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Determine reachability and minimum jumps
Problem Statement
Given an array of non-negative integers nums of length n, where nums[i] represents the maximum number of steps you can move forward from index i:
- Reachability: Determine whether it's possible to reach the last index (
n-1) starting from the first index (0). - Minimum Jumps: If the last index is reachable, compute the minimum number of jumps required to reach index
n-1.
Requirements
- Performance Target: Aim for an
O(n)time complexity andO(1)extra space complexity for the minimum jumps calculation, if possible. - Discussion: Explain your chosen algorithm, provide a proof of its correctness, analyze its time and space complexity, and discuss various edge cases. These include scenarios where zeros block progress, arrays of length
n=1, very large jump values, and cases where the last index is inherently unreachable.
AI interview prep
Core dilemma
Identifying the optimal greedy strategy to minimize jumps while ensuring reachability, contrasting its efficiency and correctness proof against less optimal dynamic programming or BFS approaches.
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Determine reachability and minimum jumps
Problem Statement
Given an array of non-negative integers nums of length n, where nums[i] represents the maximum number of steps you can move forward from index i:
- Reachability: Determine whether it's possible to reach the last index (
n-1) starting from the first index (0). - Minimum Jumps: If the last index is reachable, compute the minimum number of jumps required to reach index
n-1.
Requirements
- Performance Target: Aim for an
O(n)time complexity andO(1)extra space complexity for the minimum jumps calculation, if possible. - Discussion: Explain your chosen algorithm, provide a proof of its correctness, analyze its time and space complexity, and discuss various edge cases. These include scenarios where zeros block progress, arrays of length
n=1, very large jump values, and cases where the last index is inherently unreachable.