Python实现的数据结构与算法之基本搜索详解
本文实例讲述了Python实现的数据结构与算法之基本搜索。分享给大家供大家参考。具体分析如下：
一、顺序搜索
顺序搜索 是最简单直观的搜索方法：从列表开头到末尾，逐个比较待搜索项与列表中的项，直到找到目标项（搜索成功）或者 超出搜索范围 （搜索失败）。
根据列表中的项是否按顺序排列，可以将列表分为 无序列表 和 有序列表。对于 无序列表，超出搜索范围 是指越过列表的末尾；对于 有序列表，超过搜索范围 是指进入列表中大于目标项的区域（发生在目标项小于列表末尾项时）或者指越过列表的末尾（发生在目标项大于列表末尾项时）。
1、无序列表
在无序列表中进行顺序搜索的情况如图所示：
def sequentialSearch(items, target):
for item in items:
if item == target:
return True
return False2、有序列表
在有序列表中进行顺序搜索的情况如图所示：
def orderedSequentialSearch(items, target):
for item in items:
if item == target:
return True
elif item > target:
break
return False二、二分搜索
实际上，上述orderedSequentialSearch算法并没有很好地利用有序列表的特点。
二分搜索 充分利用了有序列表的优势，该算法的思路非常巧妙：在原列表中，将目标项（target）与列表中间项（middle）进行对比，如果target等于middle，则搜索成功；如果target小于middle，则在middle的左半列表中继续搜索；如果target大于middle，则在middle的右半列表中继续搜索。
在有序列表中进行二分搜索的情况如图所示：
根据实现方式的不同，二分搜索算法可以分为迭代版本和递归版本两种：
1、迭代版本
def iterativeBinarySearch(items, target):
first = 0
last = len(items) - 1
while first <= last:
middle = (first + last) // 2
if target == items[middle]:
return True
elif target < items[middle]:
last = middle - 1
else:
first = middle + 1
return False2、递归版本
def recursiveBinarySearch(items, target):
if len(items) == 0:
return False
else:
middle = len(items) // 2
if target == items[middle]:
return True
elif target < items[middle]:
return recursiveBinarySearch(items[:middle], target)
else:
return recursiveBinarySearch(items[middle+1:], target)三、性能比较
上述搜索算法的时间复杂度如下所示：
搜索算法 时间复杂度 ----------------------------------- sequentialSearch O(n) ----------------------------------- orderedSequentialSearch O(n) ----------------------------------- iterativeBinarySearch O(log n) ----------------------------------- recursiveBinarySearch O(log n) ----------------------------------- in O(n)
可以看出，二分搜索 的性能要优于 顺序搜索。
值得注意的是，Python的成员操作符 in 的时间复杂度是O(n)，不难猜出，操作符 in 实际采用的是 顺序搜索 算法。
四、算法测试
#!/usr/bin/env python
# -*- coding: utf-8 -*-
def test_print(algorithm, listname, target):
print(' %d is%s in %s' % (target, '' if algorithm(eval(listname), target) else ' not', listname))
if __name__ == '__main__':
testlist = [1, 2, 32, 8, 17, 19, 42, 13, 0]
orderedlist = sorted(testlist)
print('sequentialSearch:')
test_print(sequentialSearch, 'testlist', 3)
test_print(sequentialSearch, 'testlist', 13)
print('orderedSequentialSearch:')
test_print(orderedSequentialSearch, 'orderedlist', 3)
test_print(orderedSequentialSearch, 'orderedlist', 13)
print('iterativeBinarySearch:')
test_print(iterativeBinarySearch, 'orderedlist', 3)
test_print(iterativeBinarySearch, 'orderedlist', 13)
print('recursiveBinarySearch:')
test_print(recursiveBinarySearch, 'orderedlist', 3)
test_print(recursiveBinarySearch, 'orderedlist', 13)运行结果：
$ python testbasicsearch.py sequentialSearch: 3 is not in testlist 13 is in testlist orderedSequentialSearch: 3 is not in orderedlist 13 is in orderedlist iterativeBinarySearch: 3 is not in orderedlist 13 is in orderedlist recursiveBinarySearch: 3 is not in orderedlist 13 is in orderedlist
希望本文所述对大家的Python程序设计有所帮助。
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