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 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 * 10^4
• 0 <= arr[i] < arr.length
• 0 <= start < arr.length

Solution(javascript)

/**
 * @param {number[]} arr
 * @param {number} start
 * @return {boolean}
 */
const canReach = function (arr, start) {
  const visited = []
  const aux = (index) => {
    if (visited[index] !== undefined) {
      return visited[index]
    }
    if (index < 0 || index > arr.length - 1) {
      visited[index] = false
      return false
    }
    if (arr[index] === 0) {
      visited[index] = true
      return visited[index]
    }
    visited[index] = false
    visited[index] = aux(index + arr[index]) || aux(index - arr[index])
    return visited[index]
  }
  return aux(start)
}