# 55. Jump Game / Medium

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.

## Constraints:

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

# Solution 1: DP (Top-Down)

## 思路

dp[i] 代表是否能到達第i個位置，從 index 0，也就是起點開始，每一個位置都更新一輪 dp[]。最差時間複雜度 O(N^2) ，效能很差，但很直覺。

## 效能

### Complexity

• Time Complexity: O(N^2)
• Space Complexity: O(N)

### LeetCode Result

• Runtime: 1744 ms
• Memory Usage: 48.2 MB

# Solution 2: DP (Bottom-Up)

## 效能

### Complexity

• Time Complexity: O(N)
• Space Complexity: O(N)

### LeetCode Result

• Runtime: 60 ms
• Memory Usage: 48.6 MB

# Solution 3: Linear Check

## 效能

### Complexity

• Time Complexity: O(N)
• Space Complexity: O(1)

### LeetCode Result

• Runtime: 48 ms
• Memory Usage: 48.4 MB

# Solution 4: Greedy

## 效能

### Complexity

• Time Complexity: O(N)
• Space Complexity: O(1)

### LeetCode Result

• Runtime: 48 ms
• Memory Usage: 48.2 MB