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by Sumit Chourasia | Oct 02, 2020 | Category :coding | Tags : algorithm data-structure easy leetcode maths

Find Positive Integer Solution for a Given Equation - Math - Easy - LeetCode

Find Positive Integer Solution for a Given Equation - Math - Easy - LeetCode

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 represents one function from a 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

/*
 * // This is the custom function interface.
 * // You should not implement it, or speculate about its implementation
 * public 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)
 *     public int f(int x, int y);
 * };
 */

public class Solution {
    public IList<IList<int>> FindSolution(CustomFunction customfunction, int z) {
        var res = new List<IList<int>>();
        int x = 1;
        int y = 1000;
        while (x <= 1000 && y > 0) {
            int v = customfunction.f(x, y);
            if (v > z){
                --y;   
            }
            else if (v < z){
                ++x; 
            }
            else{
                var arr = new List<int>();
                arr.Add(x++);
                arr.Add(y--);
                res.Add(arr);
            }
        }
        return res;
    }
}

Time Complexity: O(n)

Space Complexity: O(n)