leetcode-problemset/leetcode-cn/originData/minimum-moves-to-pick-k-ones.json

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        "question": {
            "questionId": "3327",
            "questionFrontendId": "3086",
            "categoryTitle": "Algorithms",
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            "title": "Minimum Moves to Pick K Ones",
            "titleSlug": "minimum-moves-to-pick-k-ones",
            "content": "<p>You are given a binary array <code>nums</code> of length <code>n</code>, a <strong>positive</strong> integer <code>k</code> and a <strong>non-negative</strong> integer <code>maxChanges</code>.</p>\n\n<p>Alice plays a game, where the goal is for Alice to pick up <code>k</code> ones from <code>nums</code> using the <strong>minimum</strong> number of <strong>moves</strong>. When the game starts, Alice picks up any index <code>aliceIndex</code> in the range <code>[0, n - 1]</code> and stands there. If <code>nums[aliceIndex] == 1</code> , Alice picks up the one and <code>nums[aliceIndex]</code> becomes <code>0</code>(this <strong>does not</strong> count as a move). After this, Alice can make <strong>any</strong> number of <strong>moves</strong> (<strong>including</strong> <strong>zero</strong>) where in each move Alice must perform <strong>exactly</strong> one of the following actions:</p>\n\n<ul>\n\t<li>Select any index <code>j != aliceIndex</code> such that <code>nums[j] == 0</code> and set <code>nums[j] = 1</code>. This action can be performed <strong>at</strong> <strong>most</strong> <code>maxChanges</code> times.</li>\n\t<li>Select any two adjacent indices <code>x</code> and <code>y</code> (<code>|x - y| == 1</code>) such that <code>nums[x] == 1</code>, <code>nums[y] == 0</code>, then swap their values (set <code>nums[y] = 1</code> and <code>nums[x] = 0</code>). If <code>y == aliceIndex</code>, Alice picks up the one after this move and <code>nums[y]</code> becomes <code>0</code>.</li>\n</ul>\n\n<p>Return <em>the <strong>minimum</strong> number of moves required by Alice to pick <strong>exactly </strong></em><code>k</code> <em>ones</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\" style=\"border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;\">\n<p><strong>Input: </strong><span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\">nums = [1,1,0,0,0,1,1,0,0,1], k = 3, maxChanges = 1</span></p>\n\n<p><strong>Output: </strong><span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\">3</span></p>\n\n<p><strong>Explanation:</strong> Alice can pick up <code>3</code> ones in <code>3</code> moves, if Alice performs the following actions in each move when standing at <code>aliceIndex == 1</code>:</p>\n\n<ul>\n\t<li>&nbsp;At the start of the game Alice picks up the one and <code>nums[1]</code> becomes <code>0</code>. <code>nums</code> becomes <code>[1,<strong><u>1</u></strong>,1,0,0,1,1,0,0,1]</code>.</li>\n\t<li>Select <code>j == 2</code> and perform an action of the first type. <code>nums</code> becomes <code>[1,<strong><u>0</u></strong>,1,0,0,1,1,0,0,1]</code></li>\n\t<li>Select <code>x == 2</code> and <code>y == 1</code>, and perform an action of the second type. <code>nums</code> becomes <code>[1,<strong><u>1</u></strong>,0,0,0,1,1,0,0,1]</code>. As <code>y == aliceIndex</code>, Alice picks up the one and <code>nums</code> becomes&nbsp;<code>[1,<strong><u>0</u></strong>,0,0,0,1,1,0,0,1]</code>.