# 55. Jump Game

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.
```

{% hint style="info" %}
用一個maxReach紀錄能抵達的最大值，然後掃描整個input array一遍，看看當前的index是否比maxReach大，如果maxReach到不了當前的index，則break。如果maxReach已經大於等於最後一個位置，那麼則傳回true。
{% endhint %}

```cpp
// Greedy
bool canJump(vector<int>& nums) { // time: O(n); space: O(1)
    int n = nums.size(), maxReach = 0;
    for (int i = 0; i < n; ++i) {
        if (i > maxReach || maxReach >= n - 1) break;
        maxReach = max(maxReach, i + nums[i]);
    }
    return maxReach >= n - 1;
}
```

```cpp
// Greedy
bool canJump(vector<int>& nums) { // time: O(n); space: O(1)
    int n = nums.size(), reach = 0, idx = 0;
    while (idx < n && idx <= reach) {
        reach = max(reach, idx + nums[idx]);
        if (reach >= n - 1) return true;
        ++idx;
    }
    return false;
}
```


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