1237. Find Positive Integer Solution for a Given Equation

Given a callable function f(x, y) with a hidden formula and a value z, reverse engineer the formula and return all positive integer pairs x and y where f(x,y) == z. You may return the pairs in any order.

While the exact formula is hidden, the function is monotonically increasing, i.e.:

• f(x, y) < f(x + 1, y)
• f(x, y) < f(x, y + 1)

The function interface is defined like this:

interface CustomFunction {
public:
 // Returns some positive integer f(x, y) for two positive integers x and y based on a formula.
 int f(int x, int y);
};

We will judge your solution as follows:

• The judge has a list of 9 hidden implementations of CustomFunction, along with a way to generate an answer key of all valid pairs for a specific z.
• The judge will receive two inputs: a function_id (to determine which implementation to test your code with), and the target z.
• The judge will call your findSolution and compare your results with the answer key.
• If your results match the answer key, your solution will be Accepted.

/*
 * // This is the custom function interface.
 * // You should not implement it, or speculate about its implementation
 * class CustomFunction {
 * public:
 *     // Returns f(x, y) for any given positive integers x and y.
 *     // Note that f(x, y) is increasing with respect to both x and y.
 *     // i.e. f(x, y) < f(x + 1, y), f(x, y) < f(x, y + 1)
 *     int f(int x, int y);
 * };
 */

class Solution {
public:
    vector<vector<int>> findSolution(CustomFunction& customfunction, int z) {
        vector<vector<int>> res;
        for(int x = 1; x <= 1000; x++) {
            int l = 1, r = 1000;
            while(l <= r) {
                int m = l + (r-l) / 2;
                int y = customfunction.f(x,m);
                if(y > z) r = m - 1;
                else if(y < z) l = m + 1;
                else {
                    res.push_back({x,m});
                    break;
                }
            }
        }
        return res;
    }
};