<p>Given an array of non-negative integers <code>arr</code>, you are initially positioned at <code>start</code>&nbsp;index of the array. When you are at index <code>i</code>, you can jump&nbsp;to <code>i + arr[i]</code> or <code>i - arr[i]</code>, check if you can reach&nbsp;<strong>any</strong> index with value 0.</p>

<p>Notice that you can not jump outside of the array at any time.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> arr = [4,2,3,0,3,1,2], start = 5
<strong>Output:</strong> true
<strong>Explanation:</strong> 
All possible ways to reach at index 3 with value 0 are: 
index 5 -&gt; index 4 -&gt; index 1 -&gt; index 3 
index 5 -&gt; index 6 -&gt; index 4 -&gt; index 1 -&gt; index 3 
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> arr = [4,2,3,0,3,1,2], start = 0
<strong>Output:</strong> true 
<strong>Explanation: 
</strong>One possible way to reach at index 3 with value 0 is: 
index 0 -&gt; index 4 -&gt; index 1 -&gt; index 3
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> arr = [3,0,2,1,2], start = 2
<strong>Output:</strong> false
<strong>Explanation: </strong>There is no way to reach at index 1 with value 0.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= arr.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>0 &lt;= arr[i] &lt;&nbsp;arr.length</code></li>
	<li><code>0 &lt;= start &lt; arr.length</code></li>
</ul>

class Solution {
public:
    bool canReach(vector<int>& arr, int start) {
        int n = arr.size();
        bool flag = false;
        for(int i = 0; i < n; i++){
            if(arr[i] == 0){
                flag = true; break;
            }
        }
        if(flag == false) return false;

        if(arr[start] == 0) return true;

        vector<int> memo(n, -1);
        memo[start] = 0;
        return helper(arr, start, memo);
    }

    bool helper(vector<int>& arr, int now, vector<int>& memo){
        if(now < 0 || now > arr.size()) return false;
        if(arr[now] == 0){
            memo[now] = 1;
            return true;
        }
        bool f1 = false, f2 = false;
        int l = now - arr[now], r = now + arr[now];
        if(l >= 0 && memo[l] == -1){
            memo[l] = 0;
            f1 = helper(arr, l, memo);
        }
        if(f1 == false && r < arr.size() && memo[r] == -1){
            memo[r] = 0;
            f2 = helper(arr, r, memo);
        }
        memo[now] = f1 || f2;

        return memo[now];
    }
};
38790