1. 排序算法代码实现
/*** ascending sort* 外层循环边界条件：总共需要冒泡的轮数--每一轮都将最大或最小的数冒泡到最后* 内层循环边界条件：冒泡数字移动的边界--最终数字需冒泡到此处* 时间复杂度：O(n^2)* @param arr*/
public static void bubbleSort(int[] arr) {if (arr == null) {throw new RuntimeException("Input arr is null!");}for(int i = 0; i < arr.length - 1; i++) {for(int j = 0; j < arr.length - 1 - i; j++) { //冒泡：相邻两数比较，大的向后冒if(arr[j] > arr[j+1]) {int temp = arr[j];arr[j] = arr[j+1];arr[j+1] = temp;}}}
}/*** 每次都将未排序数组中的最大或最小元素找出来和第一个元素交换位置* 时间复杂度：O(n^2)* @param arr*/
public static void selectSort(int[] arr) {if (arr == null) {throw new RuntimeException("Input arr is null!");}for(int i = 0; i < arr.length - 1; i++) {//寻找最小元素的下标，避免频繁交换数组int min = i;for(int j = i + 1; j < arr.length; j++) {if (arr[j] < arr[min]) {min = j;}}//将最小的元素交换到未排序数组的最前面int temp = arr[i];arr[i] = arr[min];arr[min] = temp;}
}/*** 插入排序：顺次从数组中选择一个数，插入到前面已排序的数组中* 时间复杂度：O(n)~O(n^2)* @param arr*/
public static void insertSort(int[] arr) {if (arr == null) {throw new RuntimeException("Input arr is null!");}for(int i = 1; i < arr.length; i++) {int value = arr[i];//插入的位置int j = 0;//循环i前面的数，若值比插入的值大，则顺次向后移动for (j = i - 1; j >= 0; j--) {if(arr[j] > value) {arr[j+1] = arr[j];} else {break;}}arr[j+1]=value;}
}/*** 希尔排序：插入排序的改进版，也称缩小增量排序** @param arr*/
public static void shellSort(int[] arr) {if (arr == null) {throw new RuntimeException("Input arr is null!");}int length = arr.length;//区间int gap = 1;while(gap < length) {gap = gap * 3 +1;}while(gap > 0) {for(int i = gap; i < length; i++) {int tmp = arr[i];int j = i -gap;//跨区间排序while(j >= 0 && arr[j] > tmp) {arr[j+gap] = arr[j];j -= gap;}arr[j + gap] = tmp;}gap = gap / 3;}
}/*** 归并排序--核心为分治法* 时间复杂度O(nlogn)* @param arr*/
public static void mergeSort(int[] arr) {if (arr == null) {throw new RuntimeException("Input arr is null!");}int[] tmpArr = new int[arr.length];mSort(arr,tmpArr, 0, arr.length - 1);
}private static void mSort(int[] arr, int[] tmpArr, int startIndex, int endIndex) {//边界条件：数组已不可再拆if (endIndex <= startIndex) {return;}//将数组对拆为前后两个数组int middleIndex = startIndex + (endIndex - startIndex)/2;mSort(arr, tmpArr, startIndex, middleIndex);mSort(arr, tmpArr, middleIndex + 1, endIndex);merge(arr, tmpArr, startIndex, middleIndex, endIndex);
}private static void merge(int[] arr, int[] tmpArr, int startIndex, int middleIndex, int endIndex) {//将要合并的数组复制到临时数组for (int i = startIndex; i <= endIndex; i++) {tmpArr[i] = arr[i];}//左边数组起始下标int left = startIndex;//右边数组起始下标int right = middleIndex + 1;for(int k = startIndex; k <= endIndex; k++) { if (left > middleIndex) {arr[k] = tmpArr[right++];} else if (right > endIndex) {arr[k] = tmpArr[left++];} else if (tmpArr[left] < tmpArr[right]) {arr[k] = tmpArr[left++];} else {arr[k] = tmpArr[right++];} }
}/*** 快速排序：随机选取一个参考值，将比参考值小的数移到数组前段，大的值移到后段* 以参考值为临界点递归拆分数组直至数组不能拆分，此时数组本身已排好序* 快速排序时间复杂度为O(nlogn)，对于逆序数组复杂度退化为O(n^2)，为了避免极端情况，可随机选取参考值* @param arr*/
public static void quickSort(int[] arr) {if (arr == null) {throw new RuntimeException("Input arr is null!");}qSort(arr , 0, arr.length - 1);
}private static void qSort(int[] arr, int startIndex, int endIndex) {// 设置边界条件if (endIndex <= startIndex) {return;}// 将数组按参考值整理成比参考值小的前段和比参考值大的后段，返回参考值的位置int refIndex = partition(arr, startIndex, endIndex);// 参考值已确定排序后的位置，不参与数组拆分if (refIndex > startIndex) {qSort(arr, startIndex, refIndex - 1);}if (endIndex > refIndex) {qSort(arr, refIndex + 1, endIndex);}
