排序算法

名称	平均时间复杂度	最好情况	最坏情况	空间复杂度	稳定性
冒泡排序	$$O(n^2)$$	$$O(n)$$	$$O(n^2)$$	$$O(1)$$	$$Y$$
选择排序	$$O(n^2)$$	$$O(n^2)$$	$$O(n^2)$$	$$O(1)$$	$$N$$
堆排序	$$O(nlogn)$$	$$O(nlogn)$$	$$O(nlogn)$$	$$O(1)$$	$$N$$
插入排序	$$O(n^2)$$	$$O(n)$$	$$O(n^2)$$	$$O(1)$$	$$Y$$
希尔排序	$$O(nlogn)$$	$$O(n^2)$$	$$O(nlogn)$$	$$O(1)$$	$$N$$
归并排序	$$O(nlogn)$$	$$O(nlogn)$$	$$O(nlogn)$$	$$O(n)$$	$$Y$$
快速排序	$$O(nlogn)$$	$$O(nlogn)$$	$$O(n^2)$$	$$O(logn)$$	$$N$$
计数排数	$$O(n+k)$$	$$O(n+k)$$	$$O(n+k)$$	$$O(k)$$	$$Y$$
桶排序	$$O(n+k)$$	$$O(n+k)$$	$$O(n^2)$$	$$O(n+k)$$	$$Y$$
基数排序	$$O(n\times k)$$	$$O(n\times k)$$	$$O(n\times k)$$	$$O(n+k)$$	$$Y$$

一、冒泡排序

递归版

非递归

public class BubbleSort{
    
    public static void sort(int[] a) {
        
    }
    
    public void bubble(int[] a) {
        int j = a.length - 1;
        int x = 0;
        while (true) {
            
            for(int i = 0; i < j - 1; i++) {
                if (a[i] > a[i + 1]) {
                    swap(a, i, i + 1);
                  	x = i;  
                }
            }
            j = x;
            if (j == 0) {
                break;
            }
        }
    }
    
    private void swap(int[] a, int i, int j) {
        int temp = a[i];
        a[i] = a[j];
        a[j] = temp;
    }
}

二、选择排序

public class SelectSort{
    
    public static void sort(int[] a) {
        for(int i = a.length - 1; i > 0; i--) { 
            int max = i;
            
            for(int j = 0; j < i; j++) {
                if (a[j] > a[max]) {
                    max = j;
                }
            }
            if (max != i) {
                swap(a, i, max);
            } 
        }
    }
    

    
 	private void swap(int[] a, int i, int j) {
        int temp = a[i];
        a[i] = a[j];
        a[j] = temp;
    }   
}

堆排序

public class HeapSort() {
    
    public static void sort(int[] a) {
        heapify(a, a.length);
        for(int i = a.length - 1; i > 0; i--) {
            swap(a, 0, i);
            down(a, 0, i);
        }
    }
    
    public static void heapify(int[] array, int size) {
        for(int i = size / 2 - 1; i >= 0; i--) {
            down(array, i, size);
        }
    }
    
    public static void down(int[] array, int parent, int size) {
        int left = 2 * parent + 1;
        int right = left + 1;
        
        int max = parent;
        if (left < size && array[left] > array[max]) {
            max = left;
        }
        if (right < size && array[right] > array[max]) {
            max = right;
        }
        if (max != parent) {
            swap(array, max, parent);
            down(array, max, size);
        }
    }
    
    public static void swap(int[] array, int i, int j) {
        int temp = array[i];
        array[i] = array[j];
        array[j] = temp;
    }
}

插入排序

递归实现

public class InsertSort{
    
    public static void sort(int[] a) {
        insert(a, 1);
    }
    
    public static void insert(int[] a, int low) {
        if (low == a.length) {
            return ;
        }
        int t = a[low];
        int i;
        for(i = low - 1; i >= 0 && a[i] > t; i--) {
            a[i + 1] = a[i];
        }
        if (i + 1 != low) {
            a[i + 1] = t;
        }
        insert(a, low + 1);
    }
}

public class InsertSort{
    
    public static void sort(int[] a) {
        insert(a, 1);
    }
    
    public static void insert(int[] a, int low) {
        if (low == a.length) {
            return;
        }
        int temp = a[low];
       	int i = low - 1;
        while (i >= 0; a[i] > temp) {
            a[i + 1] = a[i];
            i--;
        }
        if (i + 1 != low) {
            a[i + 1] = temp;
        }
        insert(a, low + 1);
    }
}

