D - 完全背包

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Description Before ACM can do anything, a budget must be prepared and the necessary financial support obtained. The main income for this action comes from Irreversibly Bound Money (IBM). The idea behind is simple. Whenever some ACM member has any small money, he takes all the coins and throws them into a piggy-bank. You know that this process is irreversible, the coins cannot be removed without breaking the pig. After a sufficiently long time, there should be enough cash in the piggy-bank to pay everything that needs to be paid.  But there is a big problem with piggy-banks. It is not possible to determine how much money is inside. So we might break the pig into pieces only to find out that there is not enough money. Clearly, we want to avoid this unpleasant situation. The only possibility is to weigh the piggy-bank and try to guess how many coins are inside. Assume that we are able to determine the weight of the pig exactly and that we know the weights of all coins of a given currency. Then there is some minimum amount of money in the piggy-bank that we can guarantee. Your task is to find out this worst case and determine the minimum amount of cash inside the piggy-bank. We need your help. No more prematurely broken pigs!    Input The input consists of T test cases. The number of them (T) is given on the first line of the input file. Each test case begins with a line containing two integers E and F. They indicate the weight of an empty pig and of the pig filled with coins. Both weights are given in grams. No pig will weigh more than 10 kg, that means 1 <= E <= F <= 10000. On the second line of each test case, there is an integer number N (1 <= N <= 500) that gives the number of various coins used in the given currency. Following this are exactly N lines, each specifying one coin type. These lines contain two integers each, Pand W (1 <= P <= 50000, 1 <= W <=10000). P is the value of the coin in monetary units, W is it's weight in grams.    Output Print exactly one line of output for each test case. The line must contain the sentence "The minimum amount of money in the piggy-bank is X." where X is the minimum amount of money that can be achieved using coins with the given total weight. If the weight cannot be reached exactly, print a line "This is impossible.".    Sample Input 3 10 110 2 1 1 30 50 10 110 2 1 1 50 30 1 6 2 10 3 20 4   Sample Output The minimum amount of money in the piggy-bank is 60. The minimum amount of money in the piggy-bank is 100. This is impossible.   题目大意就是,存钱罐空时重E,满时重F;有N种硬币,价值为P,重量为W;求是否满足恰好装满时有最小价值的储蓄; 代码: #include<stdio.h> #include<string.h> #include<algorithm> #define INF 10000000 using namespace std; int main() { int t,e,f,n,p[1000],w[1000],i,j,wight,s[100000]; scanf("%d",&t); while(t--) { scanf("%d%d",&e,&f); scanf("%d",&n); for(i=0; i<n; i++) { scanf("%d%d",&p[i],&w[i]); } wight=f-e; for(i=1; i<=wight; i++) s[i]=INF; s[0]=0; for(i=0; i<n; i++) for(j=w[i]; j<=wight; j++) { s[j]=min(s[j],s[j-w[i]]+p[i]); } if(s[wight]==INF) printf("This is impossible.\n"); else printf("The minimum amount of money in the piggy-bank is %d.\n",s[wight]); } return 0; } 因为要找最小的,所以给s数组附上很大的值;将f[0]=0,其他值,如果是求背包最大,则设置为-inf(无穷小),如果是求背包最小,则设置为inf。唯有f[0+某商品]才真正是背包容量,其他的无穷大和无穷小的状态都是虚的。针对本题来说,如果最终f[max]仍旧是无穷大,那说明根本凑不齐恰好装满这种状态。



关键词: D - 完全背包