Task

Display a finite linear combination in an infinite vector basis 



(

e

1


,

e

2


,
…
)


{\displaystyle (e_{1},e_{2},\ldots )}

.

Write a function that, when given a finite list of scalars 



(

α

1


,

α

2


,
…
)


{\displaystyle (\alpha ^{1},\alpha ^{2},\ldots )}

, 
creates a string representing the linear combination 




∑

i



α

i



e

i




{\displaystyle \sum _{i}\alpha ^{i}e_{i}}

 in an explicit format often used in mathematics, that is:






α


i

1





e


i

1




±

|


α


i

2





|


e


i

2




±

|


α


i

3





|


e


i

3




±
…


{\displaystyle \alpha ^{i_{1}}e_{i_{1}}\pm |\alpha ^{i_{2}}|e_{i_{2}}\pm |\alpha ^{i_{3}}|e_{i_{3}}\pm \ldots }


where 




α


i

k




≠
0


{\displaystyle \alpha ^{i_{k}}\neq 0}







The output must comply to the following rules:

   don't show null terms, unless the whole combination is null. 
 e(1)     is fine,     e(1) + 0*e(3)     or     e(1) + 0     is wrong.
   don't show scalars when they are equal to one or minus one. 
 e(3)     is fine,     1*e(3)     is wrong.
   don't prefix by a minus sign if it follows a preceding term.   Instead you use subtraction. 
 e(4) - e(5)     is fine,     e(4) + -e(5)     is wrong.


Show here output for the following lists of scalars:

 1)    1,  2,  3
 2)    0,  1,  2,  3
 3)    1,  0,  3,  4
 4)    1,  2,  0
 5)    0,  0,  0
 6)    0
 7)    1,  1,  1
 8)   -1, -1, -1
 9)   -1, -2,  0, -3
10)   -1



#include <iomanip>
#include <iostream>
#include <sstream>
#include <vector>
 
template<typename T>
std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) {
    auto it = v.cbegin();
    auto end = v.cend();
 
    os << '[';
    if (it != end) {
        os << *it;
        it = std::next(it);
    }
    while (it != end) {
        os << ", " << *it;
        it = std::next(it);
    }
    return os << ']';
}
 
std::ostream& operator<<(std::ostream& os, const std::string& s) {
    return os << s.c_str();
}
 
std::string linearCombo(const std::vector<int>& c) {
    std::stringstream ss;
    for (size_t i = 0; i < c.size(); i++) {
        int n = c[i];
        if (n < 0) {
            if (ss.tellp() == 0) {
                ss << '-';
            } else {
                ss << " - ";
            }
        } else if (n > 0) {
            if (ss.tellp() != 0) {
                ss << " + ";
            }
        } else {
            continue;
        }
 
        int av = abs(n);
        if (av != 1) {
            ss << av << '*';
        }
        ss << "e(" << i + 1 << ')';
    }
    if (ss.tellp() == 0) {
        return "0";
    }
    return ss.str();
}
 
int main() {
    using namespace std;
 
    vector<vector<int>> combos{
        {1, 2, 3},
        {0, 1, 2, 3},
        {1, 0, 3, 4},
        {1, 2, 0},
        {0, 0, 0},
        {0},
        {1, 1, 1},
        {-1, -1, -1},
        {-1, -2, 0, -3},
        {-1},
    };
 
    for (auto& c : combos) {
        stringstream ss;
        ss << c;
        cout << setw(15) << ss.str() << " -> ";
        cout << linearCombo(c) << '\n';
    }
 
    return 0;
}