangedef quickSort(arr):    if len(arr)<2:        return arr    else:        flag = 0        for i in range(0,len(arr)-1):            if arr[i]>arr[i+1]:                flag = 1                break        if flag:            index = randrange(0,len(arr))            pivot = arr[index]                        small = [arr[i]  for i in range(0,len(arr)) if i!=index and arr[i]<=pivot]            big = [arr[i]  for i in range(0,len(arr)) if i!=index and arr[i]>pivot]                        return quickSort(small)+[pivot]+quickSort(big)        else:            return arrprint(quickSort([10,5,3,-5]))

[-5, 3, 5, 10]

散列表

python里面实现方式是字典

DNS实现

dns = {}dns['google.com'] = '74.125.239.133'dns['scribd.com'] = '23.235.47.175'site = input('>>> ')print(site,dns.get(site))

>>> google.comgoogle.com 74.125.239.133

投票

voted = {}def check_voter(name):    if voted.get(name):        print('已经投过票')    else:        voted[name] = True        print('可以投票')check_voter('Tom')check_voter('Vic')check_voter('Tom')

可以投票可以投票已经投过票

用户缓存

cache = {}def get_page(url):    if cache.get(url):        return chache[url]#返回缓存数据    else:        data = get_data_from_server(url)#默认配置        cache[url] = data        return data

冲突+性能

填装因子 = 存在的/全部空间

广度优先搜索(BFS)

实现图

graph = {}graph['you'] = ['alice','bob','claire']graph['bob'] = ['anuj','peggy']graph['alice'] = ['peggy']graph['claire']=['thom','jonny']graph['anuj']=[]graph['peggy']=[]graph['thom'] = []graph['jonny'] = []

队列

from collections import deque

type(search_queue)

collections.deque

def person_is_seller(name):    return name[-1] == 'm'def search(name):    search_queue = deque()#创建对列    global graph    search_queue += graph[name]#从谁开始搜索    searched = []#已经搜索，防止无限循环        while search_queue:#只要队列里有人        person = search_queue.popleft()#取出一人        if person not in searched:            if person_is_seller(person):                print(person+' is a mango seller')                return True            else:                search_queue+=graph[person]            searched.append(person)    return Falsesearch('you')

thom is a mango sellerTrue

狄克斯特拉算法

有向无环图、加权图(权值为正)

graph = {}graph['start'] = {}graph['start']['a']=6graph['start']['b'] = 2graph['a']={}graph['a']['fin'] = 1graph['b']={}graph['b']['a']=3graph['b']['fin']=5graph['fin'] = {}#终点没有邻居

infinity = float("inf")#+oo正无穷costs = {}costs['a'] =6costs['b'] =2costs['fin'] = infinity

parents = {}parents['a'] = 'start'parents['b'] = 'start'parents['fin'] = None

processed = []#已经处理过的点

def find_lowest_cost_node(costs):    lowest_cost = float("inf")    lowest_cost_node = None    for node in costs:#遍历所有节点        cost = costs[node]        global processed        if cost<lowest_cost and node not in processed:            lowest_cost = cost            lowest_cost_node = node    return lowest_cost_nodedef get_load(parents,destination):#获得路径    t = parents.get(destination)    print(destination,'<--',end=" ")    while t:        print(t,'<--',end=" ")        t = parents.get(t)    print('None')node = find_lowest_cost_node(costs)while node:#当还有节点可以处理的时候    cost = costs[node]    neighbors = graph[node]    for n in neighbors.keys():        new_cost = cost + neighbors[n]        if new_cost < costs[n]:            costs[n] = new_cost            parents[n] = node            processed.append(node)    node = find_lowest_cost_node(costs)print("cost is ",costs['fin'])get_load(parents,'fin')

cost is  6fin <-- a <-- b <-- start <-- None

贪婪算法(不一定是最优解,非常接近)

集合操作

fruits = set(['avocado','tomato','banana'])vegetables = set(['beets','carrots','tomato'])print('|:并集\n\t',fruits | vegetables)print('&:交集\n\t',fruits & vegetables)print('-:差集\n\t',fruits - vegetables)

|:并集     {'tomato', 'avocado', 'beets', 'carrots', 'banana'}&:交集     {'tomato'}-:差集     {'avocado', 'banana'}

模糊算法--集合覆盖问题

states_needed = set(['mt','wa','or','id','nv','ut','ca','az'])stations = {}stations['kone'] = set(['id','nv','ut'])stations['ktwo'] = set(['wa','id','mt'])stations['kthree'] = set(['or','nv','ca'])stations['kfour'] = set(['nv','ut'])stations['kfive'] = set(['ca','az'])final_stations = set()#最终电台while states_needed:        best_station = None#存放覆盖区域最多的电台    states_covered = set()    for station,states_for_station in stations.items():        covered = states_needed & states_for_station        if len(covered)>len(states_covered):            best_station = station            states_covered = covered                states_needed -= states_covered    final_stations.add(best_station)    del stations[best_station]#用过的删除    print(final_stations)

{'kfive', 'ktwo', 'kone', 'kthree'}