LeetCode 55: Jump Game — Python Solution

Solve LeetCode 55: Jump Game in Python with a greedy reachability approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Maintain the farthest reachable index. If the scan reaches an index beyond that frontier, progress is impossible; otherwise extend the frontier.

Algorithm

1. Maintain the farthest reachable index. If the scan reaches an index beyond that frontier, progress is impossible; otherwise extend the frontier.
2. Maintain this invariant: Every index at or before farthest is reachable from the start.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def canJump(self, nums):
        farthest = 0
        for i, jump in enumerate(nums):
            if i > farthest:
                return False
            farthest = max(farthest, i + jump)
        return True

Why this is correct

The proof follows the maintained state: Every index at or before farthest is reachable from the start. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(n) time and O(1) extra space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

A one-element array succeeds; zeros matter only when they stop the frontier.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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