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Explore Offerings by SCALER # 0-1 Knapsack

Problem Description

Given two integer arrays A and B of size N each which represent values and weights associated with N items respectively.

Also given an integer C which represents knapsack capacity.

Find out the maximum value subset of A such that sum of the weights of this subset is smaller than or equal to C.

NOTE:

• You cannot break an item, either pick the complete item, or don’t pick it (0-1 property).

Problem Constraints

1 <= N <= 103

1 <= C <= 103

1 <= A[i], B[i] <= 103

Input Format

First argument is an integer array A of size N denoting the values on N items.

Second argument is an integer array B of size N denoting the weights on N items.

Third argument is an integer C denoting the knapsack capacity.

Output Format

Return a single integer denoting the maximum value subset of A such that sum of the weights of this subset is smaller than or equal to C.

Example Input

Input 1:

``` A = [60, 100, 120]
B = [10, 20, 30]
C = 50
```

Input 2:

``` A = [10, 20, 30, 40]
B = [12, 13, 15, 19]
C = 10
```

Example Output

Output 1:

``` 220
```

Output 2:

``` 0
```

Example Explanation

Explanation 1:

``` Taking items with weight 20 and 30 will give us the maximum value i.e 100 + 120 = 220
```

Explanation 2:

``` Knapsack capacity is 10 but each item has weight greater than 10 so no items can be considered in the knapsack therefore answer is 0.
```

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details. Hints
• Hint 1
• Solution Approach
• Complete Solution

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