[LeetCode] Wiggle Sort II 擺動排序之二

 

Given an unsorted array nums, reorder it such that nums[0] < nums[1] > nums[2] < nums[3]....

Example 1:

Input: nums = [1, 5, 1, 1, 6, 4]
Output: One possible answer is [1, 4, 1, 5, 1, 6].

Example 2:

Input: nums = [1, 3, 2, 2, 3, 1]
Output: One possible answer is [2, 3, 1, 3, 1, 2].

Note:
You may assume all input has valid answer.

Follow Up:
Can you do it in O(n) time and/or in-place with O(1) extra space?

 

這道題給了我們一個無序數組，讓我們排序成擺動數組，滿足nums[0] < nums[1] > nums[2] < nums[3]...，並給了我們例子。我們可以先給數組排序，然后在做調整。調整的方法是找到數組的中間的數，相當於把有序數組從中間分成兩部分，然后從前半段的末尾取一個，在從后半的末尾去一個，這樣保證了第一個數小於第二個數，然后從前半段取倒數第二個，從后半段取倒數第二個，這保證了第二個數大於第三個數，且第三個數小於第四個數，以此類推直至都取完，參見代碼如下：

 

解法一：

// O(n) space
class Solution {
public:
    void wiggleSort(vector<int>& nums) {
        vector<int> tmp = nums;
        int n = nums.size(), k = (n + 1) / 2, j = n; 
        sort(tmp.begin(), tmp.end());
        for (int i = 0; i < n; ++i) {
            nums[i] = i & 1 ? tmp[--j] : tmp[--k];
        }
    }
};

 

這道題的Follow up讓我們用O(n)的時間復雜度和O(1)的空間復雜度，這個真的比較難，參見網友的解答，(未完待續。。)

 

解法二：

// O(1) space
class Solution {
public:
    void wiggleSort(vector<int>& nums) {
        #define A(i) nums[(1 + 2 * i) % (n | 1)]
        int n = nums.size(), i = 0, j = 0, k = n - 1;
        auto midptr = nums.begin() + n / 2;
        nth_element(nums.begin(), midptr, nums.end());
        int mid = *midptr;
        while (j <= k) {
            if (A(j) > mid) swap(A(i++), A(j++));
            else if (A(j) < mid) swap(A(j), A(k--));
            else ++j;
        }
    }
};

 

類似題目：

Sort Colors

Kth Largest Element in an Array

Wiggle Sort

 

參考資料：

https://leetcode.com/problemset/algorithms/

https://leetcode.com/problems/wiggle-sort-ii/discuss/77706/Short-simple-C%2B%2B

https://leetcode.com/problems/wiggle-sort-ii/discuss/77677/O(n)%2BO(1)-after-median-Virtual-Indexing

https://leetcode.com/problems/wiggle-sort-ii/discuss/77682/Step-by-step-explanation-of-index-mapping-in-Java

https://leetcode.com/problems/wiggle-sort-ii/discuss/77681/O(n)-time-O(1)-space-solution-with-detail-explanations

 

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