Question

928. 尽量减少恶意软件的传播 II

English Version

题目描述

给定一个由 n 个节点组成的网络，用 n x n 个邻接矩阵 graph 表示。在节点网络中，只有当 graph[i][j] = 1 时，节点 i 能够直接连接到另一个节点 j。

一些节点 initial 最初被恶意软件感染。只要两个节点直接连接，且其中至少一个节点受到恶意软件的感染，那么两个节点都将被恶意软件感染。这种恶意软件的传播将继续，直到没有更多的节点可以被这种方式感染。

假设 M(initial) 是在恶意软件停止传播之后，整个网络中感染恶意软件的最终节点数。

我们可以从 initial 中删除一个节点，并完全移除该节点以及从该节点到任何其他节点的任何连接。

请返回移除后能够使 M(initial) 最小化的节点。如果有多个节点满足条件，返回索引 最小的节点 。

 

示例 1：

输入：graph = [[1,1,0],[1,1,0],[0,0,1]], initial = [0,1]
输出：0

示例 2：

输入：graph = [[1,1,0],[1,1,1],[0,1,1]], initial = [0,1]
输出：1

示例 3：

输入：graph = [[1,1,0,0],[1,1,1,0],[0,1,1,1],[0,0,1,1]], initial = [0,1]
输出：1

 

提示：

• n == graph.length
• n == graph[i].length
• 2 <= n <= 300
• graph[i][j] 是 0 或 1.
• graph[i][j] == graph[j][i]
• graph[i][i] == 1
• 1 <= initial.length < n
• 0 <= initial[i] <= n - 1
•  initial 中每个整数都不同

解法

方法一

class Solution:
  def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
    def find(x):
      if p[x] != x:
        p[x] = find(p[x])
      return p[x]

    def union(a, b):
      pa, pb = find(a), find(b)
      if pa != pb:
        size[pb] += size[pa]
        p[pa] = pb

    n = len(graph)
    p = list(range(n))
    size = [1] * n
    clean = [True] * n
    for i in initial:
      clean[i] = False
    for i in range(n):
      if not clean[i]:
        continue
      for j in range(i + 1, n):
        if clean[j] and graph[i][j] == 1:
          union(i, j)
    cnt = Counter()
    mp = {}
    for i in initial:
      s = {find(j) for j in range(n) if clean[j] and graph[i][j] == 1}
      for root in s:
        cnt[root] += 1
      mp[i] = s

    mx, ans = -1, 0
    for i, s in mp.items():
      t = sum(size[root] for root in s if cnt[root] == 1)
      if mx < t or mx == t and i < ans:
        mx, ans = t, i
    return ans

class Solution {
  private int[] p;
  private int[] size;

  public int minMalwareSpread(int[][] graph, int[] initial) {
    int n = graph.length;
    p = new int[n];
    size = new int[n];
    for (int i = 0; i < n; ++i) {
      p[i] = i;
      size[i] = 1;
    }
    boolean[] clean = new boolean[n];
    Arrays.fill(clean, true);
    for (int i : initial) {
      clean[i] = false;
    }
    for (int i = 0; i < n; ++i) {
      if (!clean[i]) {
        continue;
      }
      for (int j = i + 1; j < n; ++j) {
        if (clean[j] && graph[i][j] == 1) {
          union(i, j);
        }
      }
    }
    int[] cnt = new int[n];
    Map<Integer, Set<Integer>> mp = new HashMap<>();
    for (int i : initial) {
      Set<Integer> s = new HashSet<>();
      for (int j = 0; j < n; ++j) {
        if (clean[j] && graph[i][j] == 1) {
          s.add(find(j));
        }
      }
      for (int root : s) {
        cnt[root] += 1;
      }
      mp.put(i, s);
    }
    int mx = -1;
    int ans = 0;
    for (Map.Entry<Integer, Set<Integer>> entry : mp.entrySet()) {
      int i = entry.getKey();
      int t = 0;
      for (int root : entry.getValue()) {
        if (cnt[root] == 1) {
          t += size[root];
        }
      }
      if (mx < t || (mx == t && i < ans)) {
        mx = t;
        ans = i;
      }
    }
    return ans;
  }

  private int find(int x) {
    if (p[x] != x) {
      p[x] = find(p[x]);
    }
    return p[x];
  }

  private void union(int a, int b) {
    int pa = find(a);
    int pb = find(b);
    if (pa != pb) {
      size[pb] += size[pa];
      p[pa] = pb;
    }
  }
}

class Solution {
public:
  vector<int> p;
  vector<int> size;

  int minMalwareSpread(vector<vector<int>>& graph, vector<int>& initial) {
    int n = graph.size();
    p.resize(n);
    size.resize(n);
    for (int i = 0; i < n; ++i) p[i] = i;
    fill(size.begin(), size.end(), 1);
    vector<bool> clean(n, true);
    for (int i : initial) clean[i] = false;
    for (int i = 0; i < n; ++i) {
      if (!clean[i]) continue;
      for (int j = i + 1; j < n; ++j)
        if (clean[j] && graph[i][j] == 1) merge(i, j);
    }
    vector<int> cnt(n, 0);
    unordered_map<int, unordered_set<int>> mp;
    for (int i : initial) {
      unordered_set<int> s;
      for (int j = 0; j < n; ++j)
        if (clean[j] && graph[i][j] == 1) s.insert(find(j));
      for (int e : s) ++cnt[e];
      mp[i] = s;
    }
    int mx = -1, ans = 0;
    for (auto& [i, s] : mp) {
      int t = 0;
      for (int root : s)
        if (cnt[root] == 1)
          t += size[root];
      if (mx < t || (mx == t && i < ans)) {
        mx = t;
        ans = i;
      }
    }
    return ans;
  }

  int find(int x) {
    if (p[x] != x) p[x] = find(p[x]);
    return p[x];
  }

  void merge(int a, int b) {
    int pa = find(a), pb = find(b);
    if (pa != pb) {
      size[pb] += size[pa];
      p[pa] = pb;
    }
  }
};

func minMalwareSpread(graph [][]int, initial []int) int {
  n := len(graph)
  p := make([]int, n)
  size := make([]int, n)
  clean := make([]bool, n)
  for i := 0; i < n; i++ {
    p[i], size[i], clean[i] = i, 1, true
  }
  for _, i := range initial {
    clean[i] = false
  }

  var find func(x int) int
  find = func(x int) int {
    if p[x] != x {
      p[x] = find(p[x])
    }
    return p[x]
  }
  union := func(a, b int) {
    pa, pb := find(a), find(b)
    if pa != pb {
      size[pb] += size[pa]
      p[pa] = pb
    }
  }

  for i := 0; i < n; i++ {
    if !clean[i] {
      continue
    }
    for j := i + 1; j < n; j++ {
      if clean[j] && graph[i][j] == 1 {
        union(i, j)
      }
    }
  }
  cnt := make([]int, n)
  mp := make(map[int]map[int]bool)
  for _, i := range initial {
    s := make(map[int]bool)
    for j := 0; j < n; j++ {
      if clean[j] && graph[i][j] == 1 {
        s[find(j)] = true
      }
    }
    for root, _ := range s {
      cnt[root]++
    }
    mp[i] = s
  }
  mx, ans := -1, 0
  for i, s := range mp {
    t := 0
    for root, _ := range s {
      if cnt[root] == 1 {
        t += size[root]
      }
    }
    if mx < t || (mx == t && i < ans) {
      mx, ans = t, i
    }
  }
  return ans
}