coin change program using dynamic programming knapsack with repetitions allowed

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.