[Solved] You are given a list of sticks with different lengths. You want to connect all sticks into one by repeatedly... Which algorithmic approach guarantees the minimum total cost to connect all sticks? | Greedy Algorithms

Greedy Algorithms - Minimum Cost to Connect Sticks

You are given a list of sticks with different lengths. You want to connect all sticks into one by repeatedly merging any two sticks, paying a cost equal to the sum of their lengths each time. Which algorithmic approach guarantees the minimum total cost to connect all sticks?

ADynamic Programming that tries all possible merge sequences to find the minimum cost

BGreedy algorithm using a min-heap to always merge the two shortest sticks first

CSorting the sticks once and merging them in sorted order from smallest to largest

DGreedy algorithm that merges the two longest sticks first to reduce future costs

Step-by-Step Solution

Solution:

Step 1: Understand the problem goal
The goal is to minimize the total cost of merging sticks, where each merge cost equals the sum of the two sticks merged.
Step 2: Identify the optimal strategy
Merging the two shortest sticks first at each step minimizes incremental cost and leads to the global minimum total cost. This is efficiently done using a min-heap.
Final Answer:
Option B -> Option B
Quick Check:
Min-heap merges shortest sticks first -> minimal total cost [OK]

Quick Trick: Always merge shortest sticks first for minimal cost [OK]

Common Mistakes:

MISTAKES

Merging longest sticks first thinking it reduces future costs
Sorting once and merging in order without reordering after merges
Assuming brute force is needed for minimal cost

Trap Explanation:

PITFALL

Sorting once and merging in order looks plausible but fails because merges change stick lengths dynamically, requiring a data structure like a heap.

Interviewer Note:

CONTEXT

Tests if candidate recognizes the greedy pattern and why min-heap is optimal.

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More Greedy Algorithms Quizzes

Which algorithmic approach guarantees the minimum total cost to connect all sticks?

Step 1: Understand the problem goal

Step 2: Identify the optimal strategy

Final Answer:

Quick Check:

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