【剑指offer】【排序】40.最小的k个数

题目链接：https://leetcode-cn.com/problems/zui-xiao-de-kge-shu-lcof/

堆排序

class Solution {
public:
    vector<int> getLeastNumbers(vector<int>& arr, int k) {
        int n = arr.size();
        arr.push_back(arr[0]);
        for(int i = n / 2; i; i--)
            down(arr, i, n);
        int m = k;
        vector<int> res;
        while(m--)
        {
            res.push_back(arr[1]);
            arr[1] = arr[n];
            n--;
            down(arr, 1, n);
        }
        return res;
    }
    void down(vector<int>& arr, int u, int n)
    {
        int t = u;
        if(u * 2 <= n && arr[u * 2] < arr[t]) t = u * 2;
        if(u * 2 + 1 <= n && arr[u * 2 + 1] < arr[t]) t = u * 2 + 1;
        if(t != u) swap(arr[t], arr[u]), down(arr, t, n);
    }
};

快速排序

在待排序的数组中找一个基准，将基准放到数组中合适的位置，左边比他小右边比他大；
递归对左右两边再进行同样的操作；

class Solution {
public:
    vector<int> getLeastNumbers(vector<int>& arr, int k) {
        int n = arr.size();
        quick_sort(arr, 0, n - 1);
        vector<int> res;
        for(int i = 0; i < k; i++)
            res.push_back(arr[i]);
        return res;
    }
    void quick_sort(vector<int>& arr, int l, int r){
        if(l >= r) return;
        int i = l - 1, j = r + 1, x = arr[l + r >> 1];
        while(i < j){
            do i++; while(arr[i] < x);
            do j--; while(arr[j] > x);
            if(i < j) swap(arr[i], arr[j]);
        }
        quick_sort(arr, l, j);
        quick_sort(arr, j + 1, r);
    }
};

归并排序

class Solution {
public:
    vector<int> getLeastNumbers(vector<int>& arr, int k) {
        merge_sort(arr, 0, arr.size() - 1);
        vector<int> res;
        for(int i = 0; i < k; i++)
            res.push_back(arr[i]);
        return res;
    }
    void merge_sort(vector<int> &arr, int l, int r)
    {
        if(l >= r) return ;
        int mid = l + r >> 1;
        merge_sort(arr, l, mid), merge_sort(arr, mid + 1, r);
        int i = l, j = mid + 1, k = 0;
        vector<int> tmp(r - l + 1);
        while(i <= mid && j <= r)
        {
            if(arr[i] < arr[j]) tmp[k++] = arr[i++];
            else tmp[k++] = arr[j++];
        }
        while(i <= mid) tmp[k++] = arr[i++];
        while(j <= r) tmp[k++] = arr[j++];
        for(int i = l, k = 0; i <= r; k++, i++) arr[i] = tmp[k];
    }
};