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2974. Minimum Number Game

Description

You are given a 0-indexed integer array nums of even length and there is also an empty array arr. Alice and Bob decided to play a game where in every round Alice and Bob will do one move. The rules of the game are as follows:

  • Every round, first Alice will remove the minimum element from nums, and then Bob does the same.
  • Now, first Bob will append the removed element in the array arr, and then Alice does the same.
  • The game continues until nums becomes empty.

Return the resulting array arr.

 

Example 1:

Input: nums = [5,4,2,3]
Output: [3,2,5,4]
Explanation: In round one, first Alice removes 2 and then Bob removes 3. Then in arr firstly Bob appends 3 and then Alice appends 2. So arr = [3,2].
At the begining of round two, nums = [5,4]. Now, first Alice removes 4 and then Bob removes 5. Then both append in arr which becomes [3,2,5,4].

Example 2:

Input: nums = [2,5]
Output: [5,2]
Explanation: In round one, first Alice removes 2 and then Bob removes 5. Then in arr firstly Bob appends and then Alice appends. So arr = [5,2].

 

Constraints:

  • 2 <= nums.length <= 100
  • 1 <= nums[i] <= 100
  • nums.length % 2 == 0

Solutions

Solution 1: Simulation + Priority Queue (Min Heap)

We can put the elements of the array $\textit{nums}$ into a min heap one by one. Each time, we take out two elements $a$ and $b$ from the min heap, and then sequentially put $b$ and $a$ into the answer array until the min heap is empty.

The time complexity is $O(n \times \log n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the array $\textit{nums}$.

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class Solution:
    def numberGame(self, nums: List[int]) -> List[int]:
        heapify(nums)
        ans = []
        while nums:
            a, b = heappop(nums), heappop(nums)
            ans.append(b)
            ans.append(a)
        return ans
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class Solution {
    public int[] numberGame(int[] nums) {
        PriorityQueue<Integer> pq = new PriorityQueue<>();
        for (int x : nums) {
            pq.offer(x);
        }
        int[] ans = new int[nums.length];
        int i = 0;
        while (!pq.isEmpty()) {
            int a = pq.poll();
            ans[i++] = pq.poll();
            ans[i++] = a;
        }
        return ans;
    }
}
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class Solution {
public:
    vector<int> numberGame(vector<int>& nums) {
        priority_queue<int, vector<int>, greater<int>> pq;
        for (int x : nums) {
            pq.push(x);
        }
        vector<int> ans;
        while (pq.size()) {
            int a = pq.top();
            pq.pop();
            int b = pq.top();
            pq.pop();
            ans.push_back(b);
            ans.push_back(a);
        }
        return ans;
    }
};
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func numberGame(nums []int) (ans []int) {
    pq := &hp{nums}
    heap.Init(pq)
    for pq.Len() > 0 {
        a := heap.Pop(pq).(int)
        b := heap.Pop(pq).(int)
        ans = append(ans, b)
        ans = append(ans, a)
    }
    return
}

type hp struct{ sort.IntSlice }

func (h *hp) Less(i, j int) bool { return h.IntSlice[i] < h.IntSlice[j] }
func (h *hp) Pop() interface{} {
    old := h.IntSlice
    n := len(old)
    x := old[n-1]
    h.IntSlice = old[0 : n-1]
    return x
}
func (h *hp) Push(x interface{}) {
    h.IntSlice = append(h.IntSlice, x.(int))
}
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function numberGame(nums: number[]): number[] {
    const pq = new MinPriorityQueue();
    for (const x of nums) {
        pq.enqueue(x);
    }
    const ans: number[] = [];
    while (pq.size()) {
        const a = pq.dequeue().element;
        const b = pq.dequeue().element;
        ans.push(b, a);
    }
    return ans;
}
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use std::cmp::Reverse;
use std::collections::BinaryHeap;

impl Solution {
    pub fn number_game(nums: Vec<i32>) -> Vec<i32> {
        let mut pq = BinaryHeap::new();

        for &x in &nums {
            pq.push(Reverse(x));
        }

        let mut ans = Vec::new();

        while let Some(Reverse(a)) = pq.pop() {
            if let Some(Reverse(b)) = pq.pop() {
                ans.push(b);
                ans.push(a);
            }
        }

        ans
    }
}

Solution 2: Sorting + Swapping

We can sort the array $\textit{nums}$, and then iterate through the array, swapping adjacent elements each time until the iteration is complete, and return the swapped array.

The time complexity is $O(n \log n)$, and the space complexity is $O(\log n)$. Here, $n$ is the length of the array $\textit{nums}$.

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class Solution:
    def numberGame(self, nums: List[int]) -> List[int]:
        nums.sort()
        for i in range(0, len(nums), 2):
            nums[i], nums[i + 1] = nums[i + 1], nums[i]
        return nums
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class Solution {
    public int[] numberGame(int[] nums) {
        Arrays.sort(nums);
        for (int i = 0; i < nums.length; i += 2) {
            int t = nums[i];
            nums[i] = nums[i + 1];
            nums[i + 1] = t;
        }
        return nums;
    }
}
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class Solution {
public:
    vector<int> numberGame(vector<int>& nums) {
        sort(nums.begin(), nums.end());
        int n = nums.size();
        for (int i = 0; i < n; i += 2) {
            swap(nums[i], nums[i + 1]);
        }
        return nums;
    }
};
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func numberGame(nums []int) []int {
    sort.Ints(nums)
    for i := 0; i < len(nums); i += 2 {
        nums[i], nums[i+1] = nums[i+1], nums[i]
    }
    return nums
}
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function numberGame(nums: number[]): number[] {
    nums.sort((a, b) => a - b);
    for (let i = 0; i < nums.length; i += 2) {
        [nums[i], nums[i + 1]] = [nums[i + 1], nums[i]];
    }
    return nums;
}
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impl Solution {
    pub fn number_game(nums: Vec<i32>) -> Vec<i32> {
        let mut nums = nums;
        nums.sort_unstable();
        for i in (0..nums.len()).step_by(2) {
            nums.swap(i, i + 1);
        }
        nums
    }
}

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