查找和排序

1.1线性查找
在Python中查看一个元素是否在一个序列中，我们可以使用‘in’操作符，如：

if key in theArray :print( "key在 array中." )else :print( "key 不在 array中." )

不难想象，其实‘in’操作符是基于线性查找实现的。接下来看一个在无序序列上的线性查找的实现。

def linearSearch( theValues, target ):  n = len( theValues )  for i in range( n ) :      #如果欲查找的元素存在于列表中，返回Ture      if theValues[i] == target          return True      return False    #如果没找到，返回False

接下来再看一个有序序列上的线性查找的实现

 def sortedLinearSearch( theValues, item ) :   n = len( theValues )   for i in range( n ) :     # 如果欲查找的元素存在于列表中，返回Ture     if theValues[i] == item :       return True # 如果欲查找的元素大于当前元素, 则不在序列中.     elif theValues[i] > item :       return False   return False # 元素不在序列中.

寻找最小值
假设要在一个无需列表中寻找最小值，这可以直接应用Python的内置方法’min()’.内部机制仍然是线性查找。接下来看一个在无需列表中寻找最小值得实现：

 def findSmallest( theValues ):   n = len( theValues )   # 假设序列中第一个元素时最小.   smallest = theValues[0]   # 查看序列中其他更小的元素.   for i in range( 1, n ) :       if theList[i] < smallest :         smallest = theValues[i]    return smallest # 返回最小值.

线性查找的时间复杂度为O(n)
1.2、二分查找
其应用的思想是分治策略，下面是一个在有序序列中应用二分查找的列子

 def binarySearch( theValues, target ) :   low = 0   high = len(theValues) - 1   #重复使用二分法知道找到元素   while low <= high :     # 确定序列中间值.    mid = (high + low) // 2     # 中间值是目标元素么?    if theValues[mid] == target :      return True    # 目标元素小于中间值?    elif target < theValues[mid] :      high = mid - 1   # 目标元素在中间值后面?    else :      low = mid + 1 # 如果序列不能再分，则结束.   return False

二分查找的时间复杂度为O(logn)，比线性查找更高效。

2、排序
冒泡排序
.

def bubbleSort( theSeq ):  n = len( theSeq )  # Perform n-1 bubble operations on the sequence  for i in range( n - 1 ) :  # Bubble the largest item to the end.  for j in range( i + n - 1 ) :    if theSeq[j] > theSeq[j + 1] : # swap the j and j+1 items.      tmp = theSeq[j]      theSeq[j] = theSeq[j + 1]      theSeq[j + 1] = tmp

选择排序
.

def selectionSort( theSeq ):  n = len( theSeq )  for i in range( n - 1 ):   # Assume the ith element is the smallest.    smallNdx = i   # Determine if any other element contains a smaller value.    for j in range( i + 1, n ):      if theSeq[j] < theSeq[smallNdx] :        smallNdx = j   # Swap the ith value and smallNdx value only if the smallest value is  # not already in its proper position. Some implementations omit testing  # the condition and always swap the two values.   if smallNdx != i :     tmp = theSeq[i]     theSeq[i] = theSeq[smallNdx]     theSeq[smallNdx] = tmp

插入排序

def insertionSort( theSeq ):  n = len( theSeq )  # Starts with the first item as the only sorted entry.  for i in range( 1, n ) :  # Save the value to be positioned.    value = theSeq[i]   # Find the position where value fits in the ordered part of the list.    pos = i    while pos > 0 and value < theSeq[pos - 1] :   # Shift the items to the right during the search.       theSeq[pos] = theSeq[pos - 1]       pos -= 1 # Put the saved value into the open slot.   theSeq[pos] = value

3、有序列表