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  • PKU 1860 Currency Exchange 最短路 bellman

    题意/Description

        Several currency exchange points are working in our city. Let us suppose that each point specializes in two particular currencies and performs exchange operations only with these currencies. There can be several points specializing in the same pair of currencies. Each point has its own exchange rates, exchange rate of A to B is the quantity of B you get for 1A. Also each exchange point has some commission, the sum you have to pay for your exchange operation. Commission is always collected in source currency. 
    For example, if you want to exchange 100 US Dollars into Russian Rubles at the exchange point, where the exchange rate is 29.75, and the commission is 0.39 you will get (100 - 0.39) * 29.75 = 2963.3975RUR. 
    You surely know that there are N different currencies you can deal with in our city. Let us assign unique integer number from 1 to N to each currency. Then each exchange point can be described with 6 numbers: integer A and B - numbers of currencies it exchanges, and real RAB, CAB, RBA and CBA - exchange rates and commissions when exchanging A to B and B to A respectively. 
    Nick has some money in currency S and wonders if he can somehow, after some exchange operations, increase his capital. Of course, he wants to have his money in currency S in the end. Help him to answer this difficult question. Nick must always have non-negative sum of money while making his operations. 

     

    读入/Input

        The first line of the input contains four numbers: N - the number of currencies, M - the number of exchange points, S - the number of currency Nick has and V - the quantity of currency units he has. The following M lines contain 6 numbers each - the description of the corresponding exchange point - in specified above order. Numbers are separated by one or more spaces. 1<=S<=N<=100, 1<=M<=100, V is real number, 0<=V<=103
        For each point exchange rates and commissions are real, given with at most two digits after the decimal point, 

    10-2<=rate<=102, 0<=commission<=102
        Let us call some sequence of the exchange operations simple if no exchange point is used more than once in this sequence. You may assume that ratio of the numeric values of the sums at the end and at the beginning of any simple sequence of the exchange operations will be less than 104

     

    输出/Output

        If Nick can increase his wealth, output YES, in other case output NO to the output file.

     

    题解/solution

        这题我一开始想把各个值变为负数,然后用bellman求一个负权的环,结果总是WA。我就想不对吗?疑问负负得正啊,诶!是否可以求一个正权的环,结果显然可以,AC啦!

     

    代码/Code

    const
      maxE=100000;
      maxV=2000000;
    type
      arr=record
        x,y:longint;
        w,q:real;
      end;
    
    var
      n,m,s:longint;
      v:real;
      a:array [0..maxV+1] of arr;
      b:array [0..maxE+1] of real;
    procedure init;
    var
      i:longint;
    begin
      readln(n,m,s,v);
      for i:=1 to m do
        begin
          with a[i*2-1] do
            begin
              read(x,y,w,q);
              a[i*2].x:=y; a[i*2].y:=x;
            end;
          readln(a[i*2].w,a[i*2].q);
        end;
      m:=m*2;
      b[s]:=v;
    end;
    
    procedure bellman;
    var
      i,j:longint;
    begin
      for i:=1 to n do
        for j:=1 to m do
          with a[j] do
            if (b[x]-q)*w>b[y] then
              b[y]:=(b[x]-q)*w;
      for i:=1 to m do
        with a[i] do
            if (b[x]-q)*w>b[y] then
              begin
                write('YES'); exit;
              end;
      write('NO');
    end;
    
    begin
      init;
      bellman;
    end.



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  • 原文地址:https://www.cnblogs.com/zyx-crying/p/9319721.html
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