Merge Sort Algorithm Assistance

Question

I'm trying to implement the merge-sort algorithm. I started with pseudocode that was available in an algorithms book. The pseudocode indicates the first position in the array as 1 and not 0. I am having a very difficult time trying to implement the code.

Here is what I have. I've tried stepping through the recursion by printing out the results at each step but it is very convoluted at this point.

#include <iostream>
#include <deque>
using size_type = std::deque<int>::size_type;
void print(std::deque<int> &v)
{
    for(const auto &ref:v)
        std::cout << ref << " ";
    std::cout << std::endl;
}
void merge(std::deque<int> &vec, size_type p, size_type q, size_type r)
{
    int n_1 = q - p;
    int n_2 = r - q;
    std::deque<int> left, right;
    for(auto i = 0; i != n_1; i++)
        left.push_back(vec[p + i]);
    for(auto j = 0; j != n_2; j++)
        right.push_back(vec[q + j]);
    int i = 0, j = 0;
    std::cout << "left = ";
    print(left);
    std::cout << "right = ";
    print(right);
    for(auto k = p; k != r; k++) {
        if((i != n_1 && j != n_2) && left[i] <= right[j]) {
            vec[k] = left[i];
            i++;
        }
        else if(j != n_2){
            vec[k] = right[j];
            j++;
        }
    }
}
void merge_sort(std::deque<int> &A, size_type p, size_type r)
{
    int q;
    if(p < r - 1) {
        q = (p + r)/2;
        merge_sort(A, p, q);
        merge_sort(A, q + 1, r);
        merge(A, p, q, r);
    }
}
int main()
{
    std::deque<int> small_vec = {1, 6, 2, 10, 5, 2, 12, 6};
    std::deque<int> samp_vec = {2, 9, 482, 72, 42, 3, 4, 9, 8, 73, 8, 0, 98, 72, 473, 72, 3, 4, 9, 7, 6, 5, 6953, 583};
    print(small_vec);
    merge_sort(small_vec, 0, small_vec.size());
    print(small_vec);
    return 0;
}

I get the following output when I run the program:

left = 1 
right = 6 
left = 1 6 
right = 2 10 
left = 2 
right = 12 6 
left = 1 2 6 10 
right = 5 2 12 6 
1 2 5 2 6 10 12 6 

Answer 1

After spending a lot of time and getting some valuable help on another post was able to get the algorithm to run correctly.

CORRECT CODE:

#include <iostream>
#include <deque>
using size_type = std::deque<int>::size_type;
void print(std::deque<int> &v)
{
    for(const auto &ref:v)
        std::cout << ref << " ";
    std::cout << std::endl;
}
void print(int arr[], int size)
{
    for(int i = 0; i != size; i++)
        std::cout << arr[i] << " ";
    std::cout << std::endl;
}
void merge(std::deque<int> &vec, size_type p, size_type q, size_type r)
{
    int n_1 = q - p + 1;
    int n_2 = r - q;
    std::deque<int> left, right;
    int i = 0, j = 0;
    while(i < n_1)
        left.push_back(vec[p + i++]);
    while(j < n_2)
        right.push_back(vec[j++ + q + 1]);
    i = 0; j = 0;
    //std::cout << "left = ";
    //print(left);
    //std::cout << "right = ";
    //print(right);
    for(auto k = p; k <= r; k++) {
        if((i < n_1 && left[i] <= right[j]) || j >= n_2) {
            vec[k] = left[i++];
        }
        else if(j < n_2){
            vec[k] = right[j++];
        }
    }
}
void merge_sort(std::deque<int> &A, size_type p, size_type r)
{
    int q;
    if(p < r) {
        q = (r + p) / 2;
        std::cout << "q = " << q << std::endl;
        //std::cout << "p = " << p << std::endl;
        merge_sort(A, p, q);
        merge_sort(A, q + 1, r);
        merge(A, p, q, r);
    }
}
int main()
{
    std::deque<int> small_vec = {10, 3, 6, 4, 1, 5, 3, 9, 7, 2, 8};
    std::deque<int> samp_vec = {2, 9, 482, 42, 3, 4, 9, 8, 73, 8, 0, 98, 72, 473, 72, 3, 4, 9, 7, 6, 5, 6953, 583};
    print(samp_vec);
    merge_sort(samp_vec, 0, samp_vec.size() - 1);
    print(samp_vec);
    return 0;
}

Answer 2

The error is here: (i != n_1 && j != n_2) && left[i] <= right[j]) when i != n_1 evaluates to false vec[k] = right[j]; is executed - correct.

But if i != n_1 evaluates to true and j != n_2 to false i.e. j = n_2 your program trys to do this vec[k] = right[j]; again i.e. accesing over the bounds of your deque.

Rewrite your for loop as follows: if (i<n_1 && (j>=n_2 || left[i] <= right[j]) This loop works only due to C++'s short circuiting of the conditions i.e. when j>=n_2 evaluates to true, left[i] <= right[j] is never checked again and you don't access the deque over bounds.

left[i] <= right[j] is being checked only if both i<n_1 is true and j>=n_2 false otherwise the 2nd branch is executed.