<p>There are <code>n</code> children standing in a line. Each child is assigned a rating value given in the integer array <code>ratings</code>.</p>

<p>You are giving candies to these children subjected to the following requirements:</p>

<ul>
	<li>Each child must have at least one candy.</li>
	<li>Children with a higher rating get more candies than their neighbors.</li>
</ul>

<p>Return <em>the minimum number of candies you need to have to distribute the candies to the children</em>.</p>

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

<pre>
<strong>Input:</strong> ratings = [1,0,2]
<strong>Output:</strong> 5
<strong>Explanation:</strong> You can allocate to the first, second and third child with 2, 1, 2 candies respectively.
</pre>

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

<pre>
<strong>Input:</strong> ratings = [1,2,2]
<strong>Output:</strong> 4
<strong>Explanation:</strong> You can allocate to the first, second and third child with 1, 2, 1 candies respectively.
The third child gets 1 candy because it satisfies the above two conditions.
</pre>

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

<ul>
	<li><code>n == ratings.length</code></li>
	<li><code>1 &lt;= n &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>0 &lt;= ratings[i] &lt;= 2 * 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    
    
    void calcCandies(vector<int>& ratings, vector<int> &candies, int crt, int min, int n) {
        if(crt == n - 1) {
            candies[crt] = min;
            return ;
        } 

        if(ratings[crt] == ratings[crt + 1]) {
            calcCandies(ratings, candies, crt + 1, 1, n);
            candies[crt] = min;
            return;
        }

        if(ratings[crt] > ratings[crt + 1]) {
            calcCandies(ratings, candies, crt + 1, 1, n);
            candies[crt] = max(candies[crt + 1] + 1, min);
        } else {
            candies[crt] = min;
            // if(ratings[crt] == ratings[crt + 1])
            //     min = 0;
            calcCandies(ratings, candies, crt + 1, min + 1, n);
        }
    }

    int candy(vector<int>& ratings) {
        int n = ratings.size();
        vector<int> candies(n, 0);
        int sum = 0;

        calcCandies(ratings, candies, 0, 1, n);

        for(int i = 0; i < n; i++) {
            sum += candies[i];
            // cout << candies[i] << " ";
        }
        // cout << endl;

        return sum;
    }
};
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