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Hi, I have n items, each item has 3 properties. I want to match the second two properties with some values A, and B, and at the lowest property[0]. Below is my best attempt at solving this issue (see "what have I tried")

This code, however, results in nans, because I'm dividing by 0 - how can I modify my code so that it works correctly, and produces the following result:
objective: 18.75
10 3 9: 1.25
5 5 7: 1.25
100 1 1: 0

What I have tried:

<pre lang="C++">
#include <iostream>
#include <tuple>
#include <vector>

using namespace std;

typedef tuple<double, double, double> Item;

pair<double, vector<pair<Item, double>>> optimize(double A, double B, vector<Item> items) {
    int n = items.size();
    double obj_value = 0;
    vector<pair<Item, double>> quantities(n);

    // Iterate over all items
    for (int i = 0; i < n; i++) {
        // Get the item information
        double price = get<0>(items[i]);
        double X = get<1>(items[i]);
        double Y = get<2>(items[i]);

        // Calculate the solution value
        quantities[i] = make_pair(items[i], 0);
        obj_value += price * get<1>(quantities[i]);

    // Constraint: sum of X * u = A
    double sum_X = 0;
    for (int i = 0; i < n; i++) {
        sum_X += get<1>(get<0>(quantities[i])) * get<1>(quantities[i]);

    if (sum_X != A) {
        for (int i = 0; i < n; i++) {
            if (get<1>(get<0>(quantities[i])) == 0) {

            double ratio = A / sum_X; // 10 / 0

            get<1>(quantities[i]) *= ratio;
            obj_value *= ratio;

    //// Constraint: sum of Y * u = B
    double sum_Y = 0;
    for (int i = 0; i < n; i++) {
        sum_Y += get<2>(get<0>(quantities[i])) * get<1>(quantities[i]);
    if (sum_Y != B) {
        for (int i = 0; i < n; i++) {
            if (get<2>(get<0>(quantities[i])) == 0) {
            double ratio = (double)B / sum_Y;
            get<1>(quantities[i]) *= ratio;
            obj_value *= ratio;

    return make_pair(obj_value, quantities);

int main() {
    vector<Item> items = {
        Item({10, 3, 9}),
        Item({5, 5, 7}),
        Item({100, 1, 1})

    pair<double, vector<pair<Item, double>>> result = optimize(10, 20, items);

    cout << "# objective: " << result.first << endl;
    for (auto i : result.second) {
        cout << "# " << get<0>(i.first) << " " << get<1>(i.first) << " " << get<2>(i.first) << ": " << i.second << endl;

    return 0;
Updated 12-Feb-23 7:09am

1 solution

Compiling does not mean your code is right! :laugh:
Think of the development process as writing an email: compiling successfully means that you wrote the email in the right language - English, rather than German for example - not that the email contained the message you wanted to send.

So now you enter the second stage of development (in reality it's the fourth or fifth, but you'll come to the earlier stages later): Testing and Debugging.

Start by looking at what it does do, and how that differs from what you wanted. This is important, because it give you information as to why it's doing it. For example, if a program is intended to let the user enter a number and it doubles it and prints the answer, then if the input / output was like this:
Input   Expected output    Actual output
  1            2                 1
  2            4                 4
  3            6                 9
  4            8                16
Then it's fairly obvious that the problem is with the bit which doubles it - it's not adding itself to itself, or multiplying it by 2, it's multiplying it by itself and returning the square of the input.
So with that, you can look at the code and it's obvious that it's somewhere here:
int Double(int value)
   return value * value;

Once you have an idea what might be going wrong, start using the debugger to find out why. Put a breakpoint on the first line of the method, and run your app. When it reaches the breakpoint, the debugger will stop, and hand control over to you. You can now run your code line-by-line (called "single stepping") and look at (or even change) variable contents as necessary (heck, you can even change the code and try again if you need to).
Think about what each line in the code should do before you execute it, and compare that to what it actually did when you use the "Step over" button to execute each line in turn. Did it do what you expect? If so, move on to the next line.
If not, why not? How does it differ?
Hopefully, that should help you locate which part of that code has a problem, and what the problem is.
This is a skill, and it's one which is well worth developing as it helps you in the real world as well as in development. And like all skills, it only improves by use!
Share this answer
ronnanteplely 12-Feb-23 13:37pm    
Hi, thanks for the reply! I've located the error - the following line: double ratio = A / sum_X; divides by 0 (A / 0). I was already aware of that, but I was looking for some advice on the linear equation solver itself, as this is a very new topic for me.
OriginalGriff 12-Feb-23 13:56pm    
So start looking at *why* sum_x is zero ... the debugger will help you there, just step though the function working out what variable values should be before you execute each line.

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