Aha! Algorithm Chapter 1 Magic Tree

Section 3 heap sorting

Create a heap of n elements. First, encode the N nodes from 1 to n in the top-down and left-right mode, in this way, N nodes can be converted into a Complete Binary Tree.

Then, from the last non-leaf node (node number is n/2) to the root node (node number is 1), scan all nodes one by one, and adjust the current node downward as needed, until the subtree with the current node as the root node meets the heap characteristics.

# Include <iostream> # include <vector> # include <algorithm> using namespace STD; // The Void shiftdown function (vector <int> & A, int N, int index) {While (Index * 2 <= N) {int T = index; if (a [T]> A [2 * Index]) t = 2 * index; if (2 * index + 1 <= N & A [T]> A [2 * index + 1]) t = 2 * index + 1; if (T! = Index) {swap (A [T], a [Index]); Index = T;} else break ;}} // Delete the largest element int deletemax (vector <int> & A, Int & N) {int res = A [1]; swap (A [1], A [n]); n --; shiftdown (A, N, 1); Return res;} // The Void shiftup (vector <int> & A, int N, int index) {If (Index = 1) return; while (index! = 1) {if (a [Index] <A [INDEX/2]) Swap (A [Index], a [INDEX/2]); else break; index/= 2 ;}/// create heap void make_heap (vector <int> & A, int N) {// note that the index starts from 0 for (INT I = n/2; I> 0; -- I) {shiftdown (A, N, I );}} void heap_sort (vector <int> & A) {int n =. size ()-1; while (n> 1) {swap (A [1], a [n]); n --; shiftdown (A, N, 1 );}} int main () {int N; CIN> N; vector <int> A (n + 1, 0); For (INT I = 1; I <= N; ++ I) {CIN> A [I] ;}// heap building make_heap (A, n); heap_sort (a); For (INT I = 1; I <= N; ++ I) {cout <A [I] <"" ;}cout <Endl; int num = N; For (INT I = 1; I <= N; ++ I) {cout <deletemax (A, num) <Endl ;}}

Heap sorting section 4th and querying Sets

There are two types of query Set Optimization: path compression and rank merge. For details, see Introduction to algorithms.

/** Query set operations */# include <iostream> # include <vector> # include <algorithm> using namespace STD; int f [1000] = {0 }; void make_set (INT size) {for (INT I = 1; I <= size; ++ I) f [I] = I ;} // use the path compression method to find the element int find_set (int x) {If (F [x] = x) return X; else {f [x] = find_set (F [x]); // query the set where the X element is located. The compressed path return f [x] During backtracing.} void union_set (int x, int y) {int T1 = find_set (x), T2 = find_set (y); If (T1! = T2) {f [T2] = T1 ;}int main () {int n, m; CIN >>n> m; make_set (N ); for (INT I = 1; I <= m; ++ I) {int X, Y; CIN >>x> Y; union_set (x, y );} int sum = 0; For (INT I = 1; I <= N; ++ I) {If (F [I] = I) sum ++ ;} cout <sum <Endl; return 0 ;}

Query set