算法题 (排序)

排序算法

#include<iostream>
#include<vector>
#include<string>
using namespace std;

vector<int> selectS(vector<int> v) {
	for (int i = 0;i < v.size() - 1;i++) {
		for (int j = i;j < v.size();j++) {
			if (v[j] < v[i]) {
				int tmp = v[j];
				v[j] = v[i];
				v[i] = tmp;
			}
		}
	}
	return v;
}

vector<int> insertS(vector<int> v) {
	for (int i = 1;i < v.size();i++) {
		int note = v[i];
		for (int j = 0;j < i; j++) {
			if (note < v[j]) {
				for (int k = i;k > j;k--) {
					v[k] = v[k - 1];
				}
				v[j] = note;
				break;
			}
		}
	}
	return v;
}

vector<int> bubleS(vector<int> v) {
	for (int i = 0;i < v.size()-1;i++) {
		for (int j = 0;j < v.size() - 1;j++) {
			if (v[j] > v[j + 1]) {
				int tmp = v[j];
				v[j] = v[j + 1];
				v[j + 1] = tmp;
			}
		}
	}
	return v;
}

vector<int> q(vector<int> v, int start, int end) {
	if (start >= end)return v;
	int i = start, j = end, x = v[start];
	while(i<j){
		while ((i <= j) && (v[j] >= x))j--;
		if (i < j) v[i++] = v[j];
		while (i < j && v[i] < x) i++;
		if (i < j) v[j--] = v[i];
	}
	v[i] = x;
	v = q(v, start, i-1);
	v = q(v, i + 1, end);
	return v;
}

vector<int> quickS(vector<int> v)
{
	return q(v, 0, v.size() - 1);
}

vector<int> merge(vector<int> v, int start, int mid, int end)
{
    vector<int> tmp;
    int i = start, j = mid + 1;

    while(i <= mid && j <= end){
        if (v[i] <= v[j]) tmp.push_back(v[i++]);
        else tmp.push_back(v[j++]);
    }
    while(i <= mid)tmp.push_back(v[i++]);
    while(j <= end)tmp.push_back(v[j++]);

    for (i = 0; i < tmp.size(); i++)v[start + i] = tmp[i];

    return v;
}

vector<int> mergeSortUp2Down(vector<int> v, int start, int end)
{
    if(v.size()==0 || start >= end)return v;

    int mid = (end + start)>>1;
    v=mergeSortUp2Down(v, start, mid);
    v=mergeSortUp2Down(v, mid+1, end);

    v=merge(v, start, mid, end);
    return v;
}

vector<int> mergeS(vector<int> v){
    return mergeSortUp2Down(v,0,v.size()-1);
}

// 以[low, high]为合法边界，以v[i]为根节点维护最大堆，其中近根节点及其两个子节点有可能不满足最大堆性质
void maxHeapify(vector<int> &v, int i, int low, int high)
{
	if(low >= high)return;
	int l = (i << 1) + 1;
	int r = (i << 1) + 2;
	int largest;	//v[i], v[l], v[r]中的最大值的索引

	// 找到三个节点中的最大值和i交换，作为父节点
	if (l <= high && v[l] > v[i])largest = l;
	else largest = i;
	if (r <= high && v[r] > v[largest])largest = r;

	if (largest != i) {
		int tmp = v[i];
		v[i] = v[largest];
		v[largest] = tmp;
		// 交换有可能破坏子树的最大堆性质，所以对子树中产生改变的节点进行一次维护，另一个节点依然有最大堆性质，保持不变。
		maxHeapify(v, largest, low, high);
	}
	else return;
}

// 从原二叉树的最后一个非叶节点开始进行调整
void buildMaxHeap(vector<int> &v)
{
	for (int i = v.size() >> 1;i >= 0;i--) { maxHeapify(v, i, 0, v.size() - 1); }
}

vector<int> heapS(vector<int> v)
{
	int length = v.size();
	//建立最大堆
	buildMaxHeap(v);
	for (int i = length - 1;i > 0;i--) {
		// 交换根节点和最后一个节点的位置
		int tmp = v[i];
		v[i] = v[0];
		v[0] = tmp;
		// 维护0到i-1的子数组依然是最大堆
		maxHeapify(v, 0, 0, i - 1);
	}
	return v;
}

int main()
{
	vector<int> v = { 2,4,5,6,32,124,654,32,213,3,432,32,1,4, };
	//v = selectS(v);
	//v = insertS(v);
	//v = bubleS(v);
	//v = quickS(v);
    //v = mergeS(v);
    v=heapS(v);

	for (int i = 0;i < v.size();i++)cout << v[i] <<' ';
	return 0;
}