算法图解：Python笔记代码

二分查找

选择排序

递归

快速排序

广度优先搜索

狄克斯特拉算法

贪婪算法

二分查找

def binary_search(lst,item):
    low = 0
    high = len(lst)-1
    
    while low <= high:
        mid = (high+low)//2
        if item == lst[mid]:
            return mid
        if item < lst[mid]:
            high = mid-1
        if item > lst[mid]:
            low = mid + 1
    return None


my_list = [1,3,5,7,9]
print(binary_search(my_list,5))

选择排序

def findsmallest(arr):
    smallest = arr[0]
    smallest_index = 0

    for i in range(1,len(arr)):
        if arr[i] < smallest:
            smallest = arr[i]
            smallest_index = i
    return smallest_index

def selection_Sort(arr):
    new_arr = []
    for i in range(len(arr)):
        new_arr.append(arr.pop(findsmallest(arr)))  # 注意pop的对象是索引
    return new_arr


arr = [3,1,5,2,9,1,1,0]
print(selection_Sort(arr))

递归

# 倒计时
def countdown(n):
    print(n)
    if n < 1:
        return
    countdown(n-1)


# 求和
def sum_1(arr):
    if arr == []:
        return 0
    return arr.pop(0) + sum_1(arr)

def sum_2(arr):
    if arr == []:
        return 0
    return arr[0] + sum_2(arr[1:])


arr = [1,2,3,4,5]
print(sum_1(arr))

# 阶乘
def fact(n):
    if n == 1:
        return 1
    return n * fact(n - 1)

# 计算元素个数
def count_arr(arr):
    if arr == []:
        return 0
    return 1 + count_arr(arr[1:])

快速排序

def quick_sort(arr):
    if len(arr) < 2:
        return arr
    else:
        pivot = arr[0]
        less = [i for i in arr[1:] if i <= pivot]
        greater = [i for i in arr[1:] if i > pivot]
        return quick_sort(less) + pivot + quick_sort(greater)

广度优先搜索

# 使用队列这种数据结构
from collections import deque 

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

# 判断是否是芒果销售商   
def person_is_seller(name):
    return name[-1] == "m"

# 广度优先搜索
def search(name):
    # 实例化队列
    search_deque = deque()
    # 将某人的一度关系网加入到队列中
    search_deque += graph[name]
    # 初始化已检查过的人
    searched = []

    # 队列中存在元素时就一直搜索
    while search_deque:
        # 从列队中弹出第一个人，并检查
        person = search_deque.popleft()
        # 此人不在已检查过的列表中
        if person not in searched:
            # 检查是否是销售商
            if person_is_seller(person):
                print("%s is mango_seller" % person)
                return True
            else:
                # 如果不是就将此人的一度关系网加入到队列中
                search_deque += graph[person]
                searched.append(person)

    return False


search("you")

狄克斯特拉算法

# 创建图的散列表
graph = {
    "start":{"a":6,"b":2},
    "a":{"fin":1},
    "b":{"a":3,"fin":5},
    "fin":{}
}
# 创建开销的散列表
costs = {
    "a":6,
    "b":2,
    "fin":float("inf")
}
# 创建存储父节点的散列表
parents = {
    "a":"start",
    "b":"start",
    "fin": None
}
# 记录处理过的节点
processed = []

# 在未处理的节点中寻找最小开销节点
def find_lowest_cost_node(costs):
    lowest_cost = float("inf")
    lowest_cost_node = None
    for node in costs:
        cost = costs[node]
        if cost < lowest_cost and node not in processed:
            lowest_cost = cost
            lowest_cost_node = node
    return lowest_cost_node

# 1、拿到起点的一度关系中的最小开销节点
node = find_lowest_cost_node(costs)
# 2、获取该节点的开销和邻居
while node is not None:
    cost = costs[node]
    neighbors = graph[node]
    # 3、遍历邻居
    for n in neighbors.keys():
        # 计算该节点到邻居的开销+起点到该节点的开销，与起点直接到改点的开销比较
        new_cost = cost + neighbors[n]
        # 如果前者开销较小则更新改邻居节点的父节点，并更新起点到该邻居节点的开销
        if new_cost < costs[n]:
            parents[n] = node
            costs[n] = new_cost
    # 4、将当前节点标记为处理过
    processed.append(node)
    # 5、找出接下来要处理的节点并循环
    node = find_lowest_cost_node(costs)

print(processed)
print(costs)
print(parents)

贪婪算法

# 目标：选择尽可能少的电台覆盖尽可能多的州
# 方法：第一步，选择覆盖州最多的电台
# 方法：第二步，选择覆盖最多“未覆盖的州（上一步剩下的州）”的电台
# 方法：第三步，重复第二步，直到覆盖所有的州

# 需要覆盖的州
states_needed = set(["mt", "wa", "or", "id", "nv", "ut","ca", "az"])

# 电台清单
stations = {
    "kone" : set(["id", "nv", "ut"]),
    "ktwo" : set(["wa", "id", "mt"]),
    "kthree" : set(["or", "nv", "ca"]),
    "kfour" : set(["nv", "ut"]),
    "kfive" : set(["ca", "az"])
}

# 该集合存储最终选择的电台
final_stations = set()

# 只要需要覆盖的州不为空就一直循环
while states_needed:
    best_station = None
    states_covered = set()
    # 从电台清单中找出覆盖未覆盖州最多的电台
    for station,states in stations.items():
        covered = states_needed & states
        if len(covered) > len(states_covered):
            best_station = station
            states_covered = covered

    # 每次确定一个最佳的电台就将其覆盖的州从总集合中减去
    states_needed -= states_covered
    # 没确定一个最佳电台就存在最终的电台集合中
    final_stations.add(best_station)

print(final_stations)