divide-intervals-into-minimum-number-of-groups

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Algorithms

You are given a 2D integer array <code>intervals</code> where <code>intervals[i] = [lefti, righti]</code> represents the inclusive interval <code>[lefti, righti]</code>.

You have to divide the intervals into one or more groups such that each interval is in exactly one group, and no two intervals that are in the same group intersect each other.

Return the minimum number of groups you need to make.

Two intervals intersect if there is at least one common number between them. For example, the intervals <code>[1, 5]</code> and <code>[5, 8]</code> intersect.

&nbsp;
Example 1:

<pre>
Input: intervals = [[5,10],[6,8],[1,5],[2,3],[1,10]]
Output: 3
Explanation: We can divide the intervals into the following groups:
- Group 1: [1, 5], [6, 8].
- Group 2: [2, 3], [5, 10].
- Group 3: [1, 10].
It can be proven that it is not possible to divide the intervals into fewer than 3 groups.
</pre>

Example 2:

<pre>
Input: intervals = [[1,3],[5,6],[8,10],[11,13]]
Output: 1
Explanation: None of the intervals overlap, so we can put all of them in one group.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= intervals.length &lt;= 105</code></li>
	<li><code>intervals[i].length == 2</code></li>
	<li><code>1 &lt;= lefti &lt;= righti &lt;= 106</code></li>
</ul>

minGroups

Divide Intervals Into Minimum Number of Groups

Merge Intervals

merge-intervals

合并区间

Minimum Number of Frogs Croaking

minimum-number-of-frogs-croaking

数青蛙

Average Height of Buildings in Each Segment

average-height-of-buildings-in-each-segment

每段建筑物的平均高度

Greedy

Array

Two Pointers

Prefix Sum

Sorting

Heap (Priority Queue)

给你一个二维整数数组&nbsp;<code>intervals</code>&nbsp;，其中&nbsp;<code>intervals[i] = [lefti, righti]</code>&nbsp;表示 闭&nbsp;区间&nbsp;<code>[lefti, righti]</code>&nbsp;。

你需要将&nbsp;<code>intervals</code> 划分为一个或者多个区间&nbsp;组&nbsp;，每个区间 只&nbsp;属于一个组，且同一个组中任意两个区间 不相交&nbsp;。

请你返回 最少&nbsp;需要划分成多少个组。

如果两个区间覆盖的范围有重叠（即至少有一个公共数字），那么我们称这两个区间是 相交&nbsp;的。比方说区间&nbsp;<code>[1, 5]</code> 和&nbsp;<code>[5, 8]</code>&nbsp;相交。

&nbsp;

示例 1：

<pre>
输入：intervals = [[5,10],[6,8],[1,5],[2,3],[1,10]]
输出：3
解释：我们可以将区间划分为如下的区间组：
- 第 1 组：[1, 5] ，[6, 8] 。
- 第 2 组：[2, 3] ，[5, 10] 。
- 第 3 组：[1, 10] 。
可以证明无法将区间划分为少于 3 个组。
</pre>

示例 2：

<pre>
输入：intervals = [[1,3],[5,6],[8,10],[11,13]]
输出：1
解释：所有区间互不相交，所以我们可以把它们全部放在一个组内。</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= intervals.length &lt;= 105</code></li>
	<li><code>intervals[i].length == 2</code></li>
	<li><code>1 &lt;= lefti &lt;= righti &lt;= 106</code></li>
</ul>