目录
排序算法的稳定性： 大小相同的元素在排序前后相对位置相同就称其为稳定的排序。
注：一个本身就是稳定的排序 是可以实现为不稳定的排序的 ；但是相反 一个本身就不稳定的排序 是不可能实现为稳定的排序的。
稳定的排序算法：插入排序 冒泡排序 归并排序
冒泡排序
public static void bubbleSort(int[] array){
for (int i = 0; i < array.length-1; i++) {
for (int j = 0; j < array.length-1; j++) {
if (array[j] > array[j+1]) {
swap(array, j, j+1);
}
}
}
}
private static void swap(int[] array, int minIndex, int i) {
int tmp = array[i];
array[i] = array[minIndex];
array[minIndex] = tmp;
}优化：
public static void bubbleSort(int[] array) {
for (int i = 0; i < array.length-1; i++) {
boolean flg = false;
for (int j = 0; j < array.length-1-i; j++) {
if(array[j] > array[j+1]) {
swap(array,j,j+1);
flg = true;
}
}
if(!flg) {
return;
}
}
}堆排序
public static void heapSort(int[] array){
createHeap(array);
for (int i = 0; i < array.length - 1; i++) {
swap(array, 0, array.length-1-i);
shiftDown(array, 0, array.length-1-i);
}
}
private static void createHeap(int[] array) {
for (int i = (array.length-1-1)/2; i >= 0; i--) {
shiftDown(array, i, array.length);
}
}
private static void shiftDown(int[] array, int i, int length) {//length个元素
int child = i * 2 + 1;
while (child < length) {
if (child + 1 < length && array[child] < array[child+1]) {
child++;
}
if (array[child] > array[i]) {
swap(array, child, i);
i = child;
}else {
break;
}
child = i * 2 + 1;
}
}
private static void swap(int[] array, int minIndex, int i) {
int tmp = array[i];
array[i] = array[minIndex];
array[minIndex] = tmp;
}插入排序
public static void insertSort(int[] array){
for (int i = 1; i < array.length; i++) {
int tmp = array[i];
int j = i - 1;
for (; j >= 0 ; j--) {
//如果此处改为array[j] >= tmp就会变成不稳定排序
if (array[j] > tmp) {
array[j+1] = array[j];
}else{
break;
}
}
array[j+1] = tmp;
}
}希尔排序
public static void shellSort(int[] array){
int gap = array.length;
while (gap > 1) {
gap = gap / 2;
shell(array, gap);
}
}
private static void shell(int[] array, int gap) {
for (int i = gap; i < array.length; i++) {
int tmp = array[i];
int j = i-gap;
for (; j >= 0; j -= gap) {
if (array[j] > tmp) {
array[j+gap] = array[j];
}else {
break;
}
}
array[j+gap] = tmp;
}
}归并排序
public void mergerSort(int[] nums, int left, int right) {//right:数组长度减一
if (left >= right) {
return;
}
int mid = (left + right) / 2;
mergerSort(nums, left, mid);
mergerSort(nums, mid + 1, right);
merger(nums, left, mid, right);
}
private void merger(int[] nums, int left, int mid, int right) {
int[] tmp = new int[right-left+1];
int i = 0;
int l = left;
int r = mid + 1;
while (l <= mid && r <= right) {
if (nums[l] < nums[r]) {
tmp[i++] = nums[l++];
}else {
tmp[i++] = nums[r++];
}
}
while (l <= mid) {
tmp[i++] = nums[l++];
}
while (r <= right) {
tmp[i++] = nums[r++];
}
i = 0;
for (int j = 0; j < tmp.length; j++) {
nums[left++] = tmp[j];
}
}快速排序
public static void quickSort(int[] array){
quick(array, 0, array.length-1);
}
private static void quick(int[] array, int left, int right) {
if (left >= right) {
return;
}
int Index = findSwap(array, left, right);
quick(array, left, Index-1);
quick(array, Index+1, right);
}
private static int findSwap(int[] array, int left, int right) {
int key = array[left];
int keyIndex = left;
while (left < right) {
//必须right先走
//如果是left先走，两个相遇的地方一定比key大
while (left < right && array[right] >= key) {
right--;
}
while (left < right && array[left] <= key) {
left++;
}
swap(array, right, left);
}
if (left == right) {
swap(array, keyIndex, left);
}
return left;
}
private static void swap(int[] array, int minIndex, int i) {
int tmp = array[i];
array[i] = array[minIndex];
array[minIndex] = tmp;
}优化
利用三数取中法来避免但分支书的形成（尽量降低树的高度）
public int[] sortArray(int[] nums) {
//快速排序
quickSort(nums, 0, nums.length-1);
return nums;
}
private void quickSort(int[] nums, int left, int right) {
if (left >= right) {
return;
}
//三数取中法
swap(nums, left, threeNumMid(nums, left, right));
//也可以在这里加一个判断当左右之间的数据个数小于一定值然后调用插入排序
//因为在排序过程中数组会趋近于有序所以插入排序的效率会很快
int pivot = quick(nums, left, right);
quickSort(nums, left, pivot-1);
quickSort(nums, pivot+1, right);
}
private int threeNumMid(int[] nums, int left, int right) {
int mid = (left + right) / 2;
if (nums[left] > nums[right]) {
if (nums[mid] > nums[left]) {
return left;
}else if (nums[mid] < nums[right]) {
return right;
}else {
return mid;
}
}else {
if (nums[mid] < nums[left]) {
return left;
}else if (nums[mid] > nums[right]) {
return right;
}else {
return mid;
}
}
}
private int quick(int[] nums, int left, int right) {
int index = left;
int key = nums[left];
while (left < right) {
while (left < right && nums[right] >= key) {
right--;
}
while (left < right && nums[left] <= key) {
left++;
}
swap(nums, right, left);
}
swap(nums, index, left);
return left;
}
private void swap(int[] nums, int left, int right) {
int tmp = nums[left];
nums[left] = nums[right];
nums[right] = tmp;
}选择排序
public static void selectSort(int[] array){
for (int i = 0; i < array.length; i++) {
int minIndex = i;
for (int j = i+1; j < array.length; j++) {
if (array[minIndex] > array[j]) {
minIndex = j;
}
}
swap(array, minIndex, i);
}
}
private static void swap(int[] array, int minIndex, int i) {
int tmp = array[i];
array[i] = array[minIndex];
array[minIndex] = tmp;
}
