# Question

Given an array of non-negative integers, you are initially positioned at the first index of the array.

Each element in the array represents your maximum jump length at that position.

Determine if you are able to reach the last index.

Example 1:

Input: [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: [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.


# DP Solution

Track whether a position could reach the last index.

class Solution:
def canJump(self, nums):
"""
:type nums: List[int]
:rtype: bool
"""
if len(nums) <= 1:
return True

dp = [False for _ in range(len(nums))]
dp[-1] = True

for i in range(len(nums) - 2, -1, -1):
k = nums[i]
for step in range(1, k + 1):
if i + step < len(nums) and dp[i + step] == True:
dp[i] = True
break

return dp



# Greedy

Track the leftmost index that can reach the last index.

class Solution:
def canJump(self, nums):
"""
:type nums: List[int]
:rtype: bool
"""
length = len(nums)
if length <= 1:
return True

good_pos = length - 1

for i in range(length - 2, -1, -1):
if nums[i] + i >= good_pos:
good_pos = i

return good_pos == 0