Find the nth element in the sequence (implemented by the partition function) and the partition Function

Find the nth element in the sequence (implemented by the partition function) and the partition Function

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

The Partition program is as follows:

Long Partition (long a [], long p1, long p2) {// pair a [p1] ~ A [p2] splits and returns the number of the Split points. p1 and p2 are the first/and last elements of the tuples, long I, j; int x; I = p1; j = p2; x = a [I]; while (I <j) {while (a [j]> = x & I, j) j --; if (I <j) {a [I] = a [j]; I ++;} while (a [I] <= x & I <j) I ++; if (I <j) {a [j] = a [I]; j --;} a [I] = x; return I ;}

The partition function is used to find the nth element. The procedure is as follows:

Long OrderStatistics (long a [], long p1, long p2, long k) {// in a [p1] ~ In a [p2], locate the minimum value and return the values long p, num; if (k <1 | k> P2-P1 + 1) return-1; if (p1> = p2) return a [p1]; // If a [p1] ~ A [p2] has only one element, returns the element p = Partition (a, p1, p2); num = p-p1; if (k = num + 1) return a [p]; // the k-th small element is the split point if (k <= num) return OrderStatistics (a, p1, P-1, k ); // The k small element in the front return OrderStatistics (a, p + 1, p2, k-num-1); // The k small element in the back}

Python cookbook provides the python implementation of this method, as shown below:

Import randomdef select (data, n): # create a new list, process indexes smaller than 0, and check the validity of indexes. data = list (data) if n <0: n + = len (data) if not 0 <= n <len (data): raise ValueError, "can't get rank % d out of % d" % (n, len (data) # main loop, which looks similar to sorting but does not require recursion while True: random = random. choice (data) pcount = 0 under, over = [], [] uappend, oappend = under. append, over. append for elem in data: if elem <latency: uappend (elem) elif elem> latency: oappend (elem) else: pcount + = 1 numunder = len (under) if n <numunder: data = under elif n <numunder + pcount: return limit else: data = over n-= numunder + pcount

As mentioned by the author, we can also use the following simple method to find the k elements:

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

The above two methods can be implemented, but "the implementation of the list-based sort method is indeed much simpler, and the implementation of select does require a little effort, however, if n is large enough and the overhead of comparative operations cannot be ignored, select reflects its value."