剑指offer算法题：最小的K个数GetLeastNumbers_Solution

输入n个整数，找出其中最小的K个数。例如输入4,5,1,6,2,7,3,8这8个数字，则最小的4个数字是1,2,3,4,。

思路：
利用快排的partition思想，指定一个目标值，使得目标值左侧都比目标值小，右侧都比目标值大；
交换完后，如果目标值的下标正好等于k - 1（从0 -> k-1共k个）那么说明目标值下标及之前就是数组中最小的k个数。

public class Solution {
    public ArrayList<Integer> GetLeastNumbers_Solution(int [] input, int k) {
        int length;
        ArrayList<Integer> result = new ArrayList<>();
        if(input == null || (length = input.length) == 0 || k > length || k == 0)
            return result;
        int index = partition(input,0,length - 1);
        while(index != k - 1) {
            if(index > k - 1) {
                index = partition(input,0,index - 1);
            }else{
                index = partition(input,index + 1,length - 1);
            }
        }
        for(int i = 0; i < k;i++) {
            result.add(input[i]);
        }
        return result;
    }
    private int partition(int[] numbers, int start,int end) {
        int target = numbers[start];
        int index = start;
        while(start < end) {
            while(start < end && numbers[end] >= target)end--;
            while(start < end && numbers[start] <= target)start++;
            if(end > start) {
                int tmp = numbers[end];
                numbers[end] = numbers[start];
                numbers[start] = tmp;
            }
        }
        int tmp = numbers[index];
        numbers[index] = numbers[end];
        numbers[end] = tmp;
        return end;
    }
}

思路：构造辅助数据容器 + 插排排序

import java.util.ArrayList;
import java.util.Arrays;
public class Solution {
    //数据容器选择的是数组，并用插排进行排序
    public ArrayList<Integer> GetLeastNumbers_Solution(int [] input, int k) {
        int length;
        ArrayList<Integer> result = new ArrayList<>();
        if(input == null || (length = input.length) == 0 || k > length || k == 0)
            return result;
        //size为k的数据容器
        Integer[] numbers = new Integer[k];
        //初始化为最大值为了比较
        for(int i = 0;i < numbers.length;i++) {
            numbers[i] = Integer.MAX_VALUE;
        }
        for(int i = 0; i < length;i++) {
            insertSort(numbers,input[i]);
        }
        result = new ArrayList(Arrays.asList(numbers));
        return result;
    }
    private void insertSort(Integer[] numbers,int number) {
        int length = numbers.length;
        //如果比最大值小，那么进入循环找出新的最大值
        if(number < numbers[length-1]) {
            numbers[length-1] = number;
            //插入排序
            for(int j = length - 1; j > 0 && numbers[j] < numbers[j - 1];j--) {
                int tmp = numbers[j];
                numbers[j] = numbers[j - 1];
                numbers[j - 1] = tmp;
            }
        }
    }
}