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3583. Count Special Triplets

Description

You are given an integer array nums.

A special triplet is defined as a triplet of indices (i, j, k) such that:

  • 0 <= i < j < k < n, where n = nums.length
  • nums[i] == nums[j] * 2
  • nums[k] == nums[j] * 2

Return the total number of special triplets in the array.

Since the answer may be large, return it modulo 109 + 7.

 

Example 1:

Input: nums = [6,3,6]

Output: 1

Explanation:

The only special triplet is (i, j, k) = (0, 1, 2), where:

  • nums[0] = 6, nums[1] = 3, nums[2] = 6
  • nums[0] = nums[1] * 2 = 3 * 2 = 6
  • nums[2] = nums[1] * 2 = 3 * 2 = 6

Example 2:

Input: nums = [0,1,0,0]

Output: 1

Explanation:

The only special triplet is (i, j, k) = (0, 2, 3), where:

  • nums[0] = 0, nums[2] = 0, nums[3] = 0
  • nums[0] = nums[2] * 2 = 0 * 2 = 0
  • nums[3] = nums[2] * 2 = 0 * 2 = 0

Example 3:

Input: nums = [8,4,2,8,4]

Output: 2

Explanation:

There are exactly two special triplets:

  • (i, j, k) = (0, 1, 3)
    • nums[0] = 8, nums[1] = 4, nums[3] = 8
    • nums[0] = nums[1] * 2 = 4 * 2 = 8
    • nums[3] = nums[1] * 2 = 4 * 2 = 8
  • (i, j, k) = (1, 2, 4)
    • nums[1] = 4, nums[2] = 2, nums[4] = 4
    • nums[1] = nums[2] * 2 = 2 * 2 = 4
    • nums[4] = nums[2] * 2 = 2 * 2 = 4

 

Constraints:

  • 3 <= n == nums.length <= 105
  • 0 <= nums[i] <= 105

Solutions

Solution 1: Enumerate Middle Number + Hash Table

We can enumerate the middle number $\textit{nums}[j]$, and use two hash tables, $\textit{left}$ and $\textit{right}$, to record the occurrence counts of numbers to the left and right of $\textit{nums}[j]$, respectively.

First, we add all numbers to $\textit{right}$. Then, we traverse each number $\textit{nums}[j]$ from left to right. During the traversal:

  1. Remove $\textit{nums}[j]$ from $\textit{right}$.
  2. Count the occurrences of the number $\textit{nums}[i] = \textit{nums}[j] * 2$ to the left of $\textit{nums}[j]$, denoted as $\textit{left}[\textit{nums}[j] * 2]$.
  3. Count the occurrences of the number $\textit{nums}[k] = \textit{nums}[j] * 2$ to the right of $\textit{nums}[j]$, denoted as $\textit{right}[\textit{nums}[j] * 2]$.
  4. Multiply $\textit{left}[\textit{nums}[j] * 2]$ and $\textit{right}[\textit{nums}[j] * 2]$ to get the number of special triplets with $\textit{nums}[j]$ as the middle number, and add the result to the answer.
  5. Add $\textit{nums}[j]$ to $\textit{left}$.

Finally, return the answer.

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

  • class Solution {
        public int specialTriplets(int[] nums) {
            Map<Integer, Integer> left = new HashMap<>();
            Map<Integer, Integer> right = new HashMap<>();
            for (int x : nums) {
                right.merge(x, 1, Integer::sum);
            }
            long ans = 0;
            final int mod = (int) 1e9 + 7;
            for (int x : nums) {
                right.merge(x, -1, Integer::sum);
                ans = (ans + 1L * left.getOrDefault(x * 2, 0) * right.getOrDefault(x * 2, 0) % mod)
                    % mod;
                left.merge(x, 1, Integer::sum);
            }
            return (int) ans;
        }
    }
    
  • class Solution {
    public:
        int specialTriplets(vector<int>& nums) {
            unordered_map<int, int> left, right;
            for (int x : nums) {
                right[x]++;
            }
            long long ans = 0;
            const int mod = 1e9 + 7;
            for (int x : nums) {
                right[x]--;
                ans = (ans + 1LL * left[x * 2] * right[x * 2] % mod) % mod;
                left[x]++;
            }
            return (int) ans;
        }
    };
    
    
  • class Solution:
        def specialTriplets(self, nums: List[int]) -> int:
            left = Counter()
            right = Counter(nums)
            ans = 0
            mod = 10**9 + 7
            for x in nums:
                right[x] -= 1
                ans = (ans + left[x * 2] * right[x * 2] % mod) % mod
                left[x] += 1
            return ans
    
    
  • func specialTriplets(nums []int) int {
    	left := make(map[int]int)
    	right := make(map[int]int)
    	for _, x := range nums {
    		right[x]++
    	}
    	ans := int64(0)
    	mod := int64(1e9 + 7)
    	for _, x := range nums {
    		right[x]--
    		ans = (ans + int64(left[x*2])*int64(right[x*2])%mod) % mod
    		left[x]++
    	}
    	return int(ans)
    }
    
    
  • function specialTriplets(nums: number[]): number {
        const left = new Map<number, number>();
        const right = new Map<number, number>();
        for (const x of nums) {
            right.set(x, (right.get(x) || 0) + 1);
        }
        let ans = 0;
        const mod = 1e9 + 7;
        for (const x of nums) {
            right.set(x, (right.get(x) || 0) - 1);
            const lx = left.get(x * 2) || 0;
            const rx = right.get(x * 2) || 0;
            ans = (ans + ((lx * rx) % mod)) % mod;
            left.set(x, (left.get(x) || 0) + 1);
        }
        return ans;
    }
    
    

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