Arbitrage

描述

Arbitrage is the use of discrepancies in currency exchange rates to transform one unit of a currency into more than one unit of the same currency. For example, suppose that 1 US Dollar buys 0.5 British pound, 1 British pound buys 10.0 French francs, and 1 French franc buys 0.21 US dollar. Then, by converting currencies, a clever trader can start with 1 US dollar and buy 0.5 10.0 0.21 = 1.05 US dollars, making a profit of 5 percent.

Your job is to write a program that takes a list of currency exchange rates as input and then determines whether arbitrage is possible or not.

输入

The input will contain one or more test cases. Om the first line of each test case there is an integer n (1<=n<=30), representing the number of different currencies. The next n lines each contain the name of one currency. Within a name no spaces will appear. The next line contains one integer m, representing the length of the table to follow. The last m lines each contain the name ci of a source currency, a real number rij which represents the exchange rate from ci to cj and a name cj of the destination currency. Exchanges which do not appear in the table are impossible.
Test cases are separated from each other by a blank line. Input is terminated by a value of zero (0) for n.

输出

For each test case, print one line telling whether arbitrage is possible or not in the format “Case case: Yes” respectively “Case case: No”.

样例输入

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3
USDollar
BritishPound
FrenchFranc
3
USDollar 0.5 BritishPound
BritishPound 10.0 FrenchFranc
FrenchFranc 0.21 USDollar

3
USDollar
BritishPound
FrenchFranc
6
USDollar 0.5 BritishPound
USDollar 4.9 FrenchFranc
BritishPound 10.0 FrenchFranc
BritishPound 1.99 USDollar
FrenchFranc 0.09 BritishPound
FrenchFranc 0.19 USDollar

0

样例输出

1
2
Case 1: Yes
Case 2: No

代码

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#include <iostream>
#include <queue>
#include <string>
#include <vector>

using namespace std;

struct currency {
    double value;
    int source;

    currency(double n, int s) : value(n), source(s) {}
};

int n = 0;
int m = 0;

string name[35];
int count[35];
vector<currency> cur[35];

double d[35];
int t[35];
int t_max;
bool in_queue[35];
queue<int> q;

int find_money(string a)
{
    for (int i = 0; i < n; i++) {
        if (!a.compare(name[i])) {
            return i;
        }
    }
    return -1;
}

int main(void)
{
    cin >> n;
    string a, b;
    double c;
    int case_number = 0;
    while (n != 0) {
        bool res = false;
        case_number ++;
        // Read value
        for (int i = 0; i < n; i++) {
            cin >> name[i];
            cur[i].clear();
        }
        cin >> m;
        for (int i = 0; i < m; i++) {
            cin >> a >> c >> b;
            cur[find_money(b)].push_back(currency(c, find_money(a)));
        }

        //SPFA
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                t[j] = 0;
                d[j] = 0;
                in_queue[j] = false;
            }
            t_max = 0;
            q.push(i);
            t[i] = 1;
            d[i] = 1;
            in_queue[i] = true;
            while ((!q.empty()) && (t_max < n)) {
                int cur_node = q.front();
                q.pop();
                in_queue[cur_node] = false;
                for (vector<currency>::iterator it = cur[cur_node].begin(); it != cur[cur_node].end(); it++) {
                    if (d[it->source] < d[cur_node] * it->value) {
                        d[it->source] = d[cur_node] * it->value;
                        if (!in_queue[it->source]) {
                            q.push(it->source);
                            if ((++t[it->source]) > t_max) {
                                t_max = t[it->source];
                            }
                            in_queue[it->source] = true;
                        }
                    }
                }
            }
            if (t_max >= n) {
                res = true;
            }
            while (!q.empty()) {
                q.pop();
            }
        }
        if(res){
            cout << "Case " << case_number << ": Yes" << endl;
        }
        else{
            cout << "Case " << case_number << ": No" << endl;
        }
        cin >> n;
    }
    return 0;
}

代码 2

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#include <cstring>
#include <iostream>
#include <queue>
#define SIZE 35

using namespace std;

struct edge {
    int s;    // source
    double v; // value

    edge(int s, double v) : s(s), v(v) {}
};

char money_name[SIZE][200];
int n, m;

int money(char name[])
{
    for (int i = 0; i < n; i++) {
        if (!strcmp(name, money_name[i])) {
            return i;
        }
    }
    return -1;
}

int main(void)
{
    int case_num = 0;
    cin >> n;
    while (n != 0) {
        case_num++;

        vector<edge> cur[SIZE];

        // ========== Input ==========
        for (int i = 0; i < n; i++) {
            cin >> money_name[i];
        }
        cin >> m;
        char src[200], dest[200];
        double value;
        for (int i = 0; i < m; i++) {
            cin >> src >> value >> dest;
            cur[money(dest)].push_back(edge(money(src), value));
        }

        // ========== SPFA ===========
        bool res = false;
        // HERE: Run n times to avoid isolated points
        for (int i = 0; i < n; i++) {

            // Variables for SPFA
            queue<int> q;
            double d[SIZE];
            bool in_queue[SIZE];
            int successor[SIZE];

            int t[SIZE];

            // Init
            for (int j = 0; j < n; j++) {
                t[j] = 0;
                d[j] = 0;
                in_queue[j] = false;
                successor[j] = j;
            }
            int t_max = 0;

            // Start point
            t[i] = 1;
            d[i] = 1;
            q.push(i);
            in_queue[i] = true;

            // Begin
            while (!q.empty() && t_max <= n) {
                int c = q.front();
                q.pop();
                in_queue[c] = false;
                for (vector<edge>::iterator it = cur[c].begin(); it != cur[c].end(); it++) {
                    // source < (source->dest) * dest
                    if (d[it->s] < d[c] * it->v) {
                        d[it->s] = d[c] * it->v;
                        successor[it->s] = c;    
                        // If not in queue, then push it
                        if (!in_queue[it->s]) {
                            q.push(it->s);
                            in_queue[it->s] = true;
                            if (++t[it->s] > t_max) {
                                t_max = t[it->s];
                            }
                        }
                    }
                }
            }
            // Negative cycle detect
            if (t_max >= n) {
                res = true;
                break;
            }
        }

        cout << "Case " << case_num << ": ";
        if (res) {
            cout << "Yes" << endl;
        }
        else {
            cout << "No" << endl;
        }

        cin >> n;
    }
    return 0;
}

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