Insert Sort
Hahah, we aim to do it as easy as we can. We also introduce merge algorithm. Merge method is always useful when we use devide & conquer technique and we can use it to merge the solutions of sub-problems.
Insert sort (C++)
vector<int> insertSort(vector<int> arr) {
int j, current;
for (int i = 1; i < arr.size(); ++i) {
current = arr[i], j = i;//save current value for it may be modified later
while (--j >= 0 && (arr[j] > current));//select proper position
arr.erase(arr.begin()+i);
arr.insert(arr.begin()+1+j, current);//insert current to suitable position
}
return arr;
}
If you need do that descendingly, just change the compare operator opposite.
while (--j >= 0 && (arr[j] < current));//select proper position
Of course, do you see that the second '‘for’’ reccurent is to scan backward in a in order sequence? That means we can use binary search to save more time. Friends can try by yourselves privately. That could be named the improved method of insert sort.
Merge Sort(C++)
Finally, we can have a look at merge sort algorithm using divide&conquer method. I divide the problem into every time but actually you can deal wtih it according to your hobby and they are almost the same indeed.
void mergeSort(vector<int> &a,int l,int r) {
if (l < r) {
int m = (l + r) / 2;
mergeSort(a,l,m);
mergeSort(a,m+1,r);
merge(a, l,m,r);
}
}
Merge(C++)
We like using containers of C++ like vector or any other to realize some problem for their safety and convenience. However, we don’t know how to use traditional array with its length transferred together in function, which makes program look ugly. If anybody knows how to access the size or length of an array when it is transferred into function as a pointer, please let me know. Thanks very much. More to say, the code of merge of this version can be much shorter if you don’t extract the two operated parts respectively. If you do, you need add some signal flag to judge whether the sub part is empty. You can try by your own, I think that will be fine for you.
void merge(vector<int> &a,int l,int m,int r) {
vector<int> a1(a.begin() + l, a.begin() + m+1);
vector<int> a2(a.begin() + m + 1, a.begin() + r + 1);
vector<int> a3;
int len1= m - l + 1, len2= r - m;
bool flag = false;
while (!a1.empty() || !a2.empty()) {
if (a1.empty()) (a3.insert(a3.end(), a2.begin(), a2.end()), flag = true);
if (a2.empty()) (a3.insert(a3.end(), a1.begin(), a1.end()), flag = true);
if (flag) break;
a3.push_back(min(*a1.begin(), *a2.begin()));
*a1.begin() > * a2.begin() ? a2.erase(a2.begin()): a1.erase(a1.begin());
}
a.erase(a.begin() + l, a.begin() + r+1);
a.insert(a.begin() + l, a3.begin(), a3.end());
}
Quick sort（C++）
void exchange(vector<int>& arr, int i, int j) {
int tmp = arr[i];
arr[i] = arr[j];
arr[j] = tmp;
}
int partition(vector<int>& arr, int p, int r) {
int i = p - 1;
for (int j = p; j < r; ++j)
if (arr[j] <= arr[r]) //The first divide value is the end of the array
if (++i != j)
exchange(arr, i, j);
exchange(arr, i + 1, r); // Put divide value to divide position
return i + 1;
}
void quickSort(vector<int> &arr, int p,int r) {
if (p < r) {
int q = partition(arr, p, r);// Get the divide point
quickSort(arr, p, q-1);// Deal with the left part
quickSort(arr, q + 1, r);//Deal with the right part
}
}
Main test (C++)
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
vector<int> insertSort(vector<int> arr) {
int j, current;
for (int i = 1; i < arr.size(); ++i) {
current = arr[i], j = i;//save current value for it may be modified later
while (--j >= 0 && (arr[j] > current));//select proper position
arr.erase(arr.begin()+i);
arr.insert(arr.begin()+1+j, current);//insert current to suitable position
}
return arr;
}
void merge(vector<int> &a,int l,int m,int r) {
vector<int> a1(a.begin() + l, a.begin() + m+1);
vector<int> a2(a.begin() + m + 1, a.begin() + r + 1);
vector<int> a3;
int len1= m - l + 1, len2= r - m;
bool flag = false;
while (!a1.empty() || !a2.empty()) {
if (a1.empty()) (a3.insert(a3.end(), a2.begin(), a2.end()), flag = true);
if (a2.empty()) (a3.insert(a3.end(), a1.begin(), a1.end()), flag = true);
if (flag) break;
a3.push_back(min(*a1.begin(), *a2.begin()));
*a1.begin() > * a2.begin() ? a2.erase(a2.begin()): a1.erase(a1.begin());
}
a.erase(a.begin() + l, a.begin() + r+1);
a.insert(a.begin() + l, a3.begin(), a3.end());
}
void mergeSort(vector<int> &a,int l,int r) {
if (l < r) {
int m = (l + r) / 2;
mergeSort(a,l,m);
mergeSort(a,m+1,r);
merge(a, l,m,r);
}
}
void exchange(vector<int>& arr, int i, int j) {
int tmp = arr[i];
arr[i] = arr[j];
arr[j] = tmp;
}
int partition(vector<int>& arr, int p, int r) {
int i = p - 1;
for (int j = p; j < r; ++j)
if (arr[j] <= arr[r]) //The first divide value is the end of the array
if (++i != j)
exchange(arr, i, j);
exchange(arr, i + 1, r); // Put divide value to divide position
return i + 1;
}
void quickSort(vector<int> &arr, int p,int r) {
if (p < r) {
int q = partition(arr, p, r);// Get the divide point
quickSort(arr, p, q-1);// Deal with the left part
quickSort(arr, q + 1, r);//Deal with the right part
}
}
int main() {
vector<int> a1{ 2,1,3,2,4,5,6,3,4,9,8,7,3,4,6,9};
for (int i:insertSort(a1))cout << i << " ";
cout<<endl;
vector<int> a2{9,4,7,5,8,6,3,2,1,0};
int len = a2.size();
mergeSort(a2,0,len-1);
for (int i : a2)cout << i << " ";
cout<<endl;
vector<int> a3{ 7,3,4,6,7,5,6,3,7,4,6,5 };
quickSort(a3,0,a.size()-1);
for (int i : a3)cout << i << " ";
cout<<endl;
}
Main test(Java) insert sort
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
public class Main {
static List<Integer> insertSort(List<Integer> arr) {
int j, current;
for (int i = 1; i < arr.size(); ++i) {
current = arr.get(i);//save current value for it may be modified later
j = i;
while (--j >= 0 && (arr.get(j) > current));//select proper position
arr.remove(i);
arr.add(1+j, current);//insert current to suitable position
}
return arr;
}
public static void main(String[] args){
List<Integer> a =Arrays.asList(2,1,3,2,4,5,6,3,4,9,8,7,3,4,6,9);
List<Integer> b=new ArrayList<>();
b.addAll(a);
for (Object i:insertSort(b)) System.out.print(i+" ");
}
}