Knapsack code - not working for some cases - c

Question

My code is as the following:
#include<stdio.h>
int max(int a,int b)
{
return a>b?a:b;
}
int Knapsack(int items,int weight[],int value[],int maxWeight)
{
int dp[items+1][maxWeight+1];
/* dp[i][w] represents maximum value that can be attained if the maximum weight is w and
items are chosen from 1...i */
/* dp[0][w] = 0 for all w because we have chosen 0 items */
int iter,w;
for(iter=0;iter<=maxWeight;iter++)
{
dp[0][iter]=0;
}
/* dp[i][0] = 0 for all w because maximum weight we can take is 0 */
for(iter=0;iter<=items;iter++)
{
dp[iter][0]=0;
}
for(iter=1;iter<=items;iter++)
{
for(w=0;w<=maxWeight;w=w+1)
{
dp[iter][w] = dp[iter-1][w]; /* If I do not take this item */
if(w-weight[iter] >=0)
{
/* suppose if I take this item */
dp[iter][w] = max( (dp[iter][w]) , (dp[iter-1][w-weight[iter]])+value[iter]);
}
}
}
return dp[items][maxWeight];
}
int main()
{
int items=9;
int weight[/*items+1*/10]={60, 10, 20, 20, 20, 20, 10, 10, 10};
int value[/*items+1*/10]={73, 81, 86, 72, 90, 77, 85, 70, 87};
int iter;
int i;
int maxWeight=180;
for (i=0;i<10;i++){
value[i] = value[i]*weight[i];
}
printf("Max value attained can be %d\n",Knapsack(items,weight,value,maxWeight));
}
My knapsack code is working when
items=12;
int weight[/*items+1*/13]={60, 20, 20, 20, 10, 20, 10, 10, 10, 20, 20, 10};
int value[/*items+1*/13]={48, 77, 46, 82, 85, 43, 49, 73, 65, 48, 47, 51};
where it returned the correct output 7820.
But it doesn't returned the correct output when
items=9;
int weight[/*items+1*/10]={60, 10, 20, 20, 20, 20, 10, 10, 10};
int value[/*items+1*/10]={73, 81, 86, 72, 90, 77, 85, 70, 87};
where it returned the output 9730, the correct output should be 14110.
From observation, the program somehow skipped the 1st value (weight=60, value =73).
I have checked the code several times, but I just cant find what's wrong.
Can someone explain to me why? Thank you!

Answer 1

In your code, you are trying to access out of bounds index for weight and value array. When iter reaches value 9, weight[iter] and value[iter] becomes out of bounds index. I guess, in C you simply get some garbage value for out of index access, but in Java, that will throw an exception. Change the code in your inner for loop to:
dp[iter][w] = dp[iter-1][w]; /* If I do not take this item */
if(w-weight[iter - 1] >=0)
{
/* suppose if I take this item */
dp[iter][w] = maximum( (dp[iter][w]) , (dp[iter-1][w-weight[iter - 1]])+value[iter - 1]);
}
and it will work fine.

Answer 2

int weight[/*items+1*/10]={60, 10, 20, 20, 20, 20, 10, 10, 10};
int value[/*items+1*/10]={73, 81, 86, 72, 90, 77, 85, 70, 87};
Your arrays are of length 10, but you are filling only 9 entries. Hence the last entry gets filled to 0. How to initialize all members of an array to the same value?
int weight[/*items+1*/10]={60, 10, 20, 20, 20, 20, 10, 10, 10, 0};
int value[/*items+1*/10]={73, 81, 86, 72, 90, 77, 85, 70, 87, 0};
But you are trying to access the indices (1 to 9) in your algorithm.
Instead try filling all entries:
int weight[/*items+1*/10]={0, 60, 10, 20, 20, 20, 20, 10, 10, 10};
int value[/*items+1*/10]={0, 73, 81, 86, 72, 90, 77, 85, 70, 87};
EDIT:
The first case gives correct output since in that case the first entry is not included in the optimal solution.