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2022-03-27

leetcode-problemset
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check-if-point-is-reachable.json

{
    "data": {
        "question": {
            "questionId": "2635",
            "questionFrontendId": "2543",
            "categoryTitle": "Algorithms",
            "boundTopicId": 2070103,
            "title": "Check if Point Is Reachable",
            "titleSlug": "check-if-point-is-reachable",
            "content": "<p>There exists an infinitely large grid. You are currently at point <code>(1, 1)</code>, and you need to reach the point <code>(targetX, targetY)</code> using a finite number of steps.</p>\n\n<p>In one <strong>step</strong>, you can move from point <code>(x, y)</code> to any one of the following points:</p>\n\n<ul>\n\t<li><code>(x, y - x)</code></li>\n\t<li><code>(x - y, y)</code></li>\n\t<li><code>(2 * x, y)</code></li>\n\t<li><code>(x, 2 * y)</code></li>\n</ul>\n\n<p>Given two integers <code>targetX</code> and <code>targetY</code> representing the X-coordinate and Y-coordinate of your final position, return <code>true</code> <em>if you can reach the point from</em> <code>(1, 1)</code> <em>using some number of steps, and </em><code>false</code><em> otherwise</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> targetX = 6, targetY = 9\n<strong>Output:</strong> false\n<strong>Explanation:</strong> It is impossible to reach (6,9) from (1,1) using any sequence of moves, so false is returned.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> targetX = 4, targetY = 7\n<strong>Output:</strong> true\n<strong>Explanation:</strong> You can follow the path (1,1) -&gt; (1,2) -&gt; (1,4) -&gt; (1,8) -&gt; (1,7) -&gt; (2,7) -&gt; (4,7).\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= targetX, targetY&nbsp;&lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "判断一个点是否可以到达",
            "translatedContent": "<p>给你一个无穷大的网格图。一开始你在&nbsp;<code>(1, 1)</code>&nbsp;，你需要通过有限步移动到达点&nbsp;<code>(targetX, targetY)</code>&nbsp;。</p>\n\n<p><b>每一步</b>&nbsp;，你可以从点&nbsp;<code>(x, y)</code>&nbsp;移动到以下点之一：</p>\n\n<ul>\n\t<li><code>(x, y - x)</code></li>\n\t<li><code>(x - y, y)</code></li>\n\t<li><code>(2 * x, y)</code></li>\n\t<li><code>(x, 2 * y)</code></li>\n</ul>\n\n<p>给你两个整数&nbsp;<code>targetX</code> 和&nbsp;<code>targetY</code>&nbsp;，分别表示你最后需要到达点的 X 和 Y 坐标。如果你可以从&nbsp;<code>(1, 1)</code>&nbsp;出发到达这个点，请你返回<code>true</code> ，否则返回<em>&nbsp;</em><code>false</code><em>&nbsp;</em>。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><b>输入：</b>targetX = 6, targetY = 9\n<b>输出：</b>false\n<b>解释：</b>没法从 (1,1) 出发到达 (6,9) ，所以返回 false 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>targetX = 4, targetY = 7\n<b>输出：</b>true\n<b>解释：</b>你可以按照以下路径到达：(1,1) -&gt; (1,2) -&gt; (1,4) -&gt; (1,8) -&gt; (1,7) -&gt; (2,7) -&gt; (4,7) 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= targetX, targetY&nbsp;&lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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            "hints": [
                "Let’s go in reverse order, from (targetX, targetY) to (1, 1). So, now we can move from (x, y) to (x+y, y), (x, y+x), (x/2, y) if x is even, and (x, y/2) if y is even.",
                "When is it optimal to use the third and fourth operations?",
                "Think how GCD of (x, y) is affected if we apply the first two operations.",
                "How can we check if we can reach (1, 1) using the GCD value calculate above?"
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