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leetcode-problemset/leetcode-cn/originData/check-if-it-is-a-good-array.json
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{
"data": {
"question": {
"questionId": "1372",
"questionFrontendId": "1250",
"categoryTitle": "Algorithms",
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"title": "Check If It Is a Good Array",
"titleSlug": "check-if-it-is-a-good-array",
"content": "<p>Given an array <code>nums</code> of&nbsp;positive integers. Your task is to select some subset of <code>nums</code>, multiply each element by an integer and add all these numbers.&nbsp;The array is said to be&nbsp;<strong>good&nbsp;</strong>if you can obtain a sum of&nbsp;<code>1</code>&nbsp;from the array by any possible subset and multiplicand.</p>\n\n<p>Return&nbsp;<code>True</code>&nbsp;if the array is <strong>good&nbsp;</strong>otherwise&nbsp;return&nbsp;<code>False</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [12,5,7,23]\n<strong>Output:</strong> true\n<strong>Explanation:</strong> Pick numbers 5 and 7.\n5*3 + 7*(-2) = 1\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [29,6,10]\n<strong>Output:</strong> true\n<strong>Explanation:</strong> Pick numbers 29, 6 and 10.\n29*1 + 6*(-3) + 10*(-1) = 1\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [3,6]\n<strong>Output:</strong> false\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10^5</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10^9</code></li>\n</ul>\n",
"translatedTitle": "检查「好数组」",
"translatedContent": "<p>给你一个正整数数组 <code>nums</code>,你需要从中任选一些子集,然后将子集中每一个数乘以一个 <strong>任意整数</strong>,并求出他们的和。</p>\n\n<p>假如该和结果为&nbsp;<code>1</code>,那么原数组就是一个「<strong>好数组</strong>」,则返回 <code>True</code>;否则请返回 <code>False</code>。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre><strong>输入:</strong>nums = [12,5,7,23]\n<strong>输出:</strong>true\n<strong>解释:</strong>挑选数字 5 和 7。\n5*3 + 7*(-2) = 1\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre><strong>输入:</strong>nums = [29,6,10]\n<strong>输出:</strong>true\n<strong>解释:</strong>挑选数字 29, 6 和 10。\n29*1 + 6*(-3) + 10*(-1) = 1\n</pre>\n\n<p><strong>示例 3</strong></p>\n\n<pre><strong>输入:</strong>nums = [3,6]\n<strong>输出:</strong>false\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10^5</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10^9</code></li>\n</ul>\n",
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"hints": [
"Eq. ax+by=1 has solution x, y if gcd(a,b) = 1.",
"Can you generalize the formula?. Check Bézout's lemma."
],
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