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# 969.Pancake-Sorting

## 969. Pancake Sorting

## 题目地址

<https://leetcode.com/problems/pancake-sorting/>

## 题目描述

```
Given an array A, we can perform a pancake flip: We choose some positive integer k <= A.length, then reverse the order of the first k elements of A.  We want to perform zero or more pancake flips (doing them one after another in succession) to sort the array A.

Return the k-values corresponding to a sequence of pancake flips that sort A.  Any valid answer that sorts the array within 10 * A.length flips will be judged as correct.

Example 1:
Input: [3,2,4,1]
Output: [4,2,4,3]
Explanation: 
We perform 4 pancake flips, with k values 4, 2, 4, and 3.
Starting state: A = [3, 2, 4, 1]
After 1st flip (k=4): A = [1, 4, 2, 3]
After 2nd flip (k=2): A = [4, 1, 2, 3]
After 3rd flip (k=4): A = [3, 2, 1, 4]
After 4th flip (k=3): A = [1, 2, 3, 4], which is sorted. 

Example 2:
Input: [1,2,3]
Output: []
Explanation: The input is already sorted, so there is no need to flip anything.
Note that other answers, such as [3, 3], would also be accepted.

Note:
1 <= A.length <= 100
A[i] is a permutation of [1, 2, ..., A.length]
```

## 代码

### Approach #1

**Explanation** Find the index `i` of the next maximum number `x`. Reverse `i + 1` numbers, so that the `x` will be at `A[0]` Reverse `x` numbers, so that `x` will be at `A[x - 1]`. Repeat this process `N` times.

**Update:** Actually, I didn't use the condition permutation of `[1,2,..., A.length]`. I searched in the descending order of `A`.

**Time Complexity**: O(N^2)

```java
class Solution {
  public List<Integer> pancakeSort(int[] A) {
    List<Integer> res = new ArrayList<>();
    for (int x = A.length, i; x > 0; --x) {
        for (i = 0; A[i] != x; ++i);
        reverse(A, i + 1); // 把最大的值移到A[0]
        res.add(i + 1);
        reverse(A, x);         // 把最大的移到A[end]
        res.add(x);
    }
    return res;
  }

  public void reverse(int[] A, int k) {
    for (int i = 0, j = k - 1; i < j; i++, j--) {
        int tmp = A[i];
        A[i] = A[j];
        A[j] = tmp;
    }
  }
}
```

### Approach #2 Sort Largest to Smallest

**Complexity Analysis**

* Time Complexity: O(N^2), where N*N* is the length of `A`.
* Space Complexity: O(N).

```java
class Solution {
  public List<Integer> pancakeSort(int[] A) {
        List<Integer> ans = new ArrayList();
    int N = A.length;

    Integer[] B = new Integer[N];
    for (int i = 0; i < N; i++) {
      B[i] = i + 1；
    }
    Arrays.sort(B, (i, j) -> A[j - 1] - A[i - 1]);

    for (int i: B) {
      for (int f: ans) {
        if (i <= f) {
          i = f + 1 - i;
        }
      }
      ans.add(i);
      ans.add(N--);
    }

    return ans;
  }
}
```