</li>\n\t<li>Select <code>x == 0</code> and <code>y == 1</code>, and perform an action of the second type. <code>nums</code> becomes <code>[0,<strong><u>1</u></strong>,0,0,0,1,1,0,0,1]</code>. As <code>y == aliceIndex</code>, Alice picks up the one and <code>nums</code> becomes&nbsp;<code>[0,<strong><u>0</u></strong>,0,0,0,1,1,0,0,1]</code>.</li>\n</ul>\n\n<p>Note that it may be possible for Alice to pick up <code>3</code> ones using some other sequence of <code>3</code> moves.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\" style=\"border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;\">\n<p><strong>Input: </strong><span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\">nums = [0,0,0,0], k = 2, maxChanges = 3</span></p>\n\n<p><strong>Output: </strong><span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\">4</span></p>\n\n<p><strong>Explanation:</strong> Alice can pick up <code>2</code> ones in <code>4</code> moves, if Alice performs the following actions in each move when standing at <code>aliceIndex == 0</code>:</p>\n\n<ul>\n\t<li>Select <code>j == 1</code> and perform an action of the first type. <code>nums</code> becomes <code>[<strong><u>0</u></strong>,1,0,0]</code>.</li>\n\t<li>Select <code>x == 1</code> and <code>y == 0</code>, and perform an action of the second type. <code>nums</code> becomes <code>[<strong><u>1</u></strong>,0,0,0]</code>. As <code>y == aliceIndex</code>, Alice picks up the one and <code>nums</code> becomes&nbsp;<code>[<strong><u>0</u></strong>,0,0,0]</code>.</li>\n\t<li>Select <code>j == 1</code> again and perform an action of the first type. <code>nums</code> becomes <code>[<strong><u>0</u></strong>,1,0,0]</code>.</li>\n\t<li>Select <code>x == 1</code> and <code>y == 0</code> again, and perform an action of the second type. <code>nums</code> becomes <code>[<strong><u>1</u></strong>,0,0,0]</code>. As <code>y == aliceIndex</code>, Alice picks up the one and <code>nums</code> becomes&nbsp;<code>[<strong><u>0</u></strong>,0,0,0]</code>.</li>\n</ul>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i] &lt;= 1</code></li>\n\t<li><code>1 &lt;= k &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= maxChanges &lt;= 10<sup>5</sup></code></li>\n\t<li><code>maxChanges + sum(nums) &gt;= k</code></li>\n</ul>\n",
            "translatedTitle": "拾起 K 个 1 需要的最少行动次数",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始的二进制数组 <code>nums</code>，其长度为 <code>n</code> ；另给你一个 <strong>正整数 </strong><code>k</code> 以及一个 <strong>非负整数 </strong><code>maxChanges</code> 。</p>\n\n<p>Alice 在玩一个游戏，游戏的目标是让&nbsp;Alice 使用 <strong>最少 </strong>数量的 <strong>行动 </strong>次数从 <code>nums</code> 中拾起 <code>k</code> 个 1 。游戏开始时，Alice 可以选择数组 <code>[0, n - 1]</code> 范围内的任何索引&nbsp;<code>aliceIndex</code> 站立。如果 <code>nums[aliceIndex] == 1</code> ，Alice 会拾起一个 1 ，并且 <code>nums[aliceIndex]</code> 变成<code>0</code>（这<strong> 不算 </strong>作一次行动）。之后，Alice 可以执行 <strong>任意数量</strong> 的 <strong>行动</strong>（<strong>包括</strong><strong>零次</strong>），在每次行动中&nbsp;Alice 必须 <strong>恰好 </strong>执行以下动作之一：</p>\n\n<ul>\n\t<li>选择任意一个下标 <code>j != aliceIndex</code> 且满足 <code>nums[j] == 0</code> ，然后将 <code>nums[j]</code> 设置为 <code>1</code> 。这个动作最多可以执行 <code>maxChanges</code> 次。</li>\n\t<li>选择任意两个相邻的下标 <code>x</code> 和 <code>y</code>（<code>|x - y| == 1</code>）且满足 <code>nums[x] == 1</code>, <code>nums[y] == 0</code> ，然后交换它们的值（将 <code>nums[y] = 1</code> 和 <code>nums[x] = 0</code>）。