What is the optimal time complexity of solving Minimum Jumps?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Minimum Jumps?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Minimum Jumps?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Minimum Jumps?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Competitive ProgrammingEasy

Minimum Jumps

Learn how to solve the 'Minimum Jumps' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function min_jumps(arr) that finds the minimum number of jumps to reach the last index of arr starting from index 0. Each element in the array represents the maximum jump length from that position. If it is impossible to reach the last index, return -1.

Constraints

•1 <= len(arr) <= 10^4
•0 <= arr[i] <= 10^4

Examples

Example 1

Input

min_jumps([1, 3, 5, 8, 9, 2, 6, 7, 6, 8, 9])

Output

Explanation

Jump from index 0 to 1 (value 3), then jump to index 4 (value 9), and then jump to the last index.

Example 2

Input

min_jumps([1, 1, 1, 1, 1])

Output

Explanation

Jump one by one from start to end, requiring 4 jumps.

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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