55-Jump Game

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题意

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: 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.

Constraints:

• 1 <= nums.length <= 3 * 10^4
• 0 <= nums[i][j] <= 10^5

思路

• 贪心算法
• 不考虑最终能不能走到终点
• 只考虑局部最优，当前index能不能走到：前面index能走的最大距离max能不能接上当前i

class Solution(object):
    def canJump(self, nums):
        """
        :type nums: List[int]
        :rtype: bool
        """
        # 
        
        max_step = 0
        for i in range(len(nums)):
            if max_step < i: # 断开了，接不上
                return False
            
            # 更新max_step
            max_step =  max(i + nums[i], max_step)
            
        return True

分析:

• Time: O(n)
• Space: O(1)