Finding the smallest nth element in a sequence (partition function implementation)

Partition is a segmentation algorithm used to divide a sequence a[n] into three parts: A[n] greater than the portion of an element x, equal to the portion of X and less than X.

The partition program is as follows:

LongPartition (LongA[],LongP1,Longp2) {//the A[P1]~A[P2] is split, returning the sequence number of the split point, P1, p2 respectively the first of the tuple//One and the last elementLongI, J;intX;i=p1;j=p2;x=A[i]; while(i<j) { while(A[j] >= x && i,j) j--;if(I&LT;J) {A[i] = a[j]; i++;} while(A[i] <= x && i<j) i++;if(I&LT;J) {A [j] = a[i]; j--;}} A[i]=x;returni;}

The program that uses the partition function to find the nth element is as follows:

LongOrderstatistics (LongA[],LongP1,LongP2,Longk) {//in A[P1]~A[P2], find the minimum value and return the valueLongp, num;if(k<1|| k>p2-p1+1)return-1; if(P1 >= p2)returnA[P1];//if A[P1]~A[P2] has only one element, the element is returnedp =Partition (A, p1, p2); Num= PP1;if(k = = num +1)returnA[P];//the K-element is the dividing pointif(k <= num)returnOrderstatistics (A, P1, p1, k);//k small element in the front sectionreturnOrderstatistics (A, p+1, p2, k-num-1);//k small element in the back part}

The python implementation of this method is given in Python cookbook, as follows:

ImportRandomdefSelect (data, N):#Create a new list, process indexes that are less than 0, and check the validity of the indexesdata =list (data)ifn<0:n+=len (data)if  not0 <= N <len (data):RaiseValueError,"can ' t get rank%d out of%d"%(n, Len (data))#main loop, which looks similar to sort but does not require recursion whileTrue:pivot=random.choice (data) Pcount=0 under, over=[], [] uappend, Oappend=Under.append, Over.append forEleminchData:ifElem <pivot:uappend (elem)elifElem >pivot:oappend (elem)Else: Pcount+ = 1Numunder=Len (under)ifN <Numunder:data=underelifN < Numunder +Pcount:returnPivotElse: Data=Over N-= Numunder +pcount

The author mentions that it is also possible to find a K-element by using the following simple method:

def selsor (data, N):     = list (data)    Data.sort ()    return Data[n]

Both of these methods can be implemented, but the "list-based sort method is much simpler to implement, and the implementation of select does require a little more effort, but if n is large enough and the overhead of the comparison operation cannot be ignored, select shows its value." ”

Finding the smallest nth element in a sequence (partition function implementation)