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2007. Find Original Array From Doubled Array

Description

An integer array original is transformed into a doubled array changed by appending twice the value of every element in original, and then randomly shuffling the resulting array.

Given an array changed, return original if changed is a doubled array. If changed is not a doubled array, return an empty array. The elements in original may be returned in any order.

 

Example 1:

Input: changed = [1,3,4,2,6,8]
Output: [1,3,4]
Explanation: One possible original array could be [1,3,4]:
- Twice the value of 1 is 1 * 2 = 2.
- Twice the value of 3 is 3 * 2 = 6.
- Twice the value of 4 is 4 * 2 = 8.
Other original arrays could be [4,3,1] or [3,1,4].

Example 2:

Input: changed = [6,3,0,1]
Output: []
Explanation: changed is not a doubled array.

Example 3:

Input: changed = [1]
Output: []
Explanation: changed is not a doubled array.

 

Constraints:

  • 1 <= changed.length <= 105
  • 0 <= changed[i] <= 105

Solutions

Solution 1: Sorting

We notice that if the array changed is a double array, then the smallest element in the array changed must also be an element in the original array. Therefore, we can first sort the array changed, and then start from the first element to traverse the array changed in ascending order.

We use a hash table or array \(cnt\) to count the occurrence of each element in the array changed. For each element \(x\) in the array changed, we first check whether \(x\) exists in \(cnt\). If it does not exist, we skip this element. Otherwise, we subtract one from \(cnt[x]\), and check whether \(x \times 2\) exists in \(cnt\). If it does not exist, we return an empty array directly. Otherwise, we subtract one from \(cnt[x \times 2]\), and add \(x\) to the answer array.

After the traversal, we return the answer array.

The time complexity is \(O(n \times \log n)\), and the space complexity is \(O(n)\), where \(n\) is the length of the array changed.

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class Solution:
    def findOriginalArray(self, changed: List[int]) -> List[int]:
        changed.sort()
        cnt = Counter(changed)
        ans = []
        for x in changed:
            if cnt[x] == 0:
                continue
            cnt[x] -= 1
            if cnt[x << 1] <= 0:
                return []
            cnt[x << 1] -= 1
            ans.append(x)
        return ans

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class Solution {
    public int[] findOriginalArray(int[] changed) {
        int n = changed.length;
        Arrays.sort(changed);
        int[] cnt = new int[changed[n - 1] + 1];
        for (int x : changed) {
            ++cnt[x];
        }
        int[] ans = new int[n >> 1];
        int i = 0;
        for (int x : changed) {
            if (cnt[x] == 0) {
                continue;
            }
            --cnt[x];
            int y = x << 1;
            if (y >= cnt.length || cnt[y] <= 0) {
                return new int[0];
            }
            --cnt[y];
            ans[i++] = x;
        }
        return ans;
    }
}

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class Solution {
public:
    vector<int> findOriginalArray(vector<int>& changed) {
        sort(changed.begin(), changed.end());
        vector<int> cnt(changed.back() + 1);
        for (int x : changed) {
            ++cnt[x];
        }
        vector<int> ans;
        for (int x : changed) {
            if (cnt[x] == 0) {
                continue;
            }
            --cnt[x];
            int y = x << 1;
            if (y >= cnt.size() || cnt[y] <= 0) {
                return {};
            }
            --cnt[y];
            ans.push_back(x);
        }
        return ans;
    }
};

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func findOriginalArray(changed []int) (ans []int) {
    sort.Ints(changed)
    cnt := make([]int, changed[len(changed)-1]+1)
    for _, x := range changed {
        cnt[x]++
    }
    for _, x := range changed {
        if cnt[x] == 0 {
            continue
        }
        cnt[x]--
        y := x << 1
        if y >= len(cnt) || cnt[y] <= 0 {
            return []int{}
        }
        cnt[y]--
        ans = append(ans, x)
    }
    return
}

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function findOriginalArray(changed: number[]): number[] {
    changed.sort((a, b) => a - b);
    const cnt: number[] = Array(changed.at(-1)! + 1).fill(0);
    for (const x of changed) {
        ++cnt[x];
    }
    const ans: number[] = [];
    for (const x of changed) {
        if (cnt[x] === 0) {
            continue;
        }
        cnt[x]--;
        const y = x << 1;
        if (y >= cnt.length || cnt[y] <= 0) {
            return [];
        }
        cnt[y]--;
        ans.push(x);
    }
    return ans;
}

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