Insertion Sort sorts array halfway

Question

I am reading a book of DS and Algortihms. I saw an algorithm named insertion sort and then tried to apply that in c++. When I sort the array, the first element of the array remains at the place it was previously while the other elements go to their appropriate place! I can't understand what's happeing. My code :

#include<iostream>
#include<vector>

using namespace std;

void vec_in(vector<unsigned>& vec, unsigned size);
void vec_out(vector<unsigned> vec);

int main(){
    vector<unsigned> vec;
    unsigned size;
    cout<<"SIZE : ";
    cin>>size;
    cout<<"ARRAY : ";
    vec_in(vec,size);
    cout<<endl;
    for(unsigned j=1; j<size; j++){
        unsigned key = vec[j];
        unsigned i=j-1;
        cout<<key<<endl;
        while(i>0&&vec[i]>key){
            vec[i+1]=vec[i];
            i--;
        }
        vec[i+1]=key;
    }
    cout<<"SORTED ARRAY : ";
    vec_out(vec);

} 

void vec_in(vector<unsigned>& vec, unsigned size){
    for(unsigned i=0; i<size; i++){
        unsigned in;
        cin>>in;
        vec.push_back(in);
    }
    cout<<endl;
}
void vec_out(vector<unsigned> vec){
    for(unsigned i=0; i<vec.size(); i++){ 
        cout<<vec[i]<<" ";
    } 
    cout<<endl;
} 

I tried this code with many samples the result remains same : the first element is never sorted.

Answer 1

You should replace while(i>0&&vec[i]>key){ by while(i>=0&&vec[i]>key){ . In this case i can get negative. Thus, it needs to be singed, ie, this code works.

If you want to stay with your types, you can replace all occurences of i with i-1 and obtain

#include<iostream>
#include<vector>

using namespace std;

void vec_in(vector<unsigned>& vec, unsigned size);
void vec_out(vector<unsigned> vec);

int main(){
    vector<unsigned> vec;
    unsigned size;
    cout<<"SIZE : ";
    cin>>size;
    cout<<"ARRAY : ";
    vec_in(vec,size);
    cout<<endl;
    for(unsigned j=1; j<size; j++){
        unsigned key = vec[j];
        unsigned i=j;
        cout<<key<<endl;
        while(i>0&&vec[i-1]>key){
            vec[i]=vec[i-1];
            i--;
        }
        vec[i]=key;
    }
    cout<<"SORTED ARRAY : ";
    vec_out(vec);

} 

void vec_in(vector<unsigned>& vec, unsigned size){
    for(unsigned i=0; i<size; i++){
        unsigned in;
        cin>>in;
        vec.push_back(in);
    }
    cout<<endl;
}
void vec_out(vector<unsigned> vec){
    for(unsigned i=0; i<vec.size(); i++){ 
        cout<<vec[i]<<" ";
    } 
    cout<<endl;
} 

which works as well .

Note that your approach need N^2 steps (where N is the size of the vector). There are much better approaches, which do it in only log(N) N steps, like quick sort. The standard library implements such an algorithm. Thus, you should always use std::sort for sorting.

Answer 2

Let's assume we have only two elements: 4 and 3 .

Now, what happens when for loop is entered.

    for(unsigned j=1; j<size; j++){
        unsigned key = vec[j];         /* key := 3      */
        unsigned i=j;                  /* i := 1        */
        cout<<key<<endl;               /* print(3)      */
        while(i>0&&vec[i-1]>key){      /* i > 0 (false) */
            vec[i]=vec[i-1];
            i--;
        }
        vec[i]=key;
    }

The while loop that does the sorting is not entered. This will always happen when trying to compare vec[0] to vec[1] .

As a rule of thumb, please do the following tests first time:

1) empty vector
2) vector with one element
3) vector with two elements a) sorted acending b) sorted descending
...

They will allow you to quickly find minor bugs.