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‎Problemset/2493-Divide Nodes Into the Maximum Number of Groups/README.md

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# 2493. Divide Nodes Into the Maximum Number of Groups
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You are given a positive integer `n` representing the number of nodes in an **undirected** graph. The nodes are labeled from `1` to `n`.
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You are also given a 2D integer array `edges`, where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is a **bidirectional** edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>. Notice that the given graph may be disconnected.
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Divide the nodes of the graph into `m` groups (**1-indexed**) such that:
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* Each node in the graph belongs to exactly one group.
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* For every pair of nodes in the graph that are connected by an edge <code>[a<sub>i</sub>, b<sub>i</sub>]</code>, if <code>a<sub>i</sub></code> belongs to the group with index `x`, and <code>b<sub>i</sub></code> belongs to the group with index `y`, then `|y - x| = 1`.
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Return *the maximum number of groups (i.e., maximum* `m`*) into which you can divide the nodes*. Return `-1` *if it is impossible to group the nodes with the given conditions*.
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#### Example 1:
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![](https://assets.leetcode.com/uploads/2022/10/13/example1.png)
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<pre>
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<strong>Input:</strong> n = 6, edges = [[1,2],[1,4],[1,5],[2,6],[2,3],[4,6]]
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<strong>Output:</strong> 4
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<strong>Explanation:</strong> As shown in the image we:
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- Add node 5 to the first group.
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- Add node 1 to the second group.
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- Add nodes 2 and 4 to the third group.
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- Add nodes 3 and 6 to the fourth group.
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We can see that every edge is satisfied.
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It can be shown that that if we create a fifth group and move any node from the third or fourth group to it, at least on of the edges will not be satisfied.
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</pre>
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#### Example 2:
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<pre>
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<strong>Input:</strong> n = 3, edges = [[1,2],[2,3],[3,1]]
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<strong>Output:</strong> -1
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<strong>Explanation:</strong> If we add node 1 to the first group, node 2 to the second group, and node 3 to the third group to satisfy the first two edges, we can see that the third edge will not be satisfied.
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It can be shown that no grouping is possible.
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</pre>
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#### Constraints:
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* `1 <= n <= 500`
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* <code>1 <= edges.length <= 10<sup>4</sup></code>
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* `edges[i].length == 2`
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* <code>1 <= a<sub>i</sub>, b<sub>i</sub> <= n</code>
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* <code>a<sub>i</sub> != b<sub>i</sub></code>
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* There is at most one edge between any pair of vertices.
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## Solutions (Python)
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### 1. Solution
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```Python
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class Solution:
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def magnificentSets(self, n: int, edges: List[List[int]]) -> int:
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parent = list(range(n + 1))
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neighbors = [[] for _ in range(n + 1)]
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unionfinds = {}
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ret = 0
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for a, b in edges:
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while parent[a] != parent[parent[a]]:
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parent[a] = parent[parent[a]]
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while parent[b] != parent[parent[b]]:
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parent[b] = parent[parent[b]]
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parent[parent[a]] = parent[b]
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neighbors[a].append(b)
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neighbors[b].append(a)
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for node in range(1, n + 1):
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while parent[node] != parent[parent[node]]:
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parent[node] = parent[parent[node]]
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if parent[node] not in unionfinds:
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unionfinds[parent[node]] = []
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unionfinds[parent[node]].append(node)
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for unionfind in unionfinds.values():
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m = 1
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for node in unionfind:
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used = {node: 1}
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queue = deque([node])
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while queue:
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node = queue.popleft()
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i = used[node]
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for neighbor in neighbors[node]:
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if neighbor not in used:
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used[neighbor] = i + 1
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queue.append(neighbor)
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m = max(m, i + 1)
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elif abs(used[neighbor] - i) != 1:
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return -1
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ret += m
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return ret
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```

