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"question": {
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"title": "Block Placement Queries",
"titleSlug": "block-placement-queries",
"content": "<p>There exists an infinite number line, with its origin at 0 and extending towards the <strong>positive</strong> x-axis.</p>\n\n<p>You are given a 2D array <code>queries</code>, which contains two types of queries:</p>\n\n<ol>\n\t<li>For a query of type 1, <code>queries[i] = [1, x]</code>. Build an obstacle at distance <code>x</code> from the origin. It is guaranteed that there is <strong>no</strong> obstacle at distance <code>x</code> when the query is asked.</li>\n\t<li>For a query of type 2, <code>queries[i] = [2, x, sz]</code>. Check if it is possible to place a block of size <code>sz</code> <em>anywhere</em> in the range <code>[0, x]</code> on the line, such that the block <strong>entirely</strong> lies in the range <code>[0, x]</code>. A block <strong>cannot </strong>be placed if it intersects with any obstacle, but it may touch it. Note that you do<strong> not</strong> actually place the block. Queries are separate.</li>\n</ol>\n\n<p>Return a boolean array <code>results</code>, where <code>results[i]</code> is <code>true</code> if you can place the block specified in the <code>i<sup>th</sup></code> query of type 2, and <code>false</code> otherwise.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">queries = [[1,2],[2,3,3],[2,3,1],[2,2,2]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[false,true,true]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/04/22/example0block.png\" style=\"padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 309px; height: 129px;\" /></strong></p>\n\n<p>For query 0, place an obstacle at <code>x = 2</code>. A block of size at most 2 can be placed before <code>x = 3</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">queries = </span>[[1,7],[2,7,6],[1,2],[2,7,5],[2,7,6]]<!-- notionvc: 4a471445-5af1-4d72-b11b-94d351a2c8e9 --></p>\n\n<p><strong>Output:</strong> [true,true,false]</p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/04/22/example1block.png\" style=\"padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 310px; height: 130px;\" /></strong></p>\n\n<ul>\n\t<li>Place an obstacle at <code>x = 7</code> for query 0. A block of size at most 7 can be placed before <code>x = 7</code>.</li>\n\t<li>Place an obstacle at <code>x = 2</code> for query 2. Now, a block of size at most 5 can be placed before <code>x = 7</code>, and a block of size at most 2 before <code>x = 2</code>.</li>\n</ul>\n</div>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= queries.length <= 15 * 10<sup>4</sup></code></li>\n\t<li><code>2 <= queries[i].length <= 3</code></li>\n\t<li><code>1 <= queries[i][0] <= 2</code></li>\n\t<li><code>1 <= x, sz <= min(5 * 10<sup>4</sup>, 3 * queries.length)</code></li>\n\t<li>The input is generated such that for queries of type 1, no obstacle exists at distance <code>x</code> when the query is asked.</li>\n\t<li>The input is generated such that there is at least one query of type 2.</li>\n</ul>\n",
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"difficulty": "Hard",
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"hints": [
"Let <code>d[x]</code> be the distance of the next obstacle after <code>x</code>.",
"For each query of type 2, we just need to check if <code>max(d[0], d[1], d[2], …d[x - sz]) > sz</code>.",
"Use segment tree to maintain <code>d[x]</code>."
],
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