#928 - Minimize Malware Spread II

Problem Description

You are given a network of n nodes represented as an n x n adjacency matrix graph, where the ith node is directly connected to the jth node if graph[i][j] == 1.

Some nodes initial are initially infected by malware. Whenever two nodes are directly connected, and at least one of those two nodes is infected by malware, both nodes will be infected by malware. This spread of malware will continue until no more nodes can be infected in this manner.

Suppose M(initial) is the final number of nodes infected with malware in the entire network after the spread of malware stops.

We will remove exactly one node from initial, completely removing it and any connections from this node to any other node.

Return the node that, if removed, would minimize M(initial). If multiple nodes could be removed to minimize M(initial), return such a node with the smallest index.

Solution

/**
 * @param {number[][]} graph
 * @param {number[]} initial
 * @return {number}
 */
var minMalwareSpread = function(graph, initial) {
  const n = graph.length;
  const initialSet = new Set(initial);

  initial.sort((a, b) => a - b);

  const infected = new Set(initial);
  const queue = [...initial];

  for (let i = 0; i < queue.length; i++) {
    const node = queue[i];
    for (let neighbor = 0; neighbor < n; neighbor++) {
      if (graph[node][neighbor] === 1 && !infected.has(neighbor)) {
        infected.add(neighbor);
        queue.push(neighbor);
      }
    }
  }

  const sourcesMap = new Array(n).fill().map(() => []);

  for (const initialNode of initial) {
    const reachable = new Set();
    const visited = new Set(initial);
    visited.delete(initialNode);

    const q = [initialNode];
    while (q.length > 0) {
      const node = q.shift();
      reachable.add(node);

      for (let neighbor = 0; neighbor < n; neighbor++) {
        if (graph[node][neighbor] === 1 && !visited.has(neighbor)) {
          visited.add(neighbor);
          q.push(neighbor);
        }
      }
    }

    for (let node = 0; node < n; node++) {
      if (reachable.has(node) && !initialSet.has(node)) {
        sourcesMap[node].push(initialNode);
      }
    }
  }

  const savedCounts = new Map();
  for (let node = 0; node < n; node++) {
    if (sourcesMap[node].length === 1) {
      const source = sourcesMap[node][0];
      savedCounts.set(source, (savedCounts.get(source) || 0) + 1);
    }
  }

  let maxSaved = 0;
  let result = initial[0];

  for (const node of initial) {
    const saved = savedCounts.get(node) || 0;
    if (saved > maxSaved) {
      maxSaved = saved;
      result = node;
    } else if (saved === maxSaved && node < result) {
      result = node;
    }
  }

  return result;
};