<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. You have to partition the array into one or more <strong>contiguous</strong> subarrays.</p>

<p>We call a partition of the array <strong>valid</strong> if each of the obtained subarrays satisfies <strong>one</strong> of the following conditions:</p>

<ol>
	<li>The subarray consists of <strong>exactly</strong> <code>2,</code> equal elements. For example, the subarray <code>[2,2]</code> is good.</li>
	<li>The subarray consists of <strong>exactly</strong> <code>3,</code> equal elements. For example, the subarray <code>[4,4,4]</code> is good.</li>
	<li>The subarray consists of <strong>exactly</strong> <code>3</code> consecutive increasing elements, that is, the difference between adjacent elements is <code>1</code>. For example, the subarray <code>[3,4,5]</code> is good, but the subarray <code>[1,3,5]</code> is not.</li>
</ol>

<p>Return <code>true</code><em> if the array has <strong>at least</strong> one valid partition</em>. Otherwise, return <code>false</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [4,4,4,5,6]
<strong>Output:</strong> true
<strong>Explanation:</strong> The array can be partitioned into the subarrays [4,4] and [4,5,6].
This partition is valid, so we return true.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,1,1,2]
<strong>Output:</strong> false
<strong>Explanation:</strong> There is no valid partition for this array.
</pre>

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

<ul>
	<li><code>2 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>
</ul>

class Solution {
public:
// [1,1,1,2,3,4,1]
//  1 1 1 , 2 3 4 , 1 ->false -> 1 bach gaya
    bool check(int ind, vector<int>&nums, vector<int>&dp){
        // base case 
        if(ind<0) return true; // empty array is always valid
        if(ind == 0) return false; // a single element is not valid;
        if(dp[ind] != -1) return dp[ind];

        bool result = false;

        // check for two
        if(ind>=1 && nums[ind] == nums[ind-1]){
            result = check(ind-2, nums, dp);
        }

        //check for three
        if(!result && ind>=2 && (nums[ind] == nums[ind-1]) && (nums[ind-1] == nums[ind-2])){
            result = check(ind-3, nums, dp);
        }

        //check for three consecutive
        if(!result && ind>=2 && (nums[ind] == nums[ind-1]+1) && (nums[ind-1] == nums[ind-2]+1)){
            result = check(ind-3, nums, dp);
        }

        return dp[ind] = result;
    }
    bool validPartition(vector<int>& nums) {
        // 2 equal
        // 3equal
        // 3 consecutive

        int n = nums.size();

        vector<int>dp(n,-1);

        return check(n-1, nums, dp);
    }
};
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