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:
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);
}
}
}