Solve the 0/1 Knapsack problem using dynamic programming to maximize the total value of items without exceeding the weight capacity.
Statement 1: All dogs are mammals. Statement 2: Some mammals are cats. Conclusion: Some cats are dogs. True or False? Answer: False, Dogs are not cats
Statement 1: All dogs are mammals.
Statement 2: Some mammals are cats.
Conclusion: Some cats are dogs. True or False?
Answer:
False, Dogs are not cats
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Defination: Maximize total value of items without exceeding weight limit using given weights and values. def knapsack(values,weights,capacity): n=len(values) dp=[[0 for _ in range(capacity+1)] for _ in range(n+1)] #Fill the dp array for i in range(1,n+1): for w in range(1,capacity+1): if weights[i-1Read more
Defination: Maximize total value of items without exceeding weight limit using given weights and values.
Explanation:
dpwheredp[i][w]represents the maximum value that can be obtained using the firstiitems with a total weight not exceedingw.i(from 1 ton), and for each weightw(from 1 tocapacity):i(weights[i-1]) is less than or equal tow, we have two choices:i: The value isdp[i-1][w].i: The value isdp[i-1][w-weights[i-1]] + values[i-1].iis greater thanw, we exclude the itemi.dp[n][capacity].