非递归实现

public class InsertSort {
    
    public static void sort(int[] a) {
        for(int i = 1; i < a.length; i++) {
            int temp = a[i];
            for(int j = i - 1; j >= 0 && a[j] > a[i]; j--) {
                a[j + 1] =a[j];
            }
            if(j != i - 1) {
                a[j + 1] = temp;
            }
        }
    }
}

public class InsertSort {
    
    public static void sort(int[] a) {
        for(int i = 1; i < a.length; i++) {
            int temp = a[i];
            int j = i - 1;
            while (j >= 0 && a[j] > temp) {
                a[j + 1] = a[j];
            }
            if(j != i - 1) {
                a[j + 1] = temp;
            }
        }
    }
}

希尔排序

public class ShellSort{
    
    public static void sort(int[] a){
        for(int gap = a.length >> 1; gap >= 1; gap = gap >> 1) {
            
            for(int i = gap; i < a.length; i++) {
                int temp =  a[i];
               	int j = i - gap;
                while (j >= 0 && a[j] > temp) {
                    a[j + gap] = a[j];
                    j -= gap;
                }
                
                if (j + gap != i) {
                    a[j + gap] = temp;
                }
            }
        }
    }
}

归并排序

递归方法

public class MergeSort{
    
    public static void sort(int[] a) {
        int[] a2 = new int[a.length];
        merge(a, 0, a.length - 1, a2);
    }
    
    public static void split(int[] a, int left, int right, int[] a2) {
        if (left == right) {
            return;
        }
        int m = (left + right) >>> 1;
        
        split(a, left, m, a2);
        split(a, m + 1, right, a2);
        
        // 合并操作
        merge(a, left, m, m + 1, right, a2);
        System.arraycopy(a2, left, a, left, right - left + 1);
        
    }
    
    public static void merge(int[] a1, int i, int iend, int j, int jend, int[] a2) {
        int k = i;
        while (i <= iend && j <= jend) {
            if (a1[i] <= a1[j]) {
                a2[k] = a1[i];
                i++;
            } else {
                a2[k] = a1[j];
                j++;
            }
            k++;
        }
        if (i > iend) {
            System.arraycopy(a1, j, a2, k, jend - j + 1);
        } 
        if (j > jend) {
            System.arraycopy(a1, i, a2, k, iend - i + 1);
        }
    }
}

非递归方式

归并加插入

public class MergeInsertionSort{
    
    public static void insertion(int[] a, int left, int right) {
        for(int i = left + 1; i <= right; i++) {
            int t = a[i];
            int j = i - 1;
            while (j >= left && a[j] > t) {
                a[j + 1] = a[j];
                j--;
            }
            if (i != j + 1) {
                a[j + 1] = t;
            }
        }
    }
    
    public static void merge(int[] a, int i, int iend, int j, int jend, int[] a2) {
        int k = 0;
        while (i <= iend && j <= jend) {
            if (a[i] <= a[j]) {
                a[k] = a[i];
                i++;
            } else {
                a[k] = a[j];
                j++;
            }
            k++;
        }
        if (j > jend) {
            System.arraycopy(a, i, a2, k, iend - i + 1);
        }
        if (i > iend) {
            System.arraycopy(a, j, a2, k, jend - j + 1);
        }
    }
    
    public static void split(int[] a, int i, int j, int[] a2) {
        if (i == j) {
            // 插入排序
            insertion(a, i, j);
            return;
        }
        int m = (i + j) >>> 1;
        
        split(a, i, m);
        split(a, m + 1, j);
        
        // 合
        merge(a, i, m, m + 1, j, a2);
        System.arraycopy(a2, left, a, left, j - i + 1);
    }
}

快排

单边循环

public class QuickSortLomuto{
    
    public static void sort(int[] a) {
        quick(a, 0, a.length - 1);
    }
    
    public static void quick(int[] a, int left, int right) {
        if (left >= right) {
            return;
        }
        int p = partition(a, left, right);
        quick(a, left, p - 1);
        quick(a, p + 1, right);
    }
    
    public static int partition(int[] a, int left, int right) {
        int pv = a[right];
        int i = left;
        int j = right;
        while (i < j) {
            if (a[j] < pv) {
                if (i != j) {
                    swap(a, i, j);
                }
                i++;
            }
            j++;
        }
        swap(a, i, right);
        return i;
    }
    
    public static void swap(int[] array, int i, int j) {
        int temp = array[i];
        array[i] = array[j];
        array[j] = temp;
    }
}

