poj 1276 Cash Machine

Description

A Bank plans toinstall a machine for cash withdrawal. The machine is able todeliver appropriate @ bills for a requested cash amount. Themachine uses exactly N distinct bill denominations, say Dk, k=1,N,and for each denomination Dk the machine has a supply of nk bills.For example,

N=3, n1=10, D1=100, n2=4, D2=50, n3=5, D3=10

means the machine has a supply of 10 bills of @100 each, 4 bills of@50 each, and 5 bills of @10 each.

Call cash the requested amount of cash the machine should deliverand write a program that computes the maximum amount of cash lessthan or equal to cash that can be effectively delivered accordingto the available bill supply of the machine.

Notes:
@ is the symbol of the currency delivered by the machine. Forinstance, @ may stand for dollar, euro, pound etc.

Input

The program input isfrom standard input. Each data set in the input stands for aparticular transaction and has the format:

cash N n1 D1 n2 D2 ... nN DN

where 0 <= cash <= 100000 is theamount of cash requested, 0 <=N <= 10is the number of bill denominations and 0 <= nk<= 1000 is the number of available bills for the Dkdenomination, 1 <= Dk <= 1000, k=1,N.White spaces can occur freely between the numbers in the input. Theinput data are correct.

Output

For each set of datathe program prints the result to the standard output on a separateline as shown in the examples below.

Sample Input

735 3  4 125  6 5  3 350633 4  500 30  6 100  1 5  0 1735 00 3  10 100  10 50  10 10

Sample Output

73563000

Hint

The first data setdesignates a transaction where the amount of cash requested is@735. The machine contains 3 bill denominations: 4 bills of @125, 6bills of @5, and 3 bills of @350. The machine can deliver the exactamount of requested cash.

In the second case the bill supply of the machine does not fit theexact amount of cash requested. The maximum cash that can bedelivered is @630. Notice that there can be several possibilitiesto combine the bills in the machine for matching the deliveredcash.

In the third case the machine is empty and no cash is delivered. Inthe fourth case the amount of cash requested is @0 and, therefore,the machine delivers no cash.

Source

Southeastern Europe 2002

 

题目大意：给出cash和n，还有n种面值的钞票，各d[i]张，求能取到不大于cash的最大价值。

 

多重背包。将每种面值的d拆成1,2,4,8,16,32,...,2^k,d[i]-2^(k+1)+1张，进行0-1背包的操作。

 

ACCODE

programpku_1276;
var f:array[0..100000] of boolean;
   d,vv,v:array[1..1000] of longint;
   n,nn,c:longint;
//============================================================================
procedure divide;
var i,j:longint;
begin
  n:=0;
  for i:=1 to nn do
  begin j:=0;
    while truedo
     if 1 shl (j+1)-1<=d[i] then
     begin
       inc(n);
       v[n]:=vv[i]*1 shl j;
       inc(j);
     end else break;
    if d[i]-1shl j+1>0 then
    begin
     inc(n);
     v[n]:=vv[i]*(d[i]-1 shl j+1);
    end;
  end;
end;
//============================================================================
procedure work;
var i,j:longint;
begin
  read(c,nn);
  for i:=1 to nn do
   read(d[i],vv[i]);
  divide;
  for i:=1 to c do f[i]:=false;
  f[0]:=true;
  for i:=1 to n do
    for j:=cdownto v[i] do
     f[j]:=f[j] or f[j-v[i]];
  for i:=c downto 0 do
    if f[i]then
    begin
     writeln(i);
     break;
    end;
end;
//============================================================================
begin
  while not(seekeof) do work;
end.