Table of contents
foreword
There is order everywhere in life.
You go to the shopping website to filter items, sorted by time, price, etc.,
And sorting is also a knowledge point that is often tested in interviews.
Today, we start with insertion and Hill sorting to explore the mysteries of classic sorting.
1. Insertion sort
1.1 Introduction
Insertion sort, as the name suggests:
He is just like when we usually play poker,
From front to back, pick up the small number and insert it in front of the big number (here the default is ascending order)
Insertion sort is like this,
Let's not talk nonsense, let's talk about the idea of realization:
1. 2 Implementation idea
To implement a sort, we need to know
The address of the first element of the array to be sorted, and the size of the array. (the basic)
The picture shows the idea of inserting and arranging:
Iterate over the array:
Starting from the second number, compare all the way forward,
Use tmp to save your own value first,
(main idea)
If it is smaller than the previous number, move the previous number backwards,
Until it is larger than the previous number, the position vacated by moving backward will be occupied.
1. 3 Code implementation
Note: a represents the address of the first element of the array array, and n represents the size of the array.
//插入排序
InsertSort(int* a, int n) {
//遍历数组
for (int i = 1; i < n; i++) {
//end位置表示要被比较的数
int end = i - 1;
//tmp存放的是正在进行插入排序的数
int tmp = a[i];
while (end >= 0) {
//如果tmp比end位置的数小
if (tmp < a[end]) {
//就让end位置的数往后挪动
a[end + 1] = a[end];
//再跟前一个end位置的数比较
end--;
}
else {
//如果tmp比end位置的数大，那就别动了
break;
}
}
//将之前因为往后挪动而空出的位置霸占
a[end + 1] = tmp;
}
}
2. Hill sort
2. 1 Introduction
Hill sort is based on insertion sort, which is why I talked about insertion sort first.
Insertion sort has a characteristic, that is, when the sorted array is closer to order,
The higher the efficiency of insertion sorting, the closer to O(N),
Hill sorting makes the array more and more close to order by means of pre-sorting.
Insertion sort is performed at the end.
2. 2 Implementation ideas
Presorting is done by dividing the array into parts and performing insertion sort on them:
For example:
We use gap equal to 3 to divide the array into three parts:
(Three different colors indicate those three parts)
They are:
9， 6， 3， 0
8， 5， 2
7， 4， 1
Perform insertion sort on them respectively, that is, pre-sort,
Each insertion can change from one-by-one comparison insertion to jumping comparison insertion, which greatly improves the efficiency.
So: (core idea)
By continuously performing efficient pre-sorting,
Finally, insertion sort is performed on the nearly ordered array,
To improve the efficiency of insertion sort, this is Hill sort.
Here is the implementation:
2. 3 Code implementation
//希尔排序
ShellSort(int* a, int n) {
//将gap初始化成数组大小（之后再慢慢让它变小）
int gap = n;
//当gap == 1，证明已经完成最后一步：插入排序
while (gap > 1) {
//不断/2，让gap不断变小进行预排，当gap == 1时进行插入排序
gap /= 2;
//这个是将gap分成的每个部分进行插入排序，也就是预排序
for (int i = 0; i < gap; i++) {
for (int j = i; j < n - gap; j += gap) {
//end位置表示要被比较的数
int end = j;
//tmp存放的是正在进行插入排序的数
int tmp = a[end + gap];
//插入排序
while (end >= 0) {
//从跳过一个数，变成跳过gap个
if (tmp < a[end]) {
a[end + gap] = a[end];
end -= gap;
}
else {
break;
}
}
a[end + gap] = tmp;
}
}
}
}Write at the end:
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