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"question": {
"questionId": "1694",
"questionFrontendId": "1590",
"categoryTitle": "Algorithms",
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"title": "Make Sum Divisible by P",
"titleSlug": "make-sum-divisible-by-p",
"content": "<p>Given an array of positive integers <code>nums</code>, remove the <strong>smallest</strong> subarray (possibly <strong>empty</strong>) such that the <strong>sum</strong> of the remaining elements is divisible by <code>p</code>. It is <strong>not</strong> allowed to remove the whole array.</p>\n\n<p>Return <em>the length of the smallest subarray that you need to remove, or </em><code>-1</code><em> if it&#39;s impossible</em>.</p>\n\n<p>A <strong>subarray</strong> is defined as a contiguous block of elements in the array.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [3,1,4,2], p = 6\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> The sum of the elements in nums is 10, which is not divisible by 6. We can remove the subarray [4], and the sum of the remaining elements is 6, which is divisible by 6.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [6,3,5,2], p = 9\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> We cannot remove a single element to get a sum divisible by 9. The best way is to remove the subarray [5,2], leaving us with [6,3] with sum 9.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,3], p = 3\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> Here the sum is 6. which is already divisible by 3. Thus we do not need to remove anything.\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>9</sup></code></li>\n\t<li><code>1 &lt;= p &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
"translatedTitle": "使数组和能被 P 整除",
"translatedContent": "<p>给你一个正整数数组&nbsp;<code>nums</code>,请你移除 <strong>最短</strong>&nbsp;子数组(可以为 <strong>空</strong>),使得剩余元素的 <strong>和</strong>&nbsp;能被 <code>p</code>&nbsp;整除。 <strong>不允许</strong>&nbsp;将整个数组都移除。</p>\n\n<p>请你返回你需要移除的最短子数组的长度,如果无法满足题目要求,返回 <code>-1</code>&nbsp;。</p>\n\n<p><strong>子数组</strong>&nbsp;定义为原数组中连续的一组元素。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre><strong>输入:</strong>nums = [3,1,4,2], p = 6\n<strong>输出:</strong>1\n<strong>解释:</strong>nums 中元素和为 10不能被 p 整除。我们可以移除子数组 [4] ,剩余元素的和为 6 。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre><strong>输入:</strong>nums = [6,3,5,2], p = 9\n<strong>输出:</strong>2\n<strong>解释:</strong>我们无法移除任何一个元素使得和被 9 整除,最优方案是移除子数组 [5,2] ,剩余元素为 [6,3],和为 9 。\n</pre>\n\n<p><strong>示例&nbsp;3</strong></p>\n\n<pre><strong>输入:</strong>nums = [1,2,3], p = 3\n<strong>输出:</strong>0\n<strong>解释:</strong>和恰好为 6 ,已经能被 3 整除了。所以我们不需要移除任何元素。\n</pre>\n\n<p><strong>示例&nbsp; 4</strong></p>\n\n<pre><strong>输入:</strong>nums = [1,2,3], p = 7\n<strong>输出:</strong>-1\n<strong>解释:</strong>没有任何方案使得移除子数组后剩余元素的和被 7 整除。\n</pre>\n\n<p><strong>示例 5</strong></p>\n\n<pre><strong>输入:</strong>nums = [1000000000,1000000000,1000000000], p = 3\n<strong>输出:</strong>0\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>9</sup></code></li>\n\t<li><code>1 &lt;= p &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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"Suppose you know the remainder for the sum of the entire array. How does removing a subarray affect that remainder? What remainder does the subarray need to have in order to make the rest of the array sum up to be divisible by k?",
"Use a map to keep track of the rightmost index for every prefix sum % p."
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