## 1237. Find Positive Integer Solution for a Given Equation

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

## Rust Solution

struct Solution;

struct CustomFunction {
fp: fn(i32, i32) -> i32,
}

impl CustomFunction {
fn f(&self, x: i32, y: i32) -> i32 {
(self.fp)(x, y)
}
}

impl Solution {
fn find_solution(customfunction: &CustomFunction, z: i32) -> Vec<Vec<i32>> {
let mut res = vec![];
for i in 0..1000 {
for j in 0..1000 {
let x = (i + 1) as i32;
let y = (j + 1) as i32;
if customfunction.f(x, y) == z {
res.push(vec![x, y]);
}
}
}
res
}
}

#[test]
fn test() {
let cf = CustomFunction { fp: |x, y| x + y };
let z = 5;
let res = vec_vec_i32![[1, 4], [2, 3], [3, 2], [4, 1]];
assert_eq!(Solution::find_solution(&cf, z), res);
let cf = CustomFunction { fp: |x, y| x * y };
let z = 5;
let res = vec_vec_i32![[1, 5], [5, 1]];
assert_eq!(Solution::find_solution(&cf, z), res);
}

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