coin change program using dynamic programming knapsack with repetitions allowed - c

Question

I have written the below code to implement the coin change problem: you are given n types of coin denominations of values v(1) < v(2) < ... < v(n) (all integers). Assume v(1) = 1, so you can always make change for any amount of money C. Give an algorithm which makes change for an amount of money C with as few coins as possible.
I modified the knapsack with repetitions allowed problem by setting all the values of each coin to -1. The program should then return the maximum value such that the weight of the required coins(denominations) add up to the size variable(required change). I cannot figure where i have went wrong. I should be getting an answer of -2 implying i need two coins but i'm getting -1 as the answer. Code:
#include <stdio.h>
#define max(a,b) (a > b ? a : b)
int matrix[100][100] = {0};
int knapsack(int index, int size, int weights[],int values[]){
int take,dontTake;
take = dontTake = 0;
if (matrix[index][size]!=0)
return matrix[index][size];
if (index==0){
if (weights[0]<=size){
matrix[index][size] = values[0];
return values[0];
}
else{
matrix[index][size] = 0;
return 0;
}
}
if (weights[index]<=size)
take = values[index] + knapsack(index, size-weights[index], weights, values); //knapsack(index) and not //knapsack(index-1)
dontTake = knapsack(index-1, size, weights, values);
matrix[index][size] = max (take, dontTake);
return matrix[index][size];
}
int main(){
int nItems = 4;
int knapsackSize = 10;
int weights[4] = {5,4,6,3};
int values[4] = {-1,-1,-1,-1};
printf("Max value = %dn",knapsack(nItems-1,knapsackSize,weights,values));
return 0;
}
Where am i going wrong and how can i fix this?

Answer 1

It is simple because, -1 > -2 and you are taking the maximum between the 2 choices at every level.
EDIT : I have impelmented a solution in which values are taken as positive, also i have made minor changes to the code, if there is something that you do not understand feel free to ask.
#include <stdio.h>
#define min(a,b) (a < b ? a : b)
#define INF 10000000
int matrix[100][100] = {0};
int knapsack(int index, int size, int weights[],int values[]){
int take = INF;
if (index == -1){
if(size == 0) return 0;
else return INF;
}
if (matrix[index][size]!=-1)
return matrix[index][size];
for(int itemcount = 0;(itemcount * weights[index]) <= size;itemcount++){
if ((weights[index] * itemcount) <= size)
take = min(take, (values[index] * itemcount) + knapsack(index - 1, size - (itemcount * weights[index]), weights, values)); //knapsack(index) and not //knapsack(index-1)
}
matrix[index][size] = take;
return matrix[index][size];
}
int main(){
int nItems = 4;
int knapsackSize = 10;
int weights[4] = {5,4,6,3};
int values[4] = {1,1,1,1};
for(int i = 0;i < 100;i++) for(int j = 0;j < 100;j++) matrix[i][j] = -1;
printf("Min value = %d\n",knapsack(nItems-1,knapsackSize,weights,values));
return 0;
}
Link to solution on Ideone : http://ideone.com/TNycZo
Here i have taken infinity as a large integer, to find minimum values, if the answer is infinity that means it is not possible to create such a denomination.