PIGBANK - Piggy-Bank

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!


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.


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:

10 110
1 1
30 50
10 110
1 1
50 30
1 6
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.

hide comments
dwij28: 2017-09-25 22:03:29

TLE in CPython and Accepted in PyPy. That's just bad. 1-D easy DP duh :)

rohit9934: 2017-09-03 10:50:46

It is a slight modification of unbounded knapsack, Just store min of price, int will go fine.

Mihir Saxena: 2017-08-30 08:02:03

Just unbounded knapsack!

amulyagaur: 2017-08-28 13:26:20

Actually its not related to knapsack in any way.... its a completely different concept :)

nessaa_05: 2017-08-06 15:34:12

seems like a unbounded knapsack problem to me

saurav52: 2017-07-25 00:41:33

AC in one go:)
1-D DP

Last edit: 2017-07-25 00:42:00
Darrell Plank: 2017-07-04 23:43:35

This is not unbounded knapsack which is solved when you have a total weight less than or equal to the capacity of the knapsack. This problem requires the weight to be exactly equal to the capacity. Also, unbounded knapsack asks to maximize value whereas this problem asks to minimize it. This is all very significantly different since asking for a minimum value while only requiring the weight to be <= capacity means the answer is always to pack zero items for a minimum of zero. Unbounded knapsack requires coin values to be positive so just negating them and asking for a maximum also fails. Integer programming or dynamic programming will work, but not unlimited knapsack without some significant modification.

namitp: 2017-07-04 15:20:14

Very Easy
AC in one Go..
Simple Knapsack...

code_aim: 2017-06-08 07:14:47

Unbounded Knapsack!!
AC in one go :-)

sagnik_66: 2017-05-31 17:32:34

Finally Solved after an hour! The feeling!! Needed 1 1-D array only :D

Added by:adrian
Time limit:5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Resource:ACM Central European Programming Contest, Prague 1999