基于二分查找算法,将查找点的选择改进为自适应选择,可以提高查找效率。当然,差值查找也属于有序查找。
O(log2(log2n))
对于表长较大,而关键字分布又比较均匀的查找表来说,插值查找算法的平均性能比折半查找要好的多。反之,数组中如果分布非常不均匀,那么插值查找未必是很合适的选择。
在介绍插值查找之前,首先考虑一个新问题,为什么二分查找算法一定要是折半,而不是折四分之一或者折更多呢?
mid=(low+high)/2,即mid=low+1/2∗(high−low);mid=(low+high)/2, 即mid=low+1/2*(high-low);mid=(low+high)/2,即mid=low+1/2∗(high−low);
通过类比,我们可以将查找的点改进为如下:
mid=low+(value−a[low])/(a[high]−a[low])∗(high−low),mid=low+(value-a[low])/(a[high]-a[low])*(high-low),mid=low+(value−a[low])/(a[high]−a[low])∗(high−low)
Class PHA.YX.Arithmetic.InsertSearch Extends %RegisteredObject
{
Method search(array As PHA.YX.Arithmetic.Array, value As %Integer)
{
if (array.length() = 0){
return -1
}
#dim low as %Integer = 0
#dim high = array.length() - 1
#dim mid as %Integer = -1
while (low <= high){
s mid = (value - array.get(low)) \ (array.get(high) - array.get(low)) * (high - low)
s mid = low + mid
w "mid:" _ mid,!
if (value > array.get(mid)){
s low = mid + 1
} elseif (value < array.get(mid)){
s high = mid - 1
}else{
return mid
}
}
return -1
}
}
/// w ##class(PHA.YX.Arithmetic).InsertSearch(44)
ClassMethod InsertSearch(x)
{
#dim array as PHA.YX.Arithmetic.Array = ##class(PHA.YX.Arithmetic.Array).%New()
d array.init(10)
d array.insert(0,11)
d array.insert(1,22)
d array.insert(2,33)
d array.insert(3,44)
d array.insert(4,55)
d array.insert(5,66)
d array.insert(6,77)
d array.insert(7,88)
d array.insert(8,99)
d array.insert(9,111)
#dim search as PHA.YX.Arithmetic.InsertSearch = ##class(PHA.YX.Arithmetic.InsertSearch).%New()
s index = search.search(array, x)
w "------插值数列-----",!
w index,!
q ""
}
DHC-APP>w ##class(PHA.YX.Arithmetic).InsertSearch(44)
mid:0
mid:1
mid:2
mid:3
------插值数列-----
3
Method recursive(array As PHA.YX.Arithmetic.Array, left As %Integer, right As %Integer, value As %Integer)
{
if (left > right) ||(value > array.get(array.length() - 1)) ||(value < array.get(0)){
ret -1
}
s mid = (right - left) * (value - array.get(left)) \ (array.get(right) - array.get(left))
s mid = left + mid
w "mid recursive:" _ mid,!
if (value > array.get(mid)){
s mid = ..recursive(array, mid + 1, right , value)
} elseif (value < array.get(mid)){
s mid = ..recursive(array, left, mid , value)
}else{
return mid
}
q mid
}
/// w ##class(PHA.YX.Arithmetic).InsertSearch(44)
ClassMethod InsertSearch(x)
{
#dim array as PHA.YX.Arithmetic.Array = ##class(PHA.YX.Arithmetic.Array).%New()
d array.init(10)
d array.insert(0,11)
d array.insert(1,22)
d array.insert(2,33)
d array.insert(3,44)
d array.insert(4,55)
d array.insert(5,66)
d array.insert(6,77)
d array.insert(7,88)
d array.insert(8,99)
d array.insert(9,111)
#dim search as PHA.YX.Arithmetic.InsertSearch = ##class(PHA.YX.Arithmetic.InsertSearch).%New()
s index = search.search(array, x)
w "------插值数列-----",!
w index,!
s index = search.recursive(array, 0, array.length() - 1,x)
w "------递归插值数列-----",!
w index,!
q ""
}
DHC-APP>w ##class(PHA.YX.Arithmetic).InsertSearch(44)
mid:0
mid:1
mid:2
mid:3
------插值数列-----
3
mid recursive:2
mid recursive:3
------递归插值数列-----
3