leetcode-problemset/leetcode-cn/originData/minimum-size-subarray-in-infinite-array.json

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            "questionId": "3141",
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            "categoryTitle": "Algorithms",
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            "title": "Minimum Size Subarray in Infinite Array",
            "titleSlug": "minimum-size-subarray-in-infinite-array",
            "content": "<p>You are given a <strong>0-indexed</strong> array <code>nums</code> and an integer <code>target</code>.</p>\n\n<p>A <strong>0-indexed</strong> array <code>infinite_nums</code> is generated by infinitely appending the elements of <code>nums</code> to itself.</p>\n\n<p>Return <em>the length of the <strong>shortest</strong> subarray of the array </em><code>infinite_nums</code><em> with a sum equal to </em><code>target</code><em>.</em> If there is no such subarray return <code>-1</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,3], target = 5\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> In this example infinite_nums = [1,2,3,1,2,3,1,2,...].\nThe subarray in the range [1,2], has the sum equal to target = 5 and length = 2.\nIt can be proven that 2 is the shortest length of a subarray with sum equal to target = 5.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,1,1,2,3], target = 4\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> In this example infinite_nums = [1,1,1,2,3,1,1,1,2,3,1,1,...].\nThe subarray in the range [4,5], has the sum equal to target = 4 and length = 2.\nIt can be proven that 2 is the shortest length of a subarray with sum equal to target = 4.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,4,6,8], target = 3\n<strong>Output:</strong> -1\n<strong>Explanation:</strong> In this example infinite_nums = [2,4,6,8,2,4,6,8,...].\nIt can be proven that there is no subarray with sum equal to target = 3.\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<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= target &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "无限数组的最短子数组",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始的数组 <code>nums</code> 和一个整数 <code>target</code> 。</p>\n\n<p>下标从 <strong>0</strong> 开始的数组 <code>infinite_nums</code> 是通过无限地将 nums 的元素追加到自己之后生成的。</p>\n\n<p>请你从 <code>infinite_nums</code> 中找出满足 <strong>元素和</strong> 等于&nbsp;<code>target</code> 的 <strong>最短</strong> 子数组，并返回该子数组的长度。如果不存在满足条件的子数组，返回 <code>-1</code> 。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [1,2,3], target = 5\n<strong>输出：</strong>2\n<strong>解释：</strong>在这个例子中 infinite_nums = [1,2,3,1,2,3,1,2,...] 。\n区间 [1,2] 内的子数组的元素和等于 target = 5 ，且长度 length = 2 。\n可以证明，当元素和等于目标值 target = 5 时，2 是子数组的最短长度。</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [1,1,1,2,3], target = 4\n<strong>输出：</strong>2\n<strong>解释：</strong>在这个例子中 infinite_nums = [1,1,1,2,3,1,1,1,2,3,1,1,...].\n区间 [4,5] 内的子数组的元素和等于 target = 4 ，且长度 length = 2 。\n可以证明，当元素和等于目标值 target = 4 时，2 是子数组的最短长度。\n</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [2,4,6,8], target = 3\n<strong>输出：</strong>-1\n<strong>解释：</strong>在这个例子中 infinite_nums = [2,4,6,8,2,4,6,8,...] 。\n可以证明，不存在元素和等于目标值 target = 3 的子数组。\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<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= target &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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                "Notice that, <code>target</code> is either: A subarray of <code>nums</code>, or <code>prefix_sum[i]</code> + <code> k * sum(nums) </code> + <code>suffix_sum[j]</code> for some <code>i, j, k</code>.",
                "You can solve the problem for those two separate cases using hash map and prefix sums."
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