Which algorithmic approach guarantees finding the minimum number of jumps efficiently?
easy🔍 Pattern Recognition Q11 of Q15
Greedy Algorithms - Jump Game II (Minimum Jumps)
You are given an array where each element represents the maximum jump length from that position. Your goal is to reach the last index in the minimum number of jumps. Which algorithmic approach guarantees finding the minimum number of jumps efficiently?
AA simple greedy approach that always jumps to the farthest reachable index from the current position.
BA breadth-first search (BFS) treating each index as a node and exploring all reachable indices level by level.
CA dynamic programming approach that computes the minimum jumps for each index by checking all previous indices.
DA depth-first search (DFS) exploring all possible jump sequences recursively and returning the minimum.
Step-by-Step Solution
Step 1: Understand problem as shortest path in graph
Each index can be seen as a node with edges to reachable indices. BFS explores nodes level by level, guaranteeing the shortest path (minimum jumps).
Step 2: Compare approaches
Greedy alone can fail on some inputs by making locally optimal but globally suboptimal jumps. DP is correct but less efficient. DFS is exponential time.
Final Answer:
Option B -> Option B
Quick Check:
BFS ensures minimum jumps by level order traversal [OK]
