LeetCode 45: Jump Game II — Python Solution

Solve LeetCode 45: Jump Game II in Python with a greedy BFS frontier 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

Scan the current jump range while computing the farthest next range. Crossing the current range boundary commits exactly one additional jump.

Algorithm

1. Scan the current jump range while computing the farthest next range. Crossing the current range boundary commits exactly one additional jump.
2. Maintain this invariant: The current boundary contains exactly the indices reachable with the current jump count.
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 jump(self, nums):
        jumps = end = farthest = 0
        for i in range(len(nums) - 1):
            farthest = max(farthest, i + nums[i])
            if i == end:
                jumps += 1
                end = farthest
        return jumps

Why this is correct

The proof follows the maintained state: The current boundary contains exactly the indices reachable with the current jump count. 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

The input guarantees reachability; a one-element input needs zero jumps.

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.

Browse the searchable 100 LeetCode Python Solutions hub. Previous: 55. Jump Game · Next: 274. H-Index