}
private static int partition(int[] arr, int startIndex, int endIndex) {// 将数组中refValue的值与最后一个数交换，随机选取参考值可避免时间复杂度退化为O(n^2)int refIndex = startIndex + new Random().nextInt(endIndex - startIndex + 1);// 深坑，当两个数指向同一个时，会影响异或结果if (refIndex != endIndex) {arr[endIndex] = arr[endIndex] ^ arr[refIndex];arr[refIndex] = arr[endIndex] ^ arr[refIndex];arr[endIndex] = arr[endIndex] ^ arr[refIndex];}// 分组下标int partitionIndex = startIndex - 1;// 数组最后一个值为参考值，不参与循环for (int dataIndex = startIndex; dataIndex < endIndex; dataIndex++) {// 与参考值进行比较，若比参考值小，则移动到数组前面if ((arr[dataIndex] < arr[endIndex]) ) {// 始终指向最后一个确定比参考值小的值++partitionIndex;// 如果当前数据的位置与参考下标不一致，将此值与参考下标指向的值交换，保证小的值交换到前面if (partitionIndex != dataIndex) {arr[dataIndex] = arr[dataIndex] ^ arr[partitionIndex] ;arr[partitionIndex] = arr[dataIndex] ^ arr[partitionIndex];arr[dataIndex] = arr[dataIndex] ^ arr[partitionIndex];} }}// 将参考值交换到指定位置++partitionIndex;if (partitionIndex != endIndex) {arr[endIndex] = arr[endIndex] ^ arr[partitionIndex] ;arr[partitionIndex] = arr[endIndex] ^ arr[partitionIndex];arr[endIndex] = arr[endIndex] ^ arr[partitionIndex];}return partitionIndex;
}/*** 堆排序--最大堆实现* 时间复杂度O(nlogn)* @param arr*/
public static void heapSort(int[] arr) {if (arr == null) {throw new RuntimeException("Input arr is null!");}int length = arr.length;//构建堆buildHeap(arr, length);for (int i = length - 1; i > 0; i--) {//将堆元素与末位元素调换int temp = arr[0];arr[0] =arr[i];arr[i] = temp;//数组长度-1 隐藏堆尾元素length--;//将堆顶元素下沉，目的是将最大的元素浮到堆顶来sink(arr, 0, length);}
}
private static void buildHeap(int[] arr, int length) {for (int i = length / 2; i >= 0; i--) {sink(arr, i , length);}
}private static void sink(int[] arr, int index, int length) {//左子节点下标int leftChild = 2 * index + 1;//右子节点下标int rigthChild = 2 * index + 2;//要调整的节点下标int present = index;//下沉左边if (leftChild < length && arr[leftChild] > arr[present]) {present = leftChild;}//下沉右边if (rigthChild < length && arr[rigthChild] > arr[present]) {present = rigthChild;}//如果下标不相等，证明调换过了if (present != index) {//交换值int temp = arr[index];arr[index] = arr[present];arr[present] = temp;//继续下沉sink(arr, present, length);}
}/*** 计数排序--时间复杂度为O(n+m)，空间大小取决于数组值，时间复杂度为O(n)* 问题点：数组中不能有负数，否则会抛出越界异常* @param arr*/
public static void countSort(int[] arr) {if (arr == null) {throw new RuntimeException("Input arr is null!");}//找出数组中的最大值int max = arr[0];for(int i = 1; i < arr.length; i++) {if (arr[i] < 0) {throw new RuntimeException("Cannot use countsort! Array contains negative number.");}if (max < arr[i]) {max = arr[i];}}//利用最大值构建一个数组，用空间换时间int[] countArr = new int[max + 1];//计数for (int i = 0; i < arr.length; i++) {countArr[arr[i]]++;}int index = 0;for (int i = 0; i < countArr.length; i++) {while (countArr[i] > 0) {arr[index++] = i;countArr[i]--;}}
}/*** 桶排序--类似于Hash分桶策略* 良好的分桶策略可实现O(n)时间复杂度* @param arr*/
