Which algorithmic approach guarantees an optimal solution for this problem?
easy🔍 Pattern Recognition Q11 of Q15
Greedy Algorithms - Maximum Units on a Truck
You have different types of boxes, each with a number of boxes and units per box. You want to load a truck with a limited capacity to maximize total units. Which algorithmic approach guarantees an optimal solution for this problem?
ADivide and conquer by splitting box types and merging results
BGreedy algorithm sorting box types by units per box in descending order and picking boxes until the truck is full
CBreadth-first search exploring all possible box selections up to truck capacity
DDynamic programming considering all combinations of boxes and capacities
Step-by-Step Solution
Solution:
Step 1: Understand problem constraints
The problem requires maximizing units loaded on a truck with limited capacity by selecting boxes with different units per box.
Step 2: Identify optimal approach
Since the problem involves discrete box counts and a capacity constraint, the greedy approach does not always guarantee an optimal solution. Dynamic programming considering all combinations ensures the optimal solution by exploring all feasible selections.
Final Answer:
Option D -> Option D
Quick Check:
DP guarantees optimality for knapsack-like problems with discrete items [OK]
Quick Trick:Use DP for discrete knapsack problems to guarantee optimality [OK]
Common Mistakes:
MISTAKES
Assuming greedy always works
Trying BFS which is inefficient
Ignoring capacity constraints
Trap Explanation:
PITFALL
Greedy is optimal only if fractional boxes are allowed; with discrete boxes, DP is needed.
Interviewer Note:
CONTEXT
Tests if candidate knows when greedy is optimal versus when DP is required.
Master "Maximum Units on a Truck" in Greedy Algorithms
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