<reponame>chaosWsF/Python-Practice<filename>leetcode/1237_find_positive_integer_solution_for_a_given_equation.py
"""
Given a function  f(x, y) and a value z, return all positive integer pairs x and y 
where f(x,y) == z.

The function is constantly 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 positive integer f(x, y) for any given positive integer x and y.
    int f(int x, int y);
    };

For custom testing purposes you're given an integer function_id and a target z as input, 
where function_id represent one function from an secret internal list, on the examples 
you'll know only two functions from the list.

You may return the solutions in any order.

Example 1:

    Input: function_id = 1, z = 5
    Output: [[1,4],[2,3],[3,2],[4,1]]
    Explanation: function_id = 1 means that f(x, y) = x + y

Example 2:

    Input: function_id = 2, z = 5
    Output: [[1,5],[5,1]]
    Explanation: function_id = 2 means that f(x, y) = x * y

Constraints:
    1. 1 <= function_id <= 9
    2. 1 <= z <= 100
    3. It's guaranteed that the solutions of f(x, y) == z will be on the range 1 <= x, y <= 1000
    4. It's also guaranteed that f(x, y) will fit in 32 bit signed integer if 1 <= x, y <= 1000
"""


"""
   This is the custom function interface.
   You should not implement it, or speculate about its implementation
   class CustomFunction:
       # 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)
       def f(self, x, y):
  
"""


class Solution:
    def findSolution(self, customfunction: 'CustomFunction', z: int):    # 24ms
        res, y = [], z+1
        for x in range(1, z+1):
            if customfunction.f(x, 1) > z:
                return res
            
            while y > 1 and customfunction.f(x, y) > z:
                y -= 1
            
            if customfunction.f(x, y) == z:
                res.append([x, y])

        return res
