Which of the following approaches correctly determines if you can reach the last index from the first index under this new constraint?
hard🎤 Interviewer Follow-up Q15 of Q15
Greedy Algorithms - Jump Game (Can Reach End?)
Suppose the Jump Game problem is modified so that you can jump backward as well as forward (i.e., jumps can be negative or positive). Which of the following approaches correctly determines if you can reach the last index from the first index under this new constraint?
AUse the original greedy approach tracking max reachable index, ignoring backward jumps
BUse a breadth-first search (BFS) or graph traversal to explore all reachable indices including backward jumps
CUse dynamic programming with memoization to recursively check reachability from each index
DSort the array and apply binary search to find reachable indices efficiently
Step-by-Step Solution
Solution:
Step 1: Understand the impact of backward jumps
Backward jumps mean the problem is no longer monotonic; maxReach tracking fails as reachable indices can decrease.
Step 2: Identify suitable approach
BFS or graph traversal explores all reachable indices in any direction, correctly handling negative jumps.
Step 3: Explain why other options fail
Greedy fails due to backward jumps; DP recursion is possible but less efficient; sorting is irrelevant.
Final Answer:
Option B -> Option B
Quick Check:
BFS explores all reachable nodes regardless of jump direction [OK]
Quick Trick:Backward jumps break greedy; BFS needed to explore all reachable indices [OK]
Common Mistakes:
MISTAKES
Trying to apply greedy despite backward jumps
Assuming sorting helps reachability
Trap Explanation:
PITFALL
Greedy looks simpler but fails with backward jumps; BFS is the robust solution.
Interviewer Note:
CONTEXT
Tests if candidate can adapt approach when problem constraints change significantly.
Master "Jump Game (Can Reach End?)" in Greedy Algorithms
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