Heap Sort, priority queue

1. Heap Sequencing

A. Definition of a heap

The n element sequence {k1,k2,..., kn} is called a heap when and only if the following relationships are met.

Ki<=k2i and ki<=k2i+1  (Keng Gen) ki>=k2i and ki>=k2i+1 (Dagen)

The following is for the maximum heap

B. Nature of the maintenance heap

Max-heapify the sub-tree with the root node of I as the maximum heap property by letting the value of a[i] "step down" in the maximum heap (the value of a[i] is less than the value of its left and right children).

max-heapify (a,i)    = left (i)    = right (i)    if l <= a.heap-size and A[l] > a[i]        = L    else largest = I    if r <= a.heap-size and A[r] > a[largest]        = R    if  largest≠i        swap (A[i],a[largest] )        Max-heapify (a,largest)

Complexity of Time: O (LGN)

C. Build a heap

The elements in sub-array A (N/2+1..N) are the leaf nodes of the tree, and each leaf node can be seen as a heap containing only one element. Build-max-heap calls the max-heapify once for other nodes in the tree.

build-max-Heap (A)    a.heap-size = a.length    for i = a.length/21          Max-heapify (a,i)

Time complexity: O (N)

D. Heap sequencing

heap-Sort (a)    Build-max-Heap (a)    for2        Swap (a[  1],a[i])        a.heap-size = a.heap-size-1        Max-heapify (A, 1)

Complexity of Time: O (N*LGN)

2. Priority queue

The specific algorithm will not talk about, to see how the priority queue in C + + is used.

 in header <queue>template<    class  T,    class Container = Std::vector<t>,    classclass priority_queue;

The default is the maximum priority queue. You can provide the compare parameter to achieve the maximum priority queue.

Compare = greater<t>

Example:

#include <functional>#include<queue>#include<vector>#include<iostream>Template<typename t>voidPrint_queue (t&q) { while(!Q.empty ()) {Std::cout<< q.top () <<" ";    Q.pop (); } std::cout<<'\ n';} intMain () {std::p riority_queue<int>Q;  for(intN: {1,8,5,6,3,4,0,9,3,2}) Q.push (n);     Print_queue (q); std::p riority_queue<int, std::vector<int, std::greater<int> >Q2;  for(intN: {1,8,5,6,3,4,0,9,3,2}) Q2.push (n); Print_queue (q2);}

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For custom types

If the comparison operator is overloaded

priority_queue<t> q// Max priority queue priority_queue<t,vector<t>,greater<t>> Q // Minimum priority queue

If you do not have an overloaded comparison operator, you need to provide a comparator passed to the Compare parameter

//Maximum priority queue Comparatorstructcomp{BOOL operator() (T &a,t &b)Const {        returnA.key <B.key; }};//minimum priority Queue Comparatorstructcomp{BOOL operator() (T &a,t &b)Const {        returnA.key >B.key; }};//UsePriority_queue<t,vector<t>,comp> Q

Reference:

Heap Sort, priority queue