leetcode-problemset/leetcode-cn/originData/find-positive-integer-solution-for-a-given-equation.json

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            "questionId": "1358",
            "questionFrontendId": "1237",
            "categoryTitle": "Algorithms",
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            "title": "Find Positive Integer Solution for a Given Equation",
            "titleSlug": "find-positive-integer-solution-for-a-given-equation",
            "content": "<p>Given a callable function <code>f(x, y)</code> <strong>with a hidden formula</strong> and a value <code>z</code>, reverse engineer the formula and return <em>all positive integer pairs </em><code>x</code><em> and </em><code>y</code><em> where </em><code>f(x,y) == z</code>. You may return the pairs in any order.</p>\n\n<p>While the exact formula is hidden, the function is monotonically increasing, i.e.:</p>\n\n<ul>\n\t<li><code>f(x, y) &lt; f(x + 1, y)</code></li>\n\t<li><code>f(x, y) &lt; f(x, y + 1)</code></li>\n</ul>\n\n<p>The function interface is defined like this:</p>\n\n<pre>\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</pre>\n\n<p>We will judge your solution as follows:</p>\n\n<ul>\n\t<li>The judge has a list of <code>9</code> hidden implementations of <code>CustomFunction</code>, along with a way to generate an <strong>answer key</strong> of all valid pairs for a specific <code>z</code>.</li>\n\t<li>The judge will receive two inputs: a <code>function_id</code> (to determine which implementation to test your code with), and the target <code>z</code>.</li>\n\t<li>The judge will call your <code>findSolution</code> and compare your results with the <strong>answer key</strong>.</li>\n\t<li>If your results match the <strong>answer key</strong>, your solution will be <code>Accepted</code>.</li>\n</ul>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> function_id = 1, z = 5\n<strong>Output:</strong> [[1,4],[2,3],[3,2],[4,1]]\n<strong>Explanation:</strong> 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 -&gt; f(1, 4) = 1 + 4 = 5.\nx=2, y=3 -&gt; f(2, 3) = 2 + 3 = 5.\nx=3, y=2 -&gt; f(3, 2) = 3 + 2 = 5.\nx=4, y=1 -&gt; f(4, 1) = 4 + 1 = 5.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> function_id = 2, z = 5\n<strong>Output:</strong> [[1,5],[5,1]]\n<strong>Explanation:</strong> 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 -&gt; f(1, 5) = 1 * 5 = 5.\nx=5, y=1 -&gt; f(5, 1) = 5 * 1 = 5.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= function_id &lt;= 9</code></li>\n\t<li><code>1 &lt;= z &lt;= 100</code></li>\n\t<li>It is guaranteed that the solutions of <code>f(x, y) == z</code> will be in the range <code>1 &lt;= x, y &lt;= 1000</code>.</li>\n\t<li>It is also guaranteed that <code>f(x, y)</code> will fit in 32 bit signed integer if <code>1 &lt;= x, y &lt;= 1000</code>.</li>\n</ul>\n",
            "translatedTitle": "找出给定方程的正整数解",
            "translatedContent": "<p>给你一个函数  <code>f(x, y)</code> 和一个目标结果 <code>z</code>，函数公式未知，请你计算方程 <code>f(x,y) == z</code> 所有可能的正整数 <strong>数对</strong> <code>x</code> 和 <code>y</code>。满足条件的结果数对可以按任意顺序返回。</p>\n\n<p>尽管函数的具体式子未知，但它是单调递增函数，也就是说：</p>\n\n<ul>\n\t<li><code>f(x, y) < f(x + 1, y)</code></li>\n\t<li><code>f(x, y) < f(x, y + 1)</code></li>\n</ul>\n\n<p>函数接口定义如下：</p>\n\n<pre>\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};</pre>\n\n<p>你的解决方案将按如下规则进行评判：</p>\n\n<ul>\n\t<li>判题程序有一个由 <code>CustomFunction</code> 的 <code>9</code> 种实现组成的列表，以及一种为特定的 <code>z</code> 生成所有有效数对的答案的方法。</li>\n\t<li>判题程序接受两个输入：<code>function_id</code>（决定使用哪种实现测试你的代码）以及目标结果 <code>z</code> 。</li>\n\t<li>判题程序将会调用你实现的 <code>findSolution</code> 并将你的结果与答案进行比较。</li>\n\t<li>如果你的结果与答案相符，那么解决方案将被视作正确答案，即 <code>Accepted</code> 。</li>\n</ul>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>function_id = 1, z = 5\n<strong>输出：</strong>[[1,4],[2,3],[3,2],[4,1]]\n<strong>解释：</strong>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</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>function_id = 2, z = 5\n<strong>输出：</strong>[[1,5],[5,1]]\n<strong>解释：</strong>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</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= function_id <= 9</code></li>\n\t<li><code>1 <= z <= 100</code></li>\n\t<li>题目保证 <code>f(x, y) == z</code> 的解处于 <code>1 <= x, y <= 1000</code> 的范围内。</li>\n\t<li>在 <code>1 <= x, y <= 1000</code> 的前提下，题目保证 <code>f(x, y)</code> 是一个 32 位有符号整数。</li>\n</ul>\n",
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