{ "data": { "question": { "questionId": "1358", "questionFrontendId": "1237", "categoryTitle": "Algorithms", "boundTopicId": 37350, "title": "Find Positive Integer Solution for a Given Equation", "titleSlug": "find-positive-integer-solution-for-a-given-equation", "content": "

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.

\n\n

While the exact formula is hidden, the function is monotonically increasing, i.e.:

\n\n\n\n

The function interface is defined like this:

\n\n
\ninterface CustomFunction {\npublic:\n  // Returns some positive integer f(x, y) for two positive integers x and y based on a formula.\n  int f(int x, int y);\n};\n
\n\n

We will judge your solution as follows:

\n\n\n\n

 

\n

Example 1:

\n\n
\nInput: function_id = 1, z = 5\nOutput: [[1,4],[2,3],[3,2],[4,1]]\nExplanation: The hidden formula for function_id = 1 is f(x, y) = x + y.\nThe following positive integer values of x and y make f(x, y) equal to 5:\nx=1, y=4 -> f(1, 4) = 1 + 4 = 5.\nx=2, y=3 -> f(2, 3) = 2 + 3 = 5.\nx=3, y=2 -> f(3, 2) = 3 + 2 = 5.\nx=4, y=1 -> f(4, 1) = 4 + 1 = 5.\n
\n\n

Example 2:

\n\n
\nInput: function_id = 2, z = 5\nOutput: [[1,5],[5,1]]\nExplanation: The hidden formula for function_id = 2 is f(x, y) = x * y.\nThe following positive integer values of x and y make f(x, y) equal to 5:\nx=1, y=5 -> f(1, 5) = 1 * 5 = 5.\nx=5, y=1 -> f(5, 1) = 5 * 1 = 5.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "找出给定方程的正整数解", "translatedContent": "

给你一个函数  f(x, y) 和一个目标结果 z，函数公式未知，请你计算方程 f(x,y) == z 所有可能的正整数 数对 x 和 y。满足条件的结果数对可以按任意顺序返回。

\n\n

尽管函数的具体式子未知，但它是单调递增函数，也就是说：

\n\n\n\n

函数接口定义如下：

\n\n
\ninterface CustomFunction {\npublic:\n  // Returns some positive integer f(x, y) for two positive integers x and y based on a formula.\n  int f(int x, int y);\n};
\n\n

你的解决方案将按如下规则进行评判：

\n\n\n\n

 

\n\n

示例 1：

\n\n
\n输入：function_id = 1, z = 5\n输出：[[1,4],[2,3],[3,2],[4,1]]\n解释：function_id = 1 暗含的函数式子为 f(x, y) = x + y\n以下 x 和 y 满足 f(x, y) 等于 5：\nx=1, y=4 -> f(1, 4) = 1 + 4 = 5\nx=2, y=3 -> f(2, 3) = 2 + 3 = 5\nx=3, y=2 -> f(3, 2) = 3 + 2 = 5\nx=4, y=1 -> f(4, 1) = 4 + 1 = 5\n
\n\n

示例 2：

\n\n
\n输入：function_id = 2, z = 5\n输出：[[1,5],[5,1]]\n解释：function_id = 2 暗含的函数式子为 f(x, y) = x * y\n以下 x 和 y 满足 f(x, y) 等于 5：\nx=1, y=5 -> f(1, 5) = 1 * 5 = 5\nx=5, y=1 -> f(5, 1) = 5 * 1 = 5
\n\n

 

\n\n

提示：

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{integer}\n * this.f = function(x, y) {\n * ...\n * };\n * };\n */\n\n/**\n * @param {CustomFunction} customfunction\n * @param {integer} z\n * @return {integer[][]}\n */\nvar findSolution = function(customfunction, z) {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# \tThis is the custom function interface.\n#\tYou should not implement it, or speculate about its implementation\n#\tclass CustomFunction:\n#\t\tdef f(self, x, y):\n# \t\t\tReturns f(x, y) for any given positive integers x and y.\n# \t\t\tNote that f(x, y) is increasing with respect to both x and y.\n# \t\t\ti.e. f(x, y) < f(x + 1, y), f(x, y) < f(x, y + 1)\n# \t\tend\n# \tend\n# \n\n# @param {CustomFunction} customfunction\n# @param {Integer} z\n# @return {List[List[Integer]]}\ndef findSolution(customfunction, z)\n \nend", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "/*\n * // This is the custom function interface.\n * // You should not 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