<p>You are given an array <code>nums</code>. You can rotate it by a non-negative integer <code>k</code> so that the array becomes <code>[nums[k], nums[k + 1], ... nums[nums.length - 1], nums[0], nums[1], ..., nums[k-1]]</code>. Afterward, any entries that are less than or equal to their index are worth one point.</p>

<ul>
	<li>For example, if we have <code>nums = [2,4,1,3,0]</code>, and we rotate by <code>k = 2</code>, it becomes <code>[1,3,0,2,4]</code>. This is worth <code>3</code> points because <code>1 &gt; 0</code> [no points], <code>3 &gt; 1</code> [no points], <code>0 &lt;= 2</code> [one point], <code>2 &lt;= 3</code> [one point], <code>4 &lt;= 4</code> [one point].</li>
</ul>

<p>Return <em>the rotation index </em><code>k</code><em> that corresponds to the highest score we can achieve if we rotated </em><code>nums</code><em> by it</em>. If there are multiple answers, return the smallest such index <code>k</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [2,3,1,4,0]
<strong>Output:</strong> 3
<strong>Explanation:</strong> Scores for each k are listed below: 
k = 0,  nums = [2,3,1,4,0],    score 2
k = 1,  nums = [3,1,4,0,2],    score 3
k = 2,  nums = [1,4,0,2,3],    score 3
k = 3,  nums = [4,0,2,3,1],    score 4
k = 4,  nums = [0,2,3,1,4],    score 3
So we should choose k = 3, which has the highest score.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,3,0,2,4]
<strong>Output:</strong> 0
<strong>Explanation:</strong> nums will always have 3 points no matter how it shifts.
So we will choose the smallest k, which is 0.
</pre>

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

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

class Solution {
public:
    int bestRotation(vector<int>& nums) {
        // subtract every element by the index to find how far above or below they are
        // each shift guaruntees that the 
        if (nums.size() == 1) {
            return 0;
        }
        
        std::map<int, int> point_deltas;

        for (int i = 0; i < nums.size(); ++i) {
            int t = i - nums[i] + 1;
            t += (t < 0) ? nums.size() : 0;
            t -= (t >= nums.size()) ? nums.size() : 0;
            --point_deltas[t];
        }
        int max = 0;
        for (int i = 1; i < nums.size(); ++i) {
            point_deltas[i] += point_deltas[i - 1] + 1;
            cout << point_deltas[i - 1] << endl;
            if (point_deltas[i] > point_deltas[max]) {
                max = i;
            }
        }

        return max;
    }
};

// 0 is an exception
// we always gain at least one point on rotation due to a value on the furthest left being brought to the right where there is a guaruntee it will score a point
// we always lose a point when an entry is rotated beyond its destination. It

// for every number of rotations enter the amount of points lost
// for every number of rotations enter the number of points gained
// 
127600