演算法的最壞執行時間表示為:2t(
n/2)
+θ(n
)2t(n/2)+\theta(n)
2t(n/2
)+θ(
n)記作:θ(n
lgn)
\theta(n\lg)
θ(nlgn)
'''
find_max_crossing_subarray(a,low,mid,hith)
sumleft=-∞
sum=0
for i=mid downto low
sum=sum+a[i]
if sum>sumleft
sumleft=sum
maxleft=i
sumright=-∞
sum=0
for j=mid+1 to hith
sum=sum+a[j]
if sum>sumright
sumright=sum
maxright=j
return(maxleft,maxright,sumleft+sumright)
'''
'''
find_max_subarray(a,low,high)
if low==hith
return(low,high,a[low])
else mid=(low+high)//2
(leftlow,lefthigh,leftsum)=
find_max_subarray(a,low,mid)
(rightlow,righthigh,rightsum)=
find_max_subarray(a,mid+1,high)
(crosslow,crosshigh,crosssum)=
find_max_crossing_subarray(a,low,mid,high)
if leftsum>=rightsum and leftsum>=crosssum
return (leftlow,lefthigh,leftsum)
elseif rightsum>=leftsum and rightsum>=crosssum
return (rightlow,righthigh,rightsum)
else
return (crosslow,crosshigh,crosssum)
'''
def
find_max_crossing_subarray
(a,low,mid,high)
:'''
a是乙個包含負數的列表
合併演算法是要返回乙個跨越分割店mid的最大陣列
'''sumleft=
float
("-inf"
) s=
0for i in
range
(mid,-1
,-1)
: s+=a[i]
if s>sumleft:
sumleft=s
maxleft=i
sumright=
float
("-inf"
) s=
0for j in
range
(mid+
1,high+1)
: s+=a[j]
if s>sumright:
sumright=s
maxright=j
return
(maxleft,maxright,sumleft+sumright)
def
find_max_subarray
(a,low,high)
:'''
a是乙個包含負數的列表
low代表列表a的最小下標,high代表最大下標
函式返回a所包含的最大連續陣列
'''if low==high:
return
(low,high,a[low]
)else
: mid=
(low+high)//2
(leftlow,lefthigh,leftsum)
=find_max_subarray(a,low,mid)
(rightlow,righthigh,rightsum)
=find_max_subarray(a,mid+
1,high)
(crosslow,crosshigh,crosssum)
=find_max_crossing_subarray(a,low,mid,high)
if leftsum>=rightsum and leftsum>=crosssum:
return
(leftlow,lefthigh,leftsum)
elif rightsum>=leftsum and rightsum>=crosssum:
return
(rightlow,righthigh,rightsum)
else
:return
(crosslow,crosshigh,crosssum)
a=[13
,-3,
-25,20
,-3,
-16,-
23,18,
20,-7
,12,-
5,-22
,15,-
4,7]
print
(a)low,high,
sum=find_max_subarray(a,0,
len(a)-1
)print
(low,high,
sum)
print
(a[low:high+1]
)[13,
-3,-
25,20,
-3,-
16,-23
,18,20
,-7,
12,-5
,-22,
15,-4
,7]7
1043[18
,20,-
7,12]
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