Sort

Quick sort

• quick sort

<= p >=p

two part

11111111112，防止分布不均

average time complexity O(nlogn)

worst O(n^2)

space complexity O(1)

non stability

先整体有序，后局部有序

public class Solution {
    /**
     * @param A: an integer array
     * @return: nothing
     */
    public void sortIntegers(int[] A) {
        if (A == null || A.length == 0) {
            return;
        }
        quickSort(A, 0, A.length - 1);
    }
    
    private void quickSort(int[] A, int start, int end) {
        if (start >= end) {
            return;
        }
        
        int left = start, right = end;
        int pivot = A[(start + end) / 2];
        //left <= right
        //32145, 不存在交集，否则不断循环
        //[12][2345]
        while (left <= right) {
            //1111111 A[left]<=pivot，全部归到左面，不均衡
            while (left <= right && A[left] < pivot) {
                left++;
            }
            while (left <= right && A[right] > pivot) {
                right--;
            }
            if (left <= right) {
                int temp = A[left];
                A[left] = A[right];
                A[right] = temp;
                left++;
                right--;
            }
        }
        quickSort(A, start, right);
        quickSort(A, left, end);
    }
}

Merge sort

• merge sort

worst O(nlogn)

space complexity O(n)

stability

先局部有序，后整体有序

public class Solution {
    public void sortIntegers(int[] A) {
        if (A == null || A.length == 0) {
            return;
        }
        int[] temp = new int[A.length];
        mergeSort(A, 0, A.length - 1, temp);
    }
    
    private void mergeSort(int[] A, int start, int end, int[] temp) {
        if (start >= end) {
            return;
        }
        mergeSort(A, start, (start + end) / 2, temp);
        mergeSort(A, (start + end) / 2 + 1, end, temp);
        merge(A, start, end, temp);
    }
    
    private void merge(int[] A, int start, int end, int[] temp) {
        int middle = (start + end) / 2;
        int leftIndex = start;
        int rightIndex = middle + 1;
        int index = start;
        while (leftIndex <= middle && rightIndex <= end) {
            if (A[leftIndex] <= A[rightIndex]) {
                temp[index++] = A[leftIndex++];
            } else {
                temp[index++] = A[rightIndex++];
            }
        }
        while (leftIndex <= middle) {
            temp[index++] = A[leftIndex++];
        }
        while (rightIndex <= end) {
            temp[index++] = A[rightIndex++];
        }
        for (int i = start; i <= end; i++) {
            A[i] = temp[i];
        }
    }
}

Quick selection

• kth largest element

O(n)

class Solution {
    /*
     * @param k : description of k
     * @param nums : array of nums
     * @return: description of return
     */
    public int kthLargestElement(int k, int[] nums) {
        if (nums == null || nums.length == 0 || k < 1 || k > nums.length){
            return -1;
        }
        return partition(nums, 0, nums.length - 1, nums.length - k);
    }
    
    private int partition(int[] nums, int start, int end, int k) {
        if (start >= end) {
            return nums[k];
        }
        
        int left = start, right = end;
        int pivot = nums[(start + end) / 2];
        
        while (left <= right) {
            while (left <= right && nums[left] < pivot) {
                left++;
            }
            while (left <= right && nums[right] > pivot) {
                right--;
            }
            if (left <= right) {
                swap(nums, left, right);
                left++;
                right--;
            }
        }
        //start-right right-left left-end 三部分
        if (k <= right) {
            return partition(nums, start, right, k);
        }
        if (k >= left) {
            return partition(nums, left, end, k);
        }
        return nums[k];
    }    
    
    private void swap(int[] nums, int i, int j) {
        int tmp = nums[i];
        nums[i] = nums[j];
        nums[j] = tmp;
    }
};