Description
Stockbrokers are known to overreact to rumors. You have been contracted to develop a method of spreading disinformation amongst the stockbrokers to give your employer the tactical edge in the stock market. For maximum effect, you have to spread the rumors in the fastest possible way.
Unfortunately for you, stockbrokers only trust information coming from their “Trusted sources” This means you have to take into account the structure of their contacts when starting a rumor. It takes a certain amount of time for a specific stockbroker to pass the rumor on to each of his colleagues. Your task will be to write a program that tells you which stockbroker to choose as your starting point for the rumor, as well as the time it will take for the rumor to spread throughout the stockbroker community. This duration is measured as the time needed for the last person to receive the information.
Input
Your program will input data for different sets of stockbrokers. Each set starts with a line with the number of stockbrokers. Following this is a line for each stockbroker which contains the number of people who they have contact with, who these people are, and the time taken for them to pass the message to each person. The format of each stockbroker line is as follows: The line starts with the number of contacts (n), followed by n pairs of integers, one pair for each contact. Each pair lists first a number referring to the contact (e.g. a ‘1’ means person number one in the set), followed by the time in minutes taken to pass a message to that person. There are no special punctuation symbols or spacing rules.
Each person is numbered 1 through to the number of stockbrokers. The time taken to pass the message on will be between 1 and 10 minutes (inclusive), and the number of contacts will range between 0 and one less than the number of stockbrokers. The number of stockbrokers will range from 1 to 100. The input is terminated by a set of stockbrokers containing 0 (zero) people.
Output
For each set of data, your program must output a single line containing the person who results in the fastest message transmission, and how long before the last person will receive any given message after you give it to this person, measured in integer minutes.
It is possible that your program will receive a network of connections that excludes some persons, i.e. some people may be unreachable. If your program detects such a broken network, simply output the message “disjoint”. Note that the time taken to pass the message from person A to person B is not necessarily the same as the time taken to pass it from B to A, if such transmission is possible at all.
Sample Input
3 2 2 4 3 5 2 1 2 3 6 2 1 2 2 2 5 3 4 4 2 8 5 3 1 5 8 4 1 6 4 10 2 7 5 2 0 2 2 5 1 5 0
Sample Output
3 2 3 10
Solution below . . .
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 | import java.util.Iterator;import java.util.NoSuchElementException;import java.util.Scanner;/* * For all-pairs shortest path problems, Floyd-Warshall is a good * option. Given a directed weighted graph, it outputs a matrix * of all shortest paths between pairs of nodes. * * For this problem, each row of the matrix represents a broker. * We read each row to find brokers who can get a message to * every other broker, and select the broker with the smallest maximum. */public class Main { public static void main(String[] args) { Scanner sc = new Scanner(System.in); AdjMatrixEdgeWeightedDigraph G; int brokers = sc.nextInt(); while (brokers != 0) { G = new AdjMatrixEdgeWeightedDigraph(brokers); for (int broker = 0; broker < brokers; broker++) { int connections = sc.nextInt(); for (int i = 0; i < connections; i++) { int w = sc.nextInt() - 1; int weight = sc.nextInt(); G.addEdge(new DirectedEdge(broker, w, weight)); } } FloydWarshall spt = new FloydWarshall(G); // find the broker with the shortest max distance int min = 9999; int minBroker = -1; for (int v = 0; v < G.V(); v++) { int max = -1; for (int w = 0; w < G.V(); w++) { if (v != w) { if (spt.hasPath(v, w)) { max = Math.max(spt.dist(v, w), max); } else { // this broker can't reach at least one target max = 9999; break; } } } if (max < min) { min = max; minBroker = v; } } if (minBroker == -1) { System.out.println("disjoint"); } else { System.out.println((minBroker + 1) + " " + min); } brokers = sc.nextInt(); } sc.close(); }}/****************************************************************** * * An edge-weighted digraph, implemented using an adjacency matrix. * ******************************************************************/class AdjMatrixEdgeWeightedDigraph { private final int V; private int E; private DirectedEdge[][] adj; public AdjMatrixEdgeWeightedDigraph(int V) { this.V = V; this.E = 0; this.adj = new DirectedEdge[V][V]; } public int V() { return V; } public int E() { return E; } public void addEdge(DirectedEdge e) { int v = e.from(); int w = e.to(); if (adj[v][w] == null) { E++; adj[v][w] = e; } } public Iterable<DirectedEdge> adj(int v) { return new AdjIterator(v); } // support iteration over graph vertices private class AdjIterator implements Iterator<DirectedEdge>, Iterable<DirectedEdge> { private int v; private int w = 0; public AdjIterator(int v) { this.v = v; } public Iterator<DirectedEdge> iterator() { return this; } public boolean hasNext() { while (w < V) { if (adj[v][w] != null) return true; w++; } return false; } public DirectedEdge next() { if (!hasNext()) { throw new NoSuchElementException(); } return adj[v][w++]; } public void remove() { throw new UnsupportedOperationException(); } }}/****************************************************************** * * Immutable weighted directed edge. * ******************************************************************/class DirectedEdge { private final int v; private final int w; private final int weight; public DirectedEdge(int v, int w, int weight) { this.v = v; this.w = w; this.weight = weight; } public int from() { return v; } public int to() { return w; } public int weight() { return weight; }}class FloydWarshall { // distTo[v][w] = length of shortest v->w path private int[][] distTo; // edgeTo[v][w] = last edge on shortest v->w path private DirectedEdge[][] edgeTo; private final int MAX = 9999; public FloydWarshall(AdjMatrixEdgeWeightedDigraph G) { int V = G.V(); distTo = new int[V][V]; edgeTo = new DirectedEdge[V][V]; // initialize distances to max value for (int v = 0; v < V; v++) { for (int w = 0; w < V; w++) { distTo[v][w] = MAX; } } // update distances using digraph for (int v = 0; v < G.V(); v++) { for (DirectedEdge e : G.adj(v)) { distTo[e.from()][e.to()] = e.weight(); edgeTo[e.from()][e.to()] = e; } } for (int i = 0; i < V; i++) { // compute shortest paths using only // 0, 1, ..., i as intermediate vertices for (int v = 0; v < V; v++) { if (edgeTo[v][i] == null) continue; // optimization for (int w = 0; w < V; w++) { if (distTo[v][w] > distTo[v][i] + distTo[i][w]) { distTo[v][w] = distTo[v][i] + distTo[i][w]; edgeTo[v][w] = edgeTo[i][w]; } } } } } public boolean hasPath(int s, int t) { return distTo[s][t] < MAX; } public int dist(int s, int t) { return distTo[s][t]; }} |