How to Solve Find Positive Integer Solution for a Given Equation Leetcode Problem - Interview Coder Guide
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How to Solve Find Positive Integer Solution for a Given Equation Problem

Master the Find Positive Integer Solution for a Given Equation LeetCode problem with undetectable real-time assistance. Get instant solutions and explanations during your coding interviews.

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Medium#1358
LeetCode Problem

Find Positive Integer Solution for a Given Equation

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 ord...

MathTwo PointersBinary Search+1 more

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Problem Breakdown

Understanding the Find Positive Integer Solution for a Given Equation Problem

Let's break down this LeetCode problem and understand what makes it challenging in interview settings.

Problem Statement

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. While the exact formula is hidden, the function is monotonically 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 some positive integer f(x, y) for two positive integers x and y based on a formula. int f(int x, int y); }; We will judge your solution as follows: 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. The judge will receive two inputs: a function_id (to determine which implementation to test your code with), and the target z. The judge will call your findSolution and compare your results with the answer key. If your results match the answer key, your solution will be Accepted.

MediumProblem #1358
LeetCode

Find Positive Integer Solution for a Given Equation

Related Topics
MathTwo PointersBinary SearchInteractive
How Interview Coder Helps

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Examples

Example 1
INPUT
function_id = 1, z = 5
OUTPUT
[[1,4],[2,3],[3,2],[4,1]]
EXPLANATION

The hidden formula for function_id = 1 is f(x, y) = x + y. The following positive integer values of x and y make f(x, y) equal to 5: x=1, y=4 -> f(1, 4) = 1 + 4 = 5. x=2, y=3 -> f(2, 3) = 2 + 3 = 5. x=3, y=2 -> f(3, 2) = 3 + 2 = 5. x=4, y=1 -> f(4, 1) = 4 + 1 = 5.

Example 2
INPUT
function_id = 2, z = 5
OUTPUT
[[1,5],[5,1]]
EXPLANATION

The hidden formula for function_id = 2 is f(x, y) = x * y. The following positive integer values of x and y make f(x, y) equal to 5: x=1, y=5 -> f(1, 5) = 1 * 5 = 5. x=5, y=1 -> f(5, 1) = 5 * 1 = 5.

Constraints

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

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