<p>You are given an integer array <code>nums</code>. You are initially positioned at the array&#39;s <strong>first index</strong>, and each element in the array represents your maximum jump length at that position.</p>

<p>Return <code>true</code><em> if you can reach the last index, or </em><code>false</code><em> otherwise</em>.</p>

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

<pre>
<strong>Input:</strong> nums = [2,3,1,1,4]
<strong>Output:</strong> true
<strong>Explanation:</strong> Jump 1 step from index 0 to 1, then 3 steps to the last index.
</pre>

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

<pre>
<strong>Input:</strong> nums = [3,2,1,0,4]
<strong>Output:</strong> false
<strong>Explanation:</strong> 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.
</pre>

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

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

class Solution {
public:
    bool solve(vector<int>& nums,int ind,int n,vector<bool>& dp)
    {
        if(ind==n-1) return dp[ind]= true;
        if(ind>=n) return false;

        if(dp[ind]) return true;

        int mxJump = nums[ind];
        for(int i=1;i<=mxJump;i++)
        {
            bool check = solve(nums,ind+i,n,dp);
            if(check) return dp[ind] = true;
        }
        return  false;    
    }
    bool canJump(vector<int>& nums) {
        // int n=nums.size();
        // int mx=*max_element(nums.begin(),nums.end());
        // vector<bool> dp(mx+n,false);
        // // return solve(nums,0,n,dp);
        // dp[n-1]=true;
        // for(int ind=n-2;ind>=0;ind--)
        // {
        //     int mxJump = nums[ind];
        //     for(int i=1;i<=mxJump;i++)
        //     {
        //         bool check = dp[ind+i];
        //         if(check) dp[ind] = true;
        //     }
              
        // }
        // return dp[0];

        //prefix sum
        int n=nums.size();
        if(n==1) return true;
        if(nums[0]==0) return false;
        vector<int> arr = nums;
        int mxElem=INT_MIN;
        for(int i=0;i<n-1;i++)
        {
            arr[i]=arr[i]+i;
            if(arr[i]>=n-1) return true;
            if(mxElem == arr[i] && nums[i]==0) return false;
            mxElem=max(mxElem , arr[i]);

        }
        return false;

    }
};
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