## 题目描述：

LeetCode 798. Smallest Rotation with Highest Score

Given an array `A`, we may rotate it by a non-negative integer `K` so that the array becomes `A[K], A[K+1], A{K+2], ... A[A.length - 1], A[0], A[1], ..., A[K-1]`.  Afterward, any entries that are less than or equal to their index are worth 1 point.

For example, if we have `[2, 4, 1, 3, 0]`, and we rotate by `K = 2`, it becomes `[1, 3, 0, 2, 4]`.  This is worth 3 points because 1 > 0 [no points], 3 > 1 [no points], 0 <= 2 [one point], 2 <= 3 [one point], 4 <= 4 [one point].

Over all possible rotations, return the rotation index K that corresponds to the highest score we could receive.  If there are multiple answers, return the smallest such index K.

```Example 1:
Input: [2, 3, 1, 4, 0]
Output: 3
Explanation:
Scores for each K are listed below:
K = 0,  A = [2,3,1,4,0],    score 2
K = 1,  A = [3,1,4,0,2],    score 3
K = 2,  A = [1,4,0,2,3],    score 3
K = 3,  A = [4,0,2,3,1],    score 4
K = 4,  A = [0,2,3,1,4],    score 3
```

So we should choose K = 3, which has the highest score.

```Example 2:
Input: [1, 3, 0, 2, 4]
Output: 0
Explanation:  A will always have 3 points no matter how it shifts.
So we will choose the smallest K, which is 0.
```

Note:

• `A` will have length at most `20000`.
• `A[i]` will be in the range `[0, A.length]`.

## 题目大意：

```mark[i] = 1 if A[i] <= i

mark[i] = 0 otherwise```

## Python代码：

``````class Solution(object):
def bestRotation(self, A):
"""
:type A: List[int]
:rtype: int
"""
cnts = collections.defaultdict(int)
ans = 0
for i, n in enumerate(A):
cnts[n - i] += 1
ans += n <= i
bestAns, bestIdx = ans, 0
for x in range(len(A) - 1, -1, -1):
y = len(A) - x - 1
if A[x] <= x + y: ans -= 1
if A[x] == 0: ans += 1
cnts[A[x] - x] -= 1
ans += cnts[y + 1]
if ans >= bestAns:
bestAns = ans
bestIdx = x
cnts[A[x] + y + 1] += 1
return bestIdx
``````

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