版权声明：本文为博主原创文章，未经博主允许不得转载。 https://cloud.tencent.com/developer/article/1434593
POJ 刷题系列：1860. Currency Exchange
传送门：1860. Currency Exchange
题意：
N种货币，任意货币之间可以相互转换，转换需要手续费commission，假设货币A当前金额为money，转换公式如下：（money - commission） * rate，现给出任意货币之间的转换手续和转换率，问从S点出发，是否存在一条路径使得回到S时，能够增值。
思路：
实际上，该问题和判断负环类似，只要在S的路径上存在一条环，使得经过该环上的结点出现增值，那么就能产生无限的现金。自然地，定义dpi：表示从源点S出发到结点i的现金流。如果不存在这样的环，必然最多经过N-1次就停止更新，否则就会无限更新下去。
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.List;
import java.util.Map;
import java.util.StringTokenizer;
public class Main{
String INPUT = "./data/judge/201712/P1860.txt";
public static void main(String[] args) throws IOException {
new Main().run();
}
class Edge{
int from;
int to;
double rate;
double commission;
Edge(int from, int to, double rate, double commission){
this.from = from;
this.to = to;
this.rate = rate;
this.commission = commission;
}
@Override
public String toString() {
return from " " to;
}
}
void read() {
int N = ni();
int M = ni();
int S = ni();
double money = nd();
List<Edge> edges = new ArrayList<Edge>();
for (int i = 0; i < M; i) {
int from = ni();
int to = ni();
from --;
to --;
double rate = nd();
double commission = nd();
edges.add(new Edge(from, to, rate, commission));
rate = nd();
commission = nd();
edges.add(new Edge(to, from, rate, commission));
}
double[] dp = new double[N];
dp[S - 1] = money;
boolean valid = false;
for (int i = 0; i < N; i) {
for (Edge e : edges) {
double preMoney = dp[e.from];
if (preMoney - e.commission >= 0) {
double nxtMoney = (preMoney - e.commission) * e.rate;
if (nxtMoney > dp[e.to]) {
dp[e.to] = nxtMoney;
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);
}
}
}
