• 彙總
• 1. 氣泡排序
• 2. 選擇排序
• 3. 插入排序
• 4. 快速排序
• 5. 歸併排序
• 6. 希爾排序
  • 6.1 希爾-氣泡排序（慢）
  • 6.2 希爾-插入排序（快）
• 7. 堆排序
• 8. 計數排序
• 9. 桶排序
• 10. 基數排序
• 11. 使用集合或 API
  • 11.1 優先佇列
  • 11.2 Java API
• 最後

彙總

1. 氣泡排序

每輪迴圈確定最值；

public void bubbleSort(int[] nums){
    int temp;
    boolean isSort = false; //優化，發現排序好就退出
    for (int i = 0; i < nums.length-1; i++) {
        for (int j = 0; j < nums.length-1-i; j++) {  //每次排序後能確定較大值
            if(nums[j] > nums[j+1]){
                isSort = true;
                temp = nums[j];
                nums[j] = nums[j+1];
                nums[j+1] = temp;
            }
        }
        if(!isSort){
            return;
        } else {
            isSort = false;
        }
    }
}
 

2. 選擇排序

每次選出最值，再交換到邊上；

public void selectSort(int[] nums){
    for (int i = 0; i < nums.length-1; i++) {
        int index = i;
        int minNum = nums[i];
        for (int j = i+1; j < nums.length; j++) {
            if(nums[j] < minNum){
                minNum = nums[j];
                index = j;
            }
        }
        if(index != i){
            nums[index] = nums[i];
            nums[i] = minNum;
        }
    }
}

3. 插入排序

對迴圈的每個數找到屬於自己的位置插入；

public void insertionSort(int[] nums){
    for (int i = 1; i < nums.length; i++) {
        int j = i;
        int insertNum = nums[i];
        while(j-1 >= 0 && nums[j-1] > insertNum){
            nums[j] = nums[j-1];
            j--;
        }
        nums[j] = insertNum;
    }
}

4. 快速排序

選一個基本值，小於它的放一邊，大於它的放另一邊；

public void quickSortDfs(int[] nums, int left, int right){
    if(left > right){
        return;
    }
    int l = left;
    int r = right;
    int baseNum = nums[left];
    while(l < r){
        //必須右邊先走
        while(nums[r] >= baseNum && l < r){
            r--;
        }
        while(nums[l] <= baseNum && l < r){
            l++;
        }
        int temp = nums[l];
        nums[l] = nums[r];
        nums[r] = temp;
    }
    nums[left] = nums[l];
    nums[l] = baseNum;
    quickSortDfs(nums, left, r-1);
    quickSortDfs(nums, l+1, right);
}

5. 歸併排序

分治演算法；

//歸
public void mergeSortDfs(int[] nums, int l, int r){
    if(l >= r){
        return;
    }
    int m = (l+r)/2;
    mergeSortDfs(nums, l, m);
    mergeSortDfs(nums, m+1, r);
    merge(nums, l, m, r);
}
//並
private void merge(int[] nums, int left, int mid, int right){
    int[] temp = new int[right-left+1];
    int l = left;
    int m = mid+1;
    int i = 0;
    while(l <= mid && m <= right){
        if(nums[l] < nums[m]){
            temp[i++] = nums[l++];
        } else {
            temp[i++] = nums[m++];
        }
    }
    while(l <= mid){
        temp[i++] = nums[l++];
    }
    while(m <= right){
        temp[i++] = nums[m++];
    }
    System.arraycopy(temp, 0, nums, left, temp.length);
}

6. 希爾排序

引入步長減少數字交換次數提高效率；

6.1 希爾-氣泡排序（慢）

public void shellBubbleSort(int[] nums){
    for (int step = nums.length/2; step > 0 ; step /= 2) {
        for (int i = step; i < nums.length; i++) {
            for (int j = i-step; j >= 0; j -= step) {
                if(nums[j] > nums[j+step]){
                    int temp = nums[j];
                    nums[j] = nums[j+step];
                    nums[j+step] = temp;
                }
            }
        }
    }
}

