堆排序；快速排序；归并排序

Posted 2023-02-20 小写丶H

快速排序算法

• 堆排序
• 快速排序
• • 递归
  • 非递归
• 归并排序
• • 递归
  • 非递归

堆排序

时间复杂度：0（N*log(N)）
空间复杂度：0（1）
稳定性：不稳定

private static void heapSort(int[] arr) 
		//建堆
        crearHeap(arr);
        for (int i = 0; i < arr.length-1; i++) 
            int heapSize=arr.length-i;
            swap(arr,heapSize-1,0);
            heapSize--;
            shiftDown(arr,heapSize,0);
        
        System.out.println(Arrays.toString(arr));
    

    private static void crearHeap(int[] arr) 
    	// 从后往前遍历(右边非叶子节点开始), 依次进行向下调整
        for (int i = (arr.length-1-1)/2; i >=0 ; i--) 
            shiftDown(arr,arr.length,i);
        
        
    
	//向下调整，形成大堆
    private static void shiftDown(int[] arr, int size, int i) 
        int parent = i;
        int child = parent*2+1;
        while (child<size)
            if (child +1< size && arr[child +1]> arr[child])
                child=child+1;
            
            if (arr[child]>arr[parent])
                swap(arr,child,parent);
            else 
                break;
            
            parent=child;
            child=parent*2+1;
        
    
	//交换
    private static void swap(int[] arr, int child, int parent) 
        int tmp =arr[child];
        arr[child] =arr[parent];
        arr[parent]=tmp;
    

快速排序

时间复杂度:O(N^ logN) 最坏的时候O(N^2) 和基准值密切相关
空间复杂度:0(logN) 最坏的时候O(N)
稳定性:不稳定

递归

private static void quick(int[] arr) 
        quickSortHelper(arr,0,arr.length-1);
        System.out.println(Arrays.toString(arr));
    

    private static void quickSortHelper(int[] arr, int left, int right) 
        if (left>=right)
            //区间只有一个元素，或者零个元素
            return;
        
        int index = partition(arr,left,right);
        quickSortHelper(arr,left,index-1);
        quickSortHelper(arr,index+1,right);
    

    private static int partition(int[] arr, int left, int right) 
        int i=left;
        int j=right;
        int baseValue=arr[right];
        while (i<j)
            while (i<j && arr[i]<=baseValue)
                i++;
            
            while (i<j && arr[j]>=baseValue)
                j--;
            
            if (i<j)
                swap(arr,i,j);
            
        
        swap(arr,i,right);
        return i;
    

    private static void swap(int[] arr, int i, int j) 
        int tmp =arr[i];
        arr[i]=arr[j];
        arr[j]=tmp;
    

非递归

public static void quickSortByLoop(int[] arr) 
        Stack<Integer> stack =new Stack<>();
        stack.push(0);
        stack.push(arr.length-1);
        while (!stack.isEmpty())
            int right = stack.pop();
            int left = stack.pop();
            if (left>=right)
                continue;
            
            int index = partition(arr,left,right);
            //右子树
            stack.push(index+1);
            stack.push(right);
            //左子树
            stack.push(left);
            stack.push(index-1);
        
        System.out.println(Arrays.toString(arr));
    

    private static int partition(int[] arr, int left, int right) 
        int baseValue =arr[right];
        int i =left;
        int j =right;
        while (i<j)
            while (i<j && arr[i]<=baseValue)
                i++;
            
            while (i<j && arr[j]>=baseValue)
                j--;
            
            if (i<j)
                swap(arr,i,j);
            
        
        swap(arr,i,right);
        return i;
    

    private static void swap(int[] arr, int i, int j) 
        int tmp = arr[i];
        arr[i] = arr[j];
        arr[j] = tmp;
    

归并排序

时间复杂度:O(NlogN)
空间复杂度:O(N） 如果是链表，可以为O(1)
稳定性:稳定

递归

public static void mergeSort(int[] arr)
        mergeSortHelper(arr,0,arr.length);
        System.out.println(Arrays.toString(arr));
    

    private static void mergeSortHelper(int[] arr, int left, int right) 
        if (right-left<=1)
            return;
        
        int mid = (right+left)/2;

        mergeSortHelper(arr,left,mid);
        mergeSortHelper(arr,mid,right);
        merge(arr,left,mid,right);
    

    private static void merge(int[] arr, int left, int mid, int right) 
        int cur1 =left;
        int cur2 =mid;
        //两个数组合并后的结果
        int[] output=new int[right-left];
        int outputIndex=0;

        while (cur1<mid && cur2<right)
            if (arr[cur1]<=arr[cur2]) 
                output[outputIndex++] = arr[cur1++];
            else 
                output[outputIndex++] = arr[cur2++];
            
        
        while (cur1<mid)
            output[outputIndex++] = arr[cur1++];
        
        while (cur2<right)
            output[outputIndex++] = arr[cur2++];
        

        for (int i = 0; i < right-left ; i++) 
            arr[left+i] = output[i];
        
    

非递归

public static void mergeSortByLoop(int[] arr)
        // gap 当前每个组中的元素个数.
        for (int gap =1;gap<arr.length;gap*=2)
            for (int i = 0; i <arr.length ; i+=2*gap) 
                //相当于把两个长度为 gap 的相邻组进行了合并
                int left =i;
                int mid =i+gap;
                int right=i+2*gap;
                if (mid > arr.length)
                    mid =arr.length;
                
                if (right>arr.length)
                    right=arr.length;
                
                merge(arr,left,mid,right);
            
        
        System.out.println(Arrays.toString(arr));