Hdu1114 piggy-bank [full backpack]

Piggy-bank Time Limit: 2000/1000 MS (Java/others) memory limit: 65536/32768 K (Java/Others) Total submission (s): 11149 accepted submission (s): 5632

Problem descriptionbefore 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 shoshould 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!
 
Inputthe 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 varous 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.
 
Outputprint 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

310 11021 130 5010 11021 150 301 6210 320 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.

The weight of an empty piggy bank and the weight of a full piggy bank are given. Given the value and weight of some coin types, each coin has countless. Q: How can I put a coin in a piggy bank to minimize the total value and the total weight is equal to the full piggy bank. Question: complete backpack entry question. The state transition equation is DP [I] [J] = min (DP [I-1] [J-K * W [I]) 0 <= k <= totalweight/W [I]. Like the 01 backpack, the full backpack DP array can also be compressed into a one-dimensional array. However, the inner layer loops in order, while the 01 backpack is in reverse order. In addition, this problem has a trap when initializing the DP array: For an array defined outside the function, if memset (DP + 1,-1, sizeof (DP + 1) is used for it )); then, only one element is initialized to-1, and all other elements are 0. however, if memset (DP,-1, sizeof (DP) is used, all arrays can be initialized to-1.

#include <stdio.h>#include <string.h>int dp[10002];int main(){    int totalWeight, weight, val, n, t, i, j;    scanf("%d", &t);    while(t--){        scanf("%d%d", &weight, &totalWeight);        totalWeight -= weight;        scanf("%d", &n);        memset(dp + 1, -1, sizeof(int) * 10001);         for(i = 1; i <= n; ++i){            scanf("%d%d", &val, &weight);            for(j = weight; j <= totalWeight; ++j){                if(dp[j - weight] != -1){                    if(dp[j] == -1 || dp[j] > dp[j - weight] + val)                        dp[j] = dp[j - weight] + val;                }            }        }        if(dp[totalWeight] == -1) printf("This is impossible.\n");        else printf("The minimum amount of money in thepiggy-bank is %d.\n", dp[totalWeight]);    }    return 0;}

Hdu1114 piggy-bank [full backpack]