python之各种二分查找

很多时候，我们需要在一堆数字查找的不仅仅是目标值，还可能是比它大的，比它小的，大于等于它的，小于等于它的临近值。现在，老师正在验收作业，我无聊的等待。。。写写python，总结一下这些二分。

array=[4,2,6,1,45,23,27,12,89,5]
# for key:find '==' value
def midfind(key):
    length=len(array)
    ans=length-1
    l=0
    r=length-1
    while(l<=r):
        mid=(l+r)>>1
        if(array[mid]<key):
            l=mid+1
        elif(array[mid]>key):
            r=mid-1
        else:
            return mid
    return -1
# for key:find '>=key' min value
def midfind1(key):
    length=len(array)
    ans=length-1
    l=0
    r=length-1
    while(l<=r):
        mid=(l+r)>>1
        if(array[mid]<key):
            ans=mid
            l=mid+1
        else: r=mid-1
    return ans+1
#for key:find '<=key' max value
def midfind2(key):
    length=len(array)
    ans=length-1
    l=0
    r=length-1
    while(l<=r):
        mid=(l+r)>>1
        if(array[mid]>key):
            ans=mid
            r=mid-1
        else: l=mid+1
    return ans-1
#for key:find > min value
def midfind3(key):
    length=len(array)
    ans=length-1
    l=0
    r=length-1
    while(l<=r):
        mid=(l+r)>>1
        if(array[mid]<=key):
            ans=mid
            l=mid+1
        else: r=mid-1
    return ans+1
#for key:find < max value
def midfind4(key):
    length=len(array)
    ans=length-1
    l=0
    r=length-1
    while(l<=r):
        mid=(l+r)>>1
        if(array[mid]>=key):
            ans=mid
            r=mid-1
        else: l=mid+1
    return ans-1
array.sort()
print('after sort (key=24)')
print array

dex=midfind(24)
dex1=midfind1(24)
dex2=midfind2(24)
dex3=midfind3(24)
dex4=midfind4(24)
if(dex==-1):  print('not found')
else: print array[dex]

print(array[dex1])
print(array[dex2])
print(array[dex3])
print(array[dex4])

对应结果：

>>> 
after sort (key=24)
[1, 2, 4, 5, 6, 12, 23, 27, 45, 89]
not found
27
23
27
23
>>> 

另一种区间查找的二分，即：已知数组所有的数字都和目标值不等，求解目标值在哪个区间？

下面代码返回查找的区间的左值位置：

a=[3,6,9,12,15,20,23,35,47]
def midfind(key):
    length=len(a)  
    l=0  
    r=length-1  
    while(l<r):
        m=(l+r)>>1
        #print ("%d %d %d"%(a[l],a[r],a[m]))
        if(a[m]<key): l=m+1
        else: r=m
    return l-1
print midfind(22)
#print "*********"
print midfind(7)

那种区间查找的过程绝对不能这样写：

while(l<r):
        m=(l+r)>>1
        #print ("%d %d %d"%(a[l],a[r],a[m]))
        if(a[m]>key): r=m-1
        else: l=m
    return l-1

试想：对于上例的list，当下标l=4,r=5，如果a[m]<key仍然成立，l=m=4，这样会无限循环下去。（这都是整除过程floor向下取整惹的祸啊……）

相关例题：http://blog.csdn.net/thearcticocean/article/details/48632391