如果 <code>y == aliceIndex</code>，在这次行动后&nbsp;Alice 拾起一个 1 ，并且 <code>nums[y]</code> 变成 <code>0</code> 。</li>\n</ul>\n\n<p>返回&nbsp;Alice 拾起 <strong>恰好 </strong><code>k</code> 个 1 所需的 <strong>最少 </strong>行动次数。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\" style=\"border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;\">\n<p><strong>输入：</strong><span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\">nums = [1,1,0,0,0,1,1,0,0,1], k = 3, maxChanges = 1</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\">3</span></p>\n\n<p><strong>解释：</strong>如果游戏开始时&nbsp;Alice 在 <code>aliceIndex == 1</code> 的位置上，按照以下步骤执行每个动作，他可以利用 <code>3</code> 次行动拾取 <code>3</code> 个 1 ：</p>\n\n<ul>\n\t<li>游戏开始时&nbsp;Alice 拾取了一个 1 ，<code>nums[1]</code> 变成了 <code>0</code>。此时 <code>nums</code> 变为 <code>[1,<strong><u>1</u></strong>,1,0,0,1,1,0,0,1]</code> 。</li>\n\t<li>选择 <code>j == 2</code> 并执行第一种类型的动作。<code>nums</code> 变为 <code>[1,<strong><u>0</u></strong>,1,0,0,1,1,0,0,1]</code></li>\n\t<li>选择 <code>x == 2</code> 和 <code>y == 1</code> ，并执行第二种类型的动作。<code>nums</code> 变为 <code>[1,<strong><u>1</u></strong>,0,0,0,1,1,0,0,1]</code> 。由于 <code>y == aliceIndex</code>，Alice 拾取了一个 1 ，<code>nums</code> 变为&nbsp; <code>[1,<strong><u>0</u></strong>,0,0,0,1,1,0,0,1]</code> 。</li>\n\t<li>选择 <code>x == 0</code> 和 <code>y == 1</code> ，并执行第二种类型的动作。<code>nums</code> 变为 <code>[0,<strong><u>1</u></strong>,0,0,0,1,1,0,0,1]</code> 。由于 <code>y == aliceIndex</code>，Alice 拾取了一个 1 ，<code>nums</code> 变为&nbsp; <code>[0,<strong><u>0</u></strong>,0,0,0,1,1,0,0,1]</code> 。</li>\n</ul>\n\n<p>请注意，Alice 也可能执行其他的 <code>3</code> 次行动序列达成拾取 <code>3</code> 个 1 。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\" style=\"border-color: var(--border-tertiary); border-left-width: 2px; color: var(--text-secondary); font-size: .875rem; margin-bottom: 1rem; margin-top: 1rem; overflow: visible; padding-left: 1rem;\"><!-- 以下是示例内容的中文翻译，同时保留了原有的HTML格式和注释 -->\n<p><strong>输入：</strong><span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\">nums = [0,0,0,0], k = 2, maxChanges = 3</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\" style=\"font-family: Menlo,sans-serif; font-size: 0.85rem;\">4</span></p>\n\n<p><strong>解释：</strong>如果游戏开始时&nbsp;Alice 在 <code>aliceIndex == 0</code> 的位置上，按照以下步骤执行每个动作，他可以利用 <code>4</code> 次行动拾取 <code>2</code> 个 1 ：</p>\n\n<ul>\n\t<li>选择 <code>j == 1</code> 并执行第一种类型的动作。<code>nums</code> 变为 <code>[<strong><u>0</u></strong>,1,0,0]</code> 。</li>\n\t<li>选择 <code>x == 1</code> 和 <code>y == 0</code> ，并执行第二种类型的动作。<code>nums</code> 变为 <code>[<strong><u>1</u></strong>,0,0,0]</code> 。由于 <code>y == aliceIndex</code>，Alice 拾起了一个 1 ，<code>nums</code> 变为 <code>[<strong><u>0</u></strong>,0,0,0]</code> 。</li>\n\t<li>再次选择 <code>j == 1</code> 并执行第一种类型的动作。<code>nums</code> 变为 <code>[<strong><u>0</u></strong>,1,0,0]</code> 。</li>\n\t<li>再次选择 <code>x == 1</code> 和 <code>y == 0</code> ，并执行第二种类型的动作。<code>nums</code> 变为 <code>[<strong><u>1</u></strong>,0,0,0]</code> 。由于<code>y == aliceIndex</code>，Alice 拾起了一个 1 ，<code>nums</code> 变为 <code>[<strong><u>0</u></strong>,0,0,0]</code> 。</li>\n</ul>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i] &lt;= 1</code></li>\n\t<li><code>1 &lt;= k &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= maxChanges &lt;= 10<sup>5</sup></code></li>\n\t<li><code>maxChanges + sum(nums) &gt;= k</code></li>\n</ul>\n",
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