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社区首页 >专栏 >3259. Wormholes

3259. Wormholes

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用户1147447
发布2019-05-26 00:28:49
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发布2019-05-26 00:28:49
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文章被收录于专栏:机器学习入门

POJ 刷题系列:3259. Wormholes

题意:

N个顶点,任意顶点之间存在双向边,权重为正,也可能存在单向边(虫洞),权重为负。给出一张图,问是否存在负环。

思路:

重新回顾了下Bellman-Ford算法,核心思路如下:从单个源点出发,如果经过N轮还在更新时,说明存在负环。证明:假设不存在负环,那么最短路径必然不会经过一个顶点两次,所以最多通过N- 1条边。

代码如下:

代码语言:javascript
复制
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.StringTokenizer;

public class Main{

    String INPUT = "./data/judge/201712/P3259.txt";

    public static void main(String[] args) throws IOException {
        new Main().run();
    }

    static final int INF = 0x3f3f3f3f;
    int N;

    class Edge{
        int from;
        int to;
        int time;
        Edge(int from, int to, int time){
            this.from = from;
            this.to   = to;
            this.time = time;
        }
    }

    Map<Integer, Edge> edges;

    void addEdge(int u, int v, int t) {
        int hash = u * N + v;
        if (!edges.containsKey(hash)) edges.put(hash, new Edge(u, v, INF));
        edges.get(hash).time = Math.min(edges.get(hash).time, t);
    }

    void read() {
        int F = ni();
        while (F --> 0) {
            N = ni();
            int M = ni();
            int W = ni();

            edges = new HashMap<Integer, Edge>();

            for (int i = 0; i < M; ++i) {
                int u = ni();
                int v = ni();
                u --;
                v --;
                int t = ni();
                addEdge(u, v, t);
                addEdge(v, u, t);
            }

            for (int i = 0; i < W; ++i) {
                int u = ni();
                int v = ni();
                u --;
                v --;
                int t = ni();
                addEdge(u, v, -t);
            }

            int[] dp = new int[N];
            Arrays.fill(dp, INF);
            dp[0] = 0;

            boolean valid = false;
            for (int i = 0; i < N ; ++i) {
                for (Edge e : edges.values()) {
                    if (dp[e.to] > dp[e.from] + e.time) {
                        dp[e.to] = dp[e.from] + e.time;
                        if (i == N - 1) valid = true;
                    }
                }
            }
            out.println(valid ? "YES" : "NO");
        }
    }

    FastScanner in;
    PrintWriter out;

    void run() throws IOException {
        boolean oj;
        try {
            oj = ! System.getProperty("user.dir").equals("F:\\oxygen_workspace\\Algorithm");
        } catch (Exception e) {
            oj = System.getProperty("ONLINE_JUDGE") != null;
        }

        InputStream is = oj ? System.in : new FileInputStream(new File(INPUT));
        in = new FastScanner(is);
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        read();
        out.flush();
        if (!oj){
            System.out.println("[" + (System.currentTimeMillis() - s) + "ms]");
        }
    }

    public boolean more(){
        return in.hasNext();
    }

    public int ni(){
        return in.nextInt();
    }

    public long nl(){
        return in.nextLong();
    }

    public double nd(){
        return in.nextDouble();
    }

    public String ns(){
        return in.nextString();
    }

    public char nc(){
        return in.nextChar();
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        boolean hasNext;

        public FastScanner(InputStream is) throws IOException {
            br = new BufferedReader(new InputStreamReader(is));
            hasNext = true;
        }

        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    hasNext = false;
                    return "##";
                }
            }
            return st.nextToken();
        }

        String next = null;
        public boolean hasNext(){
            next = nextToken();
            return hasNext;
        }

        public int nextInt() {
            if (next == null){
                hasNext();
            }
            String more = next;
            next = null;
            return Integer.parseInt(more);
        }

        public long nextLong() {
            if (next == null){
                hasNext();
            }
            String more = next;
            next = null;
            return Long.parseLong(more);
        }

        public double nextDouble() {
            if (next == null){
                hasNext();
            }
            String more = next;
            next = null;
            return Double.parseDouble(more);
        }

        public String nextString(){
            if (next == null){
                hasNext();
            }
            String more = next;
            next = null;
            return more;
        }

        public char nextChar(){
            if (next == null){
                hasNext();
            }
            String more = next;
            next = null;
            return more.charAt(0);
        }
    }

    static class D{

        public static void pp(int[][] board, int row, int col) {
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < row; ++i) {
                for (int j = 0; j < col; ++j) {
                    sb.append(board[i][j] + (j + 1 == col ? "\n" : " "));
                }
            }
            System.out.println(sb.toString());
        }

        public static void pp(char[][] board, int row, int col) {
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < row; ++i) {
                for (int j = 0; j < col; ++j) {
                    sb.append(board[i][j] + (j + 1 == col ? "\n" : " "));
                }
            }
            System.out.println(sb.toString());
        }
    }

    static class ArrayUtils {

        public static void fill(int[][] f, int value) {
            for (int i = 0; i < f.length; ++i) {
                Arrays.fill(f[i], value);
            }
        }

        public static void fill(int[][][] f, int value) {
            for (int i = 0; i < f.length; ++i) {
                fill(f[i], value);
            }
        }

        public static void fill(int[][][][] f, int value) {
            for (int i = 0; i < f.length; ++i) {
                fill(f[i], value);
            }
        }
    }

    static class Num{
        public static <K> void inc(Map<K, Integer> mem, K k) {
            if (!mem.containsKey(k)) mem.put(k, 0);
            mem.put(k, mem.get(k) + 1);
        }
    }
}
这里写图片描述
这里写图片描述
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原始发表:2017年12月22日,如有侵权请联系 cloudcommunity@tencent.com 删除

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