public static void bucketSort(int[] arr) {if (arr == null) {throw new RuntimeException("Input arr is null!");}//最大最小值int max = arr[0];int min = arr[0];int length = arr.length;for (int i = 1; i < length; i++) {if (arr[i] > max) {max = arr[i];} else if (arr[i] < min) {min = arr[i];}}//最大值与最小值的差int diff = max - min;//桶列表ArrayList<ArrayList<Integer>> bucketList = new ArrayList<>();for (int i = 0; i < length; i++) {bucketList.add(new ArrayList<>());}//每个桶的存数区间float section = (float)diff / (float)(length -1);//数据入桶for (int i = 0; i < length; i++) {//当前数除以区间得出存放桶的位置 减1后得出桶的下标int num = (int) (arr[i] / section) - 1;if (num < 0) {num = 0;}bucketList.get(num).add(arr[i]);}//桶内排序for (int i = 0; i < bucketList.size(); i++) {Collections.sort(bucketList.get(i));}//写入数据int index = 0;for (ArrayList<Integer> arrayList: bucketList) {for (int value : arrayList) {arr[index] = value;index++;}}
}/*** 基数排序* @param arr*/
public static void radixSort(int[] arr) {if (arr == null) {throw new RuntimeException("Input arr is null!");}int length = arr.length;//最大值int max = arr[0];for(int i = 0;i < length;i++){if(arr[i] > max){max = arr[i];}}//当前排序位置int location = 1;//桶列表ArrayList<ArrayList<Integer>> bucketList = new ArrayList<>();//长度为10 装入余数0-9的数据for(int i = 0; i < 10; i++){bucketList.add(new ArrayList<>());}while(true){//判断是否排完int dd = (int)Math.pow(10, (location - 1));if(max < dd){break;}//数据入桶for(int i = 0; i < length; i++){//计算余数 放入相应的桶int number = ((arr[i] / dd) % 10);bucketList.get(number).add(arr[i]);}//写回数组int nn = 0;for (int i=0;i<10;i++){int size = bucketList.get(i).size();for(int ii = 0;ii < size;ii ++){arr[nn++] = bucketList.get(i).get(ii);}bucketList.get(i).clear();}location++;}
}
2. 查询算法代码实现
/*** 顺序查找，即为遍历数组，时间复杂度为O(n)* @param arr* @param value* @return*/ public static int sequentialSearch(int[] arr, int value) {if (arr == null) {throw new RuntimeException("Input arr is null!");}for (int i = 0; i < arr.length; i++) {if (arr[i] == value) {return i;}}return -1; }/*** 二分查找针对以升序排列的数组进行，每次取数组的中间值进行查找* 时间复杂度为O(logn)* @param arr* @param value* @return*/ public static int binarySearch(int[] arr, int value) {if (arr == null) {throw new RuntimeException("Input arr is null!");}int low = 0;int high = arr.length - 1;int mid = 0;while (low <= high) {mid = (low + high)/2;if (arr[mid] == value) {return mid;} else if (arr[mid] > value) {high = mid -1;} else {low = mid + 1;}}return -1; }/*** 二分查找--递归实现* @param arr 待查询数组* @param value 查找目标值* @param low 数组起始下标* @param high 数组结束下标* @return 目标值的下标*/ public static int binarySearchByRecursion(int[] arr, int value, int low, int high) {if (arr == null) {throw new RuntimeException("Input arr is null!");}int mid = low + (high -low)/2;if (low == high && arr[mid] != value) {return -1;}if (arr[mid] == value) {return mid;} else if (arr[mid] > value) {return binarySearchByRecursion(arr, value, low, mid - 1);} else {return binarySearchByRecursion(arr, value, mid + 1, high);} }/*** 插值查找--递归实现，原理与二分查找类似，按目标值的大小计算在数组中的权重，适用于均有有序的数组* @param arr 待查询数组* @param value 查找目标值* @param low 数组起始下标* @param high 数组结束下标* @return 目标值的下标*/ public static int insertionSearch(int[] arr, int value, int low, int high) {if (arr == null) {throw new RuntimeException("Input arr is null!");}// 按目标值与最小值的差估算插值下标的位置int mid = low + ((value - arr[low]) / (arr[high] - arr[low])) * (high -low);if (low == high && arr[mid] != value) {return -1;}if (arr[mid] == value) {return mid;} else if (arr[mid] > value) {return binarySearchByRecursion(arr, value, low, mid - 1);} else {return binarySearchByRecursion(arr, value, mid + 1, high);} }
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