# 55. Jump Game (Medium)

https://leetcode.com/problems/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.
```

## Solutions

``````class Solution {
public boolean canJump(int[] nums) {
if (nums == null) {
return false;
}

int len = nums.length;
if (len == 1) {
return true;
}

boolean[] possible = new boolean[len];
Arrays.fill(possible, false);

possible[len - 1] = true;

// Scan from the tail to the head and keep the possibility for each slot whether
// it is able to reach the last index or not
for (int i = len - 2; i >= 0; i--) {

// j can move within the range [i, i + nums[i]]
// j cannot overstep the boundary of give array

for (int j = i; j < len && j <= i + nums[i]; j++) {
// if j can reach the last index, i can walk through j to reach the last index.
if (possible[j]) {
possible[i] = true;
break;
}
}
}

return possible;
}
}
``````