1237. Find Positive Integer Solution for a Given Equation Medium

1/**
2 * [1237] Find Positive Integer Solution for a Given Equation
3 *
4 * 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.
5 * While the exact formula is hidden, the function is monotonically increasing, i.e.:
6 * 
7 * 	f(x, y) < f(x + 1, y)
8 * 	f(x, y) < f(x, y + 1)
9 * 
10 * The function interface is defined like this:
11 * 
12 * interface CustomFunction {
13 * public:
14 *   // Returns some positive integer f(x, y) for two positive integers x and y based on a formula.
15 *   int f(int x, int y);
16 * };
17 * 
18 * We will judge your solution as follows:
19 * 
20 * 	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.
21 * 	The judge will receive two inputs: a function_id (to determine which implementation to test your code with), and the target z.
22 * 	The judge will call your findSolution and compare your results with the answer key.
23 * 	If your results match the answer key, your solution will be Accepted.
24 * 
25 *  
26 * Example 1:
27 * 
28 * Input: function_id = 1, z = 5
29 * Output: [[1,4],[2,3],[3,2],[4,1]]
30 * Explanation: The hidden formula for function_id = 1 is f(x, y) = x + y.
31 * The following positive integer values of x and y make f(x, y) equal to 5:
32 * x=1, y=4 -> f(1, 4) = 1 + 4 = 5.
33 * x=2, y=3 -> f(2, 3) = 2 + 3 = 5.
34 * x=3, y=2 -> f(3, 2) = 3 + 2 = 5.
35 * x=4, y=1 -> f(4, 1) = 4 + 1 = 5.
36 * 
37 * Example 2:
38 * 
39 * Input: function_id = 2, z = 5
40 * Output: [[1,5],[5,1]]
41 * Explanation: The hidden formula for function_id = 2 is f(x, y) = x * y.
42 * The following positive integer values of x and y make f(x, y) equal to 5:
43 * x=1, y=5 -> f(1, 5) = 1 * 5 = 5.
44 * x=5, y=1 -> f(5, 1) = 5 * 1 = 5.
45 * 
46 *  
47 * Constraints:
48 * 
49 * 	1 <= function_id <= 9
50 * 	1 <= z <= 100
51 * 	It is guaranteed that the solutions of f(x, y) == z will be in the range 1 <= x, y <= 1000.
52 * 	It is also guaranteed that f(x, y) will fit in 32 bit signed integer if 1 <= x, y <= 1000.
53 * 
54 */
55pub struct Solution {}
56
57// problem: https://leetcode.com/problems/find-positive-integer-solution-for-a-given-equation/
58// discuss: https://leetcode.com/problems/find-positive-integer-solution-for-a-given-equation/discuss/?currentPage=1&orderBy=most_votes&query=
59
60// submission codes start here
61
62/*
63 * // This is the custom function interface.
64 * // You should not implement it, or speculate about its implementation
65 * struct CustomFunction;
66 * impl CustomFunction {
67 *    pub fn f(x:i32,y:i32)->i32{}
68 * }
69 */
70
71impl Solution {
72    pub fn find_solution(customfunction: &CustomFunction, z: i32) -> Vec<Vec<i32>> {
73	
74    }
75}
76
77// submission codes end
78
79#[cfg(test)]
80mod tests {
81    use super::*;
82
83    #[test]
84    fn test_1237() {
85    }
86}
87