UVA 104 Arbitrage

动态规划类似FLOYD dp[i][j][k] 表示第i个点经过K次到达j点能获得的最大利润

#include <map>
#include <set>
#include <list>
#include <cmath>
#include <ctime>
#include <deque>
#include <stack>
#include <queue>
#include <cctype>
#include <cstdio>
#include <string>
#include <vector>
#include <climits>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#define LL long long
#define PI 3.1415926535897932626
using namespace std;
int gcd(int a, int b) {return a % b == 0 ? b : gcd(b, a % b);}
#define MAXN 25
double G[MAXN][MAXN];
double dp[MAXN][MAXN][MAXN];
int fa[MAXN][MAXN][MAXN];
int N;
int cnt,ans;
void init()
{
    memset(dp,0,sizeof(dp));
    memset(fa,0,sizeof(fa));
    for (int i = 1; i <= N; i++)
    {
        dp[i][i][1] = 1.0;
        for (int j = 1; j <= N; j++)
        {
            fa[i][j][1] = i;
            if (i == j) continue;
            scanf("%lf",&dp[i][j][1]);
        }
    }
}
bool judge()
{
    for (int k = 2; k <= N; k++)
        for (int i = 1; i <= N; i++)
        if (dp[i][i][k] > 1.01)
    {
        ans = i;
        cnt = k;
       //8 printf("%d %d
",ans,cnt);
        return true;
    }
    return false;
}
void output(int x,int y,int cnt)
{
    if (cnt == 0)  {printf("%d",x);return ;}
    //printf("%d %d %d %d
",x,y,cnt,fa[x][y][cnt]);
    output(x,fa[x][y][cnt],cnt - 1);
    printf(" %d",y);
}
int main()//节点i通过K次转换到达节点j能拿到的钱
{
   // freopen("sample.txt","r",stdin);
    while (scanf("%d",&N) != EOF)
    {
        init();
        for (int k = 2; k <= N; k++)
          for (int i = 1; i <= N; i++)
            for (int j = 1; j <= N; j++)
               for (int p = 1; p <= N; p++)
        {
            if (dp[i][j][k] < dp[i][p][k - 1] * dp[p][j][1])
            {
                dp[i][j][k] = dp[i][p][k - 1] * dp[p][j][1];
                fa[i][j][k] = p;//在i经过K次转换到P的过程中第K 是p->j
            }
        }
        bool found = judge();
        if (!found)  puts("no arbitrage sequence exists");
        else {  output(ans,ans,cnt); putchar('
');}
    }
    return 0;
}