55. Jump Game

Updated: 2023-03-04
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LeetCode problem

You are given an integer array nums. You are initially positioned at the array’s first index, and each element in the array represents your maximum jump length at that position.

Return true if you can reach the last index, or false otherwise.

Example 1:

Input: nums = [2,3,1,1,4]
Output: true
Explanation: Jump 1 step from index 0 to 1, then 3 steps to the last index.

Example 2:

Input: nums = [3,2,1,0,4]
Output: false
Explanation: You will always arrive at index 3 no matter what. Its maximum jump length is 0, which makes it impossible to reach the last index.

Approach 1:

Idea: go forward on each step and mark next cell if can achieve it.

class Solution:
    def canJump(self, nums: List[int]) -> bool:
        last_i = len(nums)
        if last_i == 1:
            return True
        nn = [0] * last_i
        nn[0] = nums[0]
        for i in range(last_i):
            el = nums[i]
            if el or nn[i+1]:
                for j in range(el):
                    nn[i+j+1] = el
                    if nn[last_i - 1]:
                        return True
                return False
        return False

Approach 2:

Going forwards. m tells the maximum index we can reach so far.

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

class Solution:
  def canJump(self, nums: List[int]) -> bool:
    i = 0
    m = 0
    while i < len(nums) and i <= m:
      m = max(m, i + nums[i])
      i += 1
    return i == len(nums)