Operation(+ and -) with 3x3 2D vector elements(int) - c++

Question

I need to write a program that takes the input of 3 positive integers. Then find their distinct permutations in increasing order. e.g.
{
{1 2 3}
{1 3 2}
{2 1 3}
{2 3 1}
{3 1 2}
{3 2 1}
}
Then, insert operators '+' or '-' between each two numbers to form an equation and print the result of
it. For each operation, both + and – should be considered. For example, for the permutation of 1 2 3,
we need to consider four cases: 1 + 2 + 3 = 6, 1 + 2 – 3 = 0, 1 – 2 + 3 = 2, and 1 – 2 – 3 = -4.
The output should display all possible equations and their calculation results in an increasing order
sorted by the result of the equation. If two equations have the same result, further sort the equations
in an increasing order of the permutations. For example, 1 + 2 + 3 = 6 should be output before
1 + 3 + 2 = 6 because permutation 1 2 3 is smaller than 1 3 2 according to the definition above.
The order of permutation is defined as follow:
• compare the number in the left-most place first. The permutation with the smaller leftmost number is said to be smaller, e.g., 1 3 2 is smaller than 2 1 3.
• If the left-most number are the same, compare the next one, e.g., 2 1 3 is smaller than 2 3 1
My code :
I wrote two functions.
permutation to find the distinct permutation of 3 integers.
sortPermutation to sort the permutation in an increasing order. But I am not sure if I am doing the right thing in this function.
I have no idea how to perform the + and - operation for the permutation, as well as to sort them in increasing order and display them afterwards. I have searched for resources online but still do not have an idea. Any help will be appreciated!!
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
vector<vector<int>> sortPermutation(vector<int> &result);
vector<vector<int>> permutation(vector<int>num);
int main()
{
int a, b, c;
cout << "Enter three different positive numbers: ";
cin >> a >> b >> c;
vector<int> num = { a,b,c };
int size = num.size();
vector<vector<int>> result = permutation(num);
for (int i = 0; i < result.size(); i++)
{
for (int j = 0; j < result[i].size(); j++)
{
cout << result[i][j];
}
cout << endl;
}
}
vector<vector<int>> sortPermutation(vector<vector<int>>& result)
{
sort(result.begin(),
result.end(),
[](const std::vector<int>& a, const std::vector<int>& b)
{
return a[0] < b[0];
});
return result;
}
vector<vector<int>> permutation(vector<int>num)
{
vector<vector<int>> permu;
if (num.size() <= 1)
{
return { num };
}
for (int i = 0; i < num.size(); i++)
{
vector<int>v(num.begin(), num.end()); // 1,2,3
v.erase(v.begin() + i); //2,3 // 3 // 2
auto res = permutation(v);//3 // 2 // 1 // 3 // 1 // 2
for (int j = 0; j < res.size(); j++)
{
vector<int>_v = res[j];
_v.insert(_v.begin(), num[i]);
permu.push_back(_v);
}
}
return sortPermutation(permu);
}
This is a sample output for permutation 1 2 3
1 - 2 - 3 = -4
1 - 3 - 2 = -4
2 - 1 - 3 = -2
2 - 3 - 1 = -2
1 + 2 - 3 = 0
1 - 3 + 2 = 0
2 + 1 - 3 = 0
2 - 3 + 1 = 0
3 - 1 - 2 = 0
3 - 2 - 1 = 0
1 - 2 + 3 = 2
1 + 3 - 2 = 2
3 + 1 - 2 = 2
3 - 2 + 1 = 2
2 - 1 + 3 = 4
2 + 3 - 1 = 4
3 - 1 + 2 = 4
3 + 2 - 1 = 4
1 + 2 + 3 = 6
1 + 3 + 2 = 6
2 + 1 + 3 = 6
2 + 3 + 1 = 6
3 + 1 + 2 = 6
3 + 2 + 1 = 6