1306. Jump Game III
Description
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 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
Solutions
Solution 1: BFS
We can use BFS to determine whether we can reach the index with a value of $0$.
Define a queue $q$ to store the currently reachable indices. Initially, enqueue the $start$ index.
When the queue is not empty, take out the front index $i$ of the queue. If $arr[i] = 0$, return true
. Otherwise, mark the index $i$ as visited. If $i + arr[i]$ and $i - arr[i]$ are within the array range and have not been visited, enqueue them and continue searching.
Finally, if the queue is empty, it means that we cannot reach the index with a value of $0$, so return false
.
The time complexity is $O(n)$, and the space complexity is $O(n)$. Where $n$ is the length of the array.
1 2 3 4 5 6 7 8 9 10 11 12 13 |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 |
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 |
|