‎Problemset/2493-Divide Nodes Into the Maximum Number of Groups/README_CN.md

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# 2493. 将节点分成尽可能多的组
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给你一个正整数 `n` ，表示一个 **无向** 图中的节点数目，节点编号从 `1` 到 `n` 。
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同时给你一个二维整数数组 `edges` ，其中 <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> 表示节点 <code>a<sub>i</sub></code> 和 <code>b<sub>i</sub></code> 之间有一条 **双向** 边。注意给定的图可能是不连通的。
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请你将图划分为 `m` 个组（编号从 **1** 开始），满足以下要求：
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* 图中每个节点都只属于一个组。
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* 图中每条边连接的两个点 <code>[a<sub>i</sub>, b<sub>i</sub>]</code> ，如果 <code>a<sub>i</sub></code> 属于编号为 `x` 的组，<code>b<sub>i</sub></code> 属于编号为 `y` 的组，那么 `|y - x| = 1` 。
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请你返回最多可以将节点分为多少个组（也就是最大的 `m` ）。如果没办法在给定条件下分组，请你返回 `-1` 。
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#### 示例 1:
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![](https://assets.leetcode.com/uploads/2022/10/13/example1.png)
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<pre>
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<strong>输入:</strong> n = 6, edges = [[1,2],[1,4],[1,5],[2,6],[2,3],[4,6]]
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<strong>输出:</strong> 4
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<strong>解释:</strong> 如上图所示，
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- 节点 5 在第一个组。
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- 节点 1 在第二个组。
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- 节点 2 和节点 4 在第三个组。
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- 节点 3 和节点 6 在第四个组。
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所有边都满足题目要求。
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如果我们创建第五个组，将第三个组或者第四个组中任何一个节点放到第五个组，至少有一条边连接的两个节点所属的组编号不符合题目要求。
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</pre>
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#### 示例 2:
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<pre>
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<strong>输入:</strong> n = 3, edges = [[1,2],[2,3],[3,1]]
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<strong>输出:</strong> -1
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<strong>解释:</strong> 如果我们将节点 1 放入第一个组，节点 2 放入第二个组，节点 3 放入第三个组，前两条边满足题目要求，但第三条边不满足题目要求。
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没有任何符合题目要求的分组方式。
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</pre>
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#### 提示:
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* `1 <= n <= 500`
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* <code>1 <= edges.length <= 10<sup>4</sup></code>
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* `edges[i].length == 2`
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* <code>1 <= a<sub>i</sub>, b<sub>i</sub> <= n</code>
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* <code>a<sub>i</sub> != b<sub>i</sub></code>
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* 两个点之间至多只有一条边。
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## 题解 (Python)
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### 1. 题解
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```Python
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class Solution:
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def magnificentSets(self, n: int, edges: List[List[int]]) -> int:
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parent = list(range(n + 1))
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neighbors = [[] for _ in range(n + 1)]
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unionfinds = {}
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ret = 0
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for a, b in edges:
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while parent[a] != parent[parent[a]]:
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parent[a] = parent[parent[a]]
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while parent[b] != parent[parent[b]]:
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parent[b] = parent[parent[b]]
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parent[parent[a]] = parent[b]
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neighbors[a].append(b)
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neighbors[b].append(a)
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for node in range(1, n + 1):
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while parent[node] != parent[parent[node]]:
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parent[node] = parent[parent[node]]
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if parent[node] not in unionfinds:
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unionfinds[parent[node]] = []
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unionfinds[parent[node]].append(node)
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for unionfind in unionfinds.values():
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m = 1
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for node in unionfind:
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used = {node: 1}
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queue = deque([node])
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while queue:
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node = queue.popleft()
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i = used[node]
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for neighbor in neighbors[node]:
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if neighbor not in used:
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used[neighbor] = i + 1
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queue.append(neighbor)
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m = max(m, i + 1)
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elif abs(used[neighbor] - i) != 1:
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return -1
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ret += m
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return ret
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```

‎Problemset/2493-Divide Nodes Into the Maximum Number of Groups/Solution.py

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class Solution:
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def magnificentSets(self, n: int, edges: List[List[int]]) -> int:
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parent = list(range(n + 1))
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neighbors = [[] for _ in range(n + 1)]
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unionfinds = {}
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ret = 0
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for a, b in edges:
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while parent[a] != parent[parent[a]]:
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parent[a] = parent[parent[a]]
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while parent[b] != parent[parent[b]]:
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parent[b] = parent[parent[b]]
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parent[parent[a]] = parent[b]
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neighbors[a].append(b)
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neighbors[b].append(a)
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for node in range(1, n + 1):
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while parent[node] != parent[parent[node]]:
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parent[node] = parent[parent[node]]
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if parent[node] not in unionfinds:
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unionfinds[parent[node]] = []
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unionfinds[parent[node]].append(node)
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for unionfind in unionfinds.values():
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m = 1
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for node in unionfind:
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used = {node: 1}
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queue = deque([node])
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while queue:
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node = queue.popleft()
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i = used[node]
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for neighbor in neighbors[node]:
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if neighbor not in used:
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used[neighbor] = i + 1
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queue.append(neighbor)
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m = max(m, i + 1)
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elif abs(used[neighbor] - i) != 1:
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return -1
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ret += m
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return ret

