unbound_bottom.py

def unbound_knapsack(profits, weights, capacity):
    n = len(profits)
    
    # base case
    if capacity <= 0 or n == 0 or len(weights) != n:
        return 0
    
    dp = [[-1 for _ in range(capacity+1)] for _ in range(len(profits))]
    
    # initiaite the capacity = 0 columns
    for i in range(n):
        dp[i][0] = 0
        
    for i in range(n):
        for c in range(1, capacity+1):
            profit1, profit2 = 0, 0
            if weights[i] <= c:
                profit1 = profits[i] + dp[i][c - weights[i]]
            if i > 0:
                profif2 = dp[i-1][c]
            
            dp[i][c] = max(profit1, profit2)
    return dp[-1][-1]