双边循环

注意事项

• 加内层循环的i < j 条件
• 先处理j，后处理i
• 随机元素作为基准点

public class QuickSortLomuto{
    
    public static void sort(int[] a) {
        quick(a, 0, a.length - 1);
    }
    
    public static void quick(int[] a, int left, int right) {
        if (left >= right) {
            return;
        }
        int p = partition(a, left, right);
        quick(a, left, p - 1);
        quick(a, p + 1, right);
    }
    
    public static int partition(int[] a, int left, int right) {
        int pv = a[left];
        int i = left;
        int j = right;
        while (i < j) {
            while (i < j && a[j] > pv) {
                j--;
            }
            while (i < j && a[i] <= pv) {
                i++;
            }
            
            swap(a, i, j);
        }
        swap(a, left, i);
        return i;
    }
    
    public static void swap(int[] array, int i, int j) {
        int temp = array[i];
        array[i] = array[j];
        array[j] = temp;
    }
}

改进

public class QuickSortLomuto{
    
    public static void sort(int[] a) {
        quick(a, 0, a.length - 1);
    }
    
    public static void quick(int[] a, int left, int right) {
        if (left >= right) {
            return;
        }
        int p = partition(a, left, right);
        quick(a, left, p - 1);
        quick(a, p + 1, right);
    }
    
    public static int partition(int[] a, int left, int right) {
        int pv = a[left];
        int i = left;
        int j = right;
        while (i <= j) {
            while (i <= j && a[i] < pv) {
                i++;
            }
            while (i <= j && a[j] > pv) {
                j--;
            }
            if (i <= j) {
                swap(a, i, j);
            }
        }
        swap(a, left, j);
        return j;
    }
    
    public static void swap(int[] array, int i, int j) {
        int temp = array[i];
        array[i] = array[j];
        array[j] = temp;
    }
}

计数排序

public class CountSort{
    
    public static void sort(int[] a) {
    	int max = a[0];
        for(int num : a) {
            if (num > max) {
                max = num;
            }
        }
        int[] counts = new int[max + 1];
        
        for(int i = 0; i < a.length; i++) {
            counts[a[i]]++;
        }
        
        int k = 0;
        for(int i = 0; i < count.length; i++) {
            while (count[i] > 0) {
                a[k++] = i;
                count[i]--;
            }
        }
        
    } 
}

代码改进

public class CountSort{
    
    public static void sort(int[] a) {
    	int max = a[0];
        int min = a[0];
        for(int num : a) {
            if (num > max) {
                max = num;
            }
            if (num < min) {
                min = num;
            }
        }
        int[] counts = new int[max - min + 1];
        
        //for(int i = 0; i < a.length; i++) {
        //    counts[a[i]]++;
        //}
        // 使用增强for循环
        for(int num : a) {
            counts[num - min]++;
        }
        int k = 0;
        for(int i = 0; i < counts.length; i++) {
            while (counts[i] > 0) {
                a[k++] = i + min;
                count[i]--;
            }
        }
        
    } 
}

桶排序

public clsss BucketSor{
    
    public static void sort(int[] a) {
        List buckets = new ArrayList[10];
        for(int i = 0; i < a.length; i++) {
            buckets[i] = new ArrayList();
        }
        
        for(int num : a) {
            buckets[num % 10] = num;
        }
        int k = 0;
        for(List bucket : buckets) {
            int[] array = new int[bucket.size()];
            if (bucket.size() > 0) {
                for(int i = 0; i < bucket.size(); i++) {
                    array[i] = bucket.get(i);
                }
            }
            InsertSort.sort(array);
            for(int i : array) {
                a[k++] = i;
            }
        }
    } 
}

基数排序

public class RadixSort{
    
    public static void sort(String[] a, int length) {
        ArrayList<String>[] buckets = new ArrayList<>[10];
        for(int i = 0; i < 10; i++) {
            buckets[i] = new ArrayList<>();
        }
        for(int i = length - 1; i >= 0; i--) {
            for(String s : a) {
                bucket[s.charAt(i) - '0'].add(s);
            }

            int k = 0;
            for(ArrayList<String> bucket : buckets) {
                for(String s : bucket) {
                    a[k++] = s;
                }
                bucket.clear();
            }
        }
    } 
}