‎README.md

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[2488][2488l]|[Count Subarrays With Median K][2488] |![rs]
17711771
[2490][2490l]|[Circular Sentence][2490] |![py]
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[2491][2491l]|[Divide Players Into Teams of Equal Skill][2491] |![rs]
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[2493][2493l]|[Divide Nodes Into the Maximum Number of Groups][2493] |![py]
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[2496][2496l]|[Maximum Value of a String in an Array][2496] |![rs]
17741775
[2497][2497l]|[Maximum Star Sum of a Graph][2497] |![rs]
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[2498][2498l]|[Frog Jump II][2498] |![rs]
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[2488]:Problemset/2488-Count%20Subarrays%20With%20Median%20K/README.md#2488-count-subarrays-with-median-k
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[2490]:Problemset/2490-Circular%20Sentence/README.md#2490-circular-sentence
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[2491]:Problemset/2491-Divide%20Players%20Into%20Teams%20of%20Equal%20Skill/README.md#2491-divide-players-into-teams-of-equal-skill
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[2493]:Problemset/2493-Divide%20Nodes%20Into%20the%20Maximum%20Number%20of%20Groups/README.md#2493-divide-nodes-into-the-maximum-number-of-groups
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[2496]:Problemset/2496-Maximum%20Value%20of%20a%20String%20in%20an%20Array/README.md#2496-maximum-value-of-a-string-in-an-array
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[2497]:Problemset/2497-Maximum%20Star%20Sum%20of%20a%20Graph/README.md#2497-maximum-star-sum-of-a-graph
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[2498]:Problemset/2498-Frog%20Jump%20II/README.md#2498-frog-jump-ii
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55065508
[2488l]:https://leetcode.com/problems/count-subarrays-with-median-k/
55075509
[2490l]:https://leetcode.com/problems/circular-sentence/
55085510
[2491l]:https://leetcode.com/problems/divide-players-into-teams-of-equal-skill/
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[2493l]:https://leetcode.com/problems/divide-nodes-into-the-maximum-number-of-groups/
55095512
[2496l]:https://leetcode.com/problems/maximum-value-of-a-string-in-an-array/
55105513
[2497l]:https://leetcode.com/problems/maximum-star-sum-of-a-graph/
55115514
[2498l]:https://leetcode.com/problems/frog-jump-ii/

‎README_CN.md

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[2488][2488l]|[统计中位数为 K 的子数组][2488] |![rs]
17711771
[2490][2490l]|[回环句][2490] |![py]
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[2491][2491l]|[划分技能点相等的团队][2491] |![rs]
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[2493][2493l]|[将节点分成尽可能多的组][2493] |![py]
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[2496][2496l]|[数组中字符串的最大值][2496] |![rs]
17741775
[2497][2497l]|[图中最大星和][2497] |![rs]
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[2498][2498l]|[青蛙过河 II][2498] |![rs]
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36413642
[2488]:Problemset/2488-Count%20Subarrays%20With%20Median%20K/README_CN.md#2488-统计中位数为-k-的子数组
36423643
[2490]:Problemset/2490-Circular%20Sentence/README_CN.md#2490-回环句
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[2491]:Problemset/2491-Divide%20Players%20Into%20Teams%20of%20Equal%20Skill/README_CN.md#2491-划分技能点相等的团队
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[2493]:Problemset/2493-Divide%20Nodes%20Into%20the%20Maximum%20Number%20of%20Groups/README_CN.md#2493-将节点分成尽可能多的组
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[2496]:Problemset/2496-Maximum%20Value%20of%20a%20String%20in%20an%20Array/README_CN.md#2496-数组中字符串的最大值
36453647
[2497]:Problemset/2497-Maximum%20Star%20Sum%20of%20a%20Graph/README_CN.md#2497-图中最大星和
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[2498]:Problemset/2498-Frog%20Jump%20II/README_CN.md#2498-frog-jump-ii
@@ -5506,6 +5508,7 @@
55065508
[2488l]:https://leetcode.cn/problems/count-subarrays-with-median-k/
55075509
[2490l]:https://leetcode.cn/problems/circular-sentence/
55085510
[2491l]:https://leetcode.cn/problems/divide-players-into-teams-of-equal-skill/
5511+
[2493l]:https://leetcode.cn/problems/divide-nodes-into-the-maximum-number-of-groups/
55095512
[2496l]:https://leetcode.cn/problems/maximum-value-of-a-string-in-an-array/
55105513
[2497l]:https://leetcode.cn/problems/maximum-star-sum-of-a-graph/
55115514
[2498l]:https://leetcode.com/problems/frog-jump-ii/

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