# 1306. Jump Game III

Medium
Given an array of non-negative integers `arr`, you are initially positioned at `start` index of the array. When you are at index `i`, you can jump to `i + arr[i]` or `i - arr[i]`, check if you can reach to any index with value 0.
Notice that you can not jump outside of the array at any time.
Example 1:
Input: arr = [4,2,3,0,3,1,2], start = 5
Output:
true
Explanation:
All possible ways to reach at index 3 with value 0 are:
index 5 -> index 4 -> index 1 -> index 3
index 5 -> index 6 -> index 4 -> index 1 -> index 3
Example 2:
Input: arr = [4,2,3,0,3,1,2], start = 0
Output:
true
Explanation:
One possible way to reach at index 3 with value 0 is:
index 0 -> index 4 -> index 1 -> index 3
Example 3:
Input: arr = [3,0,2,1,2], start = 2
Output:
false
Explanation:
There is no way to reach at index 1 with value 0.
Constraints:
• `1 <= arr.length <= 5 * 104`
• `0 <= arr[i] < arr.length`
• `0 <= start < arr.length`

### 解題

DFS
Runtime: 68 ms, faster than 75.44%
Memory Usage: 11.1 MB, less than 36.84%
func canReach(arr []int, start int) bool {
record := make([]bool, len(arr))
var jump func(int) bool
jump = func(index int) bool {
if index < 0 || index >= len(arr) {
return false
}
if record[index] {
return false
}
if arr[index] == 0 {
return true
}
record[index] = true
return jump(index + arr[index]) || jump(index - arr[index])
}
return jump(start)
}