Leetcode #1340: Jump Game V
In this guide, we solve Leetcode #1340 Jump Game V in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given an array of integers arr and an integer d. In one step you can jump from index i to index: i + x where: i + x < arr.length and 0 < x <= d.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Array, Dynamic Programming, Sorting
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: arr = [6,4,14,6,8,13,9,7,10,6,12], d = 2
Output: 4
Explanation: You can start at index 10. You can jump 10 --> 8 --> 6 --> 7 as shown.
Note that if you start at index 6 you can only jump to index 7. You cannot jump to index 5 because 13 > 9. You cannot jump to index 4 because index 5 is between index 4 and 6 and 13 > 9.
Similarly You cannot jump from index 3 to index 2 or index 1.
Python Solution
class Solution:
def maxJumps(self, arr: List[int], d: int) -> int:
def dfs(i):
ans = 1
for j in range(i - 1, -1, -1):
if i - j > d or arr[j] >= arr[i]:
break
ans = max(ans, 1 + dfs(j))
for j in range(i + 1, n):
if j - i > d or arr[j] >= arr[i]:
break
ans = max(ans, 1 + dfs(j))
return ans
n = len(arr)
return max(dfs(i) for i in range(n))
Complexity
The time complexity is O(n·m) (typical). The space complexity is O(n·m) or optimized.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.