Java综合整理堆排序 快速排序 归并排序

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));
    }

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