[Solved] You are given an array where each element represents the maximum jump length from that position.... Which algorithmic approach guarantees an optimal solution with linear time complexity? | Greedy Algorithms

Greedy Algorithms - Jump Game (Can Reach End?)

You are given an array where each element represents the maximum jump length from that position. You need to determine if you can reach the last index starting from the first index. Which algorithmic approach guarantees an optimal solution with linear time complexity?

ADynamic Programming with bottom-up tabulation to check reachability for each index

BBreadth-first search using a queue to explore reachable indices level by level

CDepth-first search exploring all possible jump paths recursively without memoization

DGreedy algorithm tracking the maximum reachable index while iterating through the array

Step-by-Step Solution

Solution:

Step 1: Understand problem constraints
The problem requires checking if the last index is reachable from the first index using jumps defined by array values.
Step 2: Identify optimal approach
Greedy approach efficiently tracks the furthest reachable index in one pass, guaranteeing O(n) time complexity, unlike exhaustive search or DP which are slower.
Final Answer:
Option D -> Option D
Quick Check:
Greedy approach is linear and optimal for this problem [OK]

Quick Trick: Greedy tracks max reachable index in one pass [OK]

Common Mistakes:

MISTAKES

Confusing DP with greedy, thinking recursion is needed

Trap Explanation:

PITFALL

DP or BFS seem plausible but are less efficient; greedy is optimal and simpler.

Interviewer Note:

CONTEXT

Tests if candidate recognizes the pattern and optimal approach under pressure.

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More Greedy Algorithms Quizzes

Which algorithmic approach guarantees an optimal solution with linear time complexity?

Step 1: Understand problem constraints

Step 2: Identify optimal approach

Final Answer:

Quick Check:

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