# [LeetCode]#1237. Find Positive Integer Solution for a Given Equation

Environment: Python 3.7

Key technique: if

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

Analysis:

1. We don’t know all function.
2. Use linear search. x is 1 to 1000 and y is 1000 to 1.
3. if f(x,y) >z , y=y-1
4. if f(x,y) <z, x=x+1
5. if f(x,y)=z, record [x,y].

Solution:

`class Solution:    def findSolution(self, customfunction: 'CustomFunction', z: int) -> List[List[int]]:        ans=[]        x=1        y=1000        while x<=1000 and y>=1:            fxy=customfunction.f(x,y)            if fxy>z:                y-=1            elif fxy<z:                x+=1            else:                ans.append([x,y])                x+=1        return ans`

Submissions:

Reference:

https://blog.csdn.net/CSerwangjun/article/details/102774683

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