<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:
    int candy(vector<int>& ratings) {
        vector<int> ans = {1};
        for (int i = 1; i < ratings.size(); i++) {
            if (ratings[i] > ratings[i-1]) {
                ans.push_back(ans[i-1] + 1);
            } else {
                ans.push_back(1);
            }
        }
        for (int i = ratings.size()-2; i >= 0; i--) {
            if (ratings[i] > ratings[i+1] && ans[i] <= ans[i+1]) {
                ans[i] = ans[i+1] + 1;
            }
        }
        return accumulate(ans.begin(), ans.end(), 0);
    }
};
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