6.2 希爾-插入排序（快）

public void shellInsertSort(int[] nums){
    for (int step = nums.length/2; step > 0; step /= 2) {
        for (int i = step; i < nums.length; i++) {
            int j = i;
            int insertNum = nums[i];
            while(j-step >= 0 && nums[j-step] > insertNum){
                nums[j] = nums[j-step];
                j-=step;
            }
            nums[j] = insertNum;
        }
    }
}

7. 堆排序

大頂堆實現升序，每次將最大值移到堆的最後一個位置上；

public void heapSort2(int[] nums) {
    for(int i = nums.length/2-1; i >= 0; i--){
        sift(nums, i, nums.length);
    }
    for (int i = nums.length-1; i > 0; i--) {
        int temp = nums[0];
        nums[0] = nums[i];
        nums[i] = temp;
        sift(nums, 0, i);
    }
}
private void sift(int[] nums, int parent, int len) {
    int value = nums[parent];
    for (int child = 2*parent +1; child < len; child = child*2 +1) {
        if(child+1 < len && nums[child+1] > nums[child]){
            child++;
        }
        if(nums[child] > value){
            nums[parent] = nums[child];
            parent = child;
        } else {
            break;
        }
    }
    nums[parent] = value;
}

8. 計數排序

按順序統計每個數出現次數；

public void countSort(int[] nums){
    int max = Integer.MIN_VALUE;
    int min = Integer.MAX_VALUE;
    for(int num : nums){
        max = Math.max(max, num);
        min = Math.min(min, num);
    }

    int[] countMap = new int[max-min+1];
    for(int num : nums){
        countMap[num-min]++;
    }
    int i = 0;
    int j = 0;
    while(i < nums.length && j < countMap.length){
        if(countMap[j] > 0){
            nums[i] = j+min;
            i++;
            countMap[j]--;
        } else {
            j++;
        }
    }
}

9. 桶排序

類似計數排序，不同點在於統計的是某個區間（桶）裡的數；

public void bucketSort(int[] nums){
    int max = Integer.MIN_VALUE;
    int min = Integer.MAX_VALUE;
    for(int num : nums){
        max = Math.max(max, num);
        min = Math.min(min, num);
    }
    int bucketCount = (max-min)/nums.length+1;
    List<List<Integer>> bucketList = new ArrayList<>();
    for (int i = 0; i < bucketCount; i++) {
        bucketList.add(new ArrayList<>());
    }

    for(int num : nums){
        int index = (num-min)/nums.length;
        bucketList.get(index).add(num);
    }
    for(List<Integer> bucket : bucketList){
        Collections.sort(bucket);
    }

    int j = 0;
    for(List<Integer> bucket : bucketList){
        for(int num : bucket){
            nums[j] = num;
            j++;
        }
    }
}

10. 基數排序

按個、十、百位依次歸類排序；

public  void radixSort(int[] nums){
    int min = Integer.MAX_VALUE;
    int max = Integer.MIN_VALUE;
    for (int num : nums) {
        min = Math.min(min, num);
        max = Math.max(max, num);
    }
    for (int i = 0; i < nums.length; i++) {
        nums[i] -= min;
    }
    max -= min;
    int maxLen = (max+"").length();

    int[][] bucket = new int[nums.length][10];
    int[] bucketCount = new int[10];

    for (int i = 0, n = 1; i < maxLen; i++, n*=10) {
        for (int num : nums) {
            int digitVal = num / n % 10;
            bucket[bucketCount[digitVal]][digitVal] = num;
            bucketCount[digitVal]++;
        }
        int index = 0;
        for (int j = 0; j < bucketCount.length; j++) {
            if(bucketCount[j] > 0){
                for (int k = 0; k < bucketCount[j]; k++) {
                    nums[index] = bucket[k][j];
                    index++;
                }
            }
            bucketCount[j] = 0;
        }
    }
    for (int i = 0; i < nums.length; i++) {
        nums[i] += min;
    }
}

11. 使用集合或 API

11.1 優先佇列

public void priorityQueueSort(int[] nums){
    PriorityQueue<Integer> queue = new PriorityQueue<>();
    for(int num : nums){
        queue.offer(num);
    }
    for (int i = 0; i < nums.length; i++) {
        nums[i] = queue.poll();
    }
}

11.2 Java API

public void arraysApiSort(int[] nums){
    Arrays.sort(nums);
}

最後