1512. Number of Good Pairs - Explanation

Description

You are given an array of integers nums, return the number of good pairs.

A pair (i, j) is called good if nums[i] == nums[j] and i < j.

Example 1:

Input: nums = [1,2,3,1,1,3]

Output: 4

Explanation: There are 4 good pairs (0,3), (0,4), (3,4), (2,5) 0-indexed.

Example 2:

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

Output: 6

Explanation: Each pair in the array are good.

Example 3:

Input: nums = [1,2,3]

Output: 0

Constraints:

1 <= nums.length <= 100
1 <= nums[i] <= 100

Topics

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Prerequisites

Before attempting this problem, you should be comfortable with:

Hash Maps - Using dictionaries to count frequencies of elements in O(1) time
Combinatorics - Understanding how to count pairs using the formula n*(n-1)/2 for choosing 2 items from n

1. Brute Force

Intuition

A good pair is defined as a pair (i, j) where i < j and nums[i] == nums[j]. The simplest approach is to check every possible pair of indices and count those that satisfy both conditions.

Algorithm

Initialize a counter res to zero.
Use two nested loops: the outer loop picks index i, and the inner loop picks index j where j > i.
For each pair, if nums[i] == nums[j], increment res.
Return res.

class Solution:
    def numIdenticalPairs(self, nums: List[int]) -> int:
        res = 0
        for i in range(len(nums)):
            for j in range(i + 1, len(nums)):
                if nums[i] == nums[j]:
                    res += 1
        return res

public class Solution {
    public int numIdenticalPairs(int[] nums) {
        int res = 0;
        for (int i = 0; i < nums.length; i++) {
            for (int j = i + 1; j < nums.length; j++) {
                if (nums[i] == nums[j]) {
                    res++;
                }
            }
        }
        return res;
    }
}

class Solution {
public:
    int numIdenticalPairs(vector<int>& nums) {
        int res = 0;
        for (int i = 0; i < nums.size(); i++) {
            for (int j = i + 1; j < nums.size(); j++) {
                if (nums[i] == nums[j]) {
                    res++;
                }
            }
        }
        return res;
    }
};

class Solution {
    /**
     * @param {number[]} nums
     * @return {number}
     */
    numIdenticalPairs(nums) {
        let res = 0;
        for (let i = 0; i < nums.length; i++) {
            for (let j = i + 1; j < nums.length; j++) {
                if (nums[i] == nums[j]) {
                    res++;
                }
            }
        }
        return res;
    }
}

public class Solution {
    public int NumIdenticalPairs(int[] nums) {
        int res = 0;
        for (int i = 0; i < nums.Length; i++) {
            for (int j = i + 1; j < nums.Length; j++) {
                if (nums[i] == nums[j]) {
                    res++;
                }
            }
        }
        return res;
    }
}

func numIdenticalPairs(nums []int) int {
    res := 0
    for i := 0; i < len(nums); i++ {
        for j := i + 1; j < len(nums); j++ {
            if nums[i] == nums[j] {
                res++
            }
        }
    }
    return res
}

class Solution {
    fun numIdenticalPairs(nums: IntArray): Int {
        var res = 0
        for (i in nums.indices) {
            for (j in i + 1 until nums.size) {
                if (nums[i] == nums[j]) {
                    res++
                }
            }
        }
        return res
    }
}

class Solution {
    func numIdenticalPairs(_ nums: [Int]) -> Int {
        var res = 0
        for i in 0..<nums.count {
            for j in (i + 1)..<nums.count {
                if nums[i] == nums[j] {
                    res += 1
                }
            }
        }
        return res
    }
}

impl Solution {
    pub fn num_identical_pairs(nums: Vec<i32>) -> i32 {
        let mut res = 0;
        for i in 0..nums.len() {
            for j in (i + 1)..nums.len() {
                if nums[i] == nums[j] {
                    res += 1;
                }
            }
        }
        res
    }
}

Time & Space Complexity

Time complexity: $O(n ^ 2)$
Space complexity: $O(1)$

2. Hash Map (Math)

Intuition

If a value appears c times, the number of good pairs using that value equals the number of ways to choose 2 indices from c positions, which is c * (c - 1) / 2. We can count frequencies first, then sum up the pairs for each value.

Algorithm

Count the frequency of each number using a hash map.
For each frequency c, add c * (c - 1) / 2 to the res.
Return the total sum.

class Solution:
    def numIdenticalPairs(self, nums: List[int]) -> int:
        count = Counter(nums)
        res = 0
        for num, c in count.items():
            res += c * (c - 1) // 2
        return res

public class Solution {
    public int numIdenticalPairs(int[] nums) {
        Map<Integer, Integer> count = new HashMap<>();
        int res = 0;
        for (int num : nums) {
            count.put(num, count.getOrDefault(num, 0) + 1);
        }
        for (int c : count.values()) {
            res += c * (c - 1) / 2;
        }
        return res;
    }
}

class Solution {
public:
    int numIdenticalPairs(vector<int>& nums) {
        unordered_map<int, int> count;
        int res = 0;
        for (int num : nums) {
            count[num]++;
        }
        for (auto& [num, c] : count) {
            res += c * (c - 1) / 2;
        }
        return res;
    }
};

class Solution {
    /**
     * @param {number[]} nums
     * @return {number}
     */
    numIdenticalPairs(nums) {
        const count = {};
        let res = 0;
        for (const num of nums) {
            count[num] = (count[num] || 0) + 1;
        }
        for (const c of Object.values(count)) {
            res += (c * (c - 1)) / 2;
        }
        return res;
    }
}

public class Solution {
    public int NumIdenticalPairs(int[] nums) {
        var count = new Dictionary<int, int>();
        int res = 0;
        foreach (int num in nums) {
            if (!count.ContainsKey(num)) count[num] = 0;
            count[num]++;
        }
        foreach (int c in count.Values) {
            res += c * (c - 1) / 2;
        }
        return res;
    }
}

func numIdenticalPairs(nums []int) int {
    count := make(map[int]int)
    res := 0
    for _, num := range nums {
        count[num]++
    }
    for _, c := range count {
        res += c * (c - 1) / 2
    }
    return res
}

class Solution {
    fun numIdenticalPairs(nums: IntArray): Int {
        val count = mutableMapOf<Int, Int>()
        var res = 0
        for (num in nums) {
            count[num] = count.getOrDefault(num, 0) + 1
        }
        for (c in count.values) {
            res += c * (c - 1) / 2
        }
        return res
    }
}

class Solution {
    func numIdenticalPairs(_ nums: [Int]) -> Int {
        var count = [Int: Int]()
        var res = 0
        for num in nums {
            count[num, default: 0] += 1
        }
        for c in count.values {
            res += c * (c - 1) / 2
        }
        return res
    }
}

impl Solution {
    pub fn num_identical_pairs(nums: Vec<i32>) -> i32 {
        let mut count = HashMap::new();
        let mut res = 0;
        for &num in &nums {
            *count.entry(num).or_insert(0) += 1;
        }
        for &c in count.values() {
            res += c * (c - 1) / 2;
        }
        res
    }
}

Time & Space Complexity

Time complexity: $O(n)$
Space complexity: $O(n)$

3. Hash Map

Intuition

Instead of counting all frequencies first and then computing pairs, we can count pairs on the fly. As we traverse the array, each new occurrence of a value can form a good pair with every previous occurrence of that same value. We track the count of each value seen so far and add it to the res before updating the count.

Algorithm

Initialize a hash map to store the count of each number seen so far.
For each number in the array:
- Add the current count of that number to the res (this is the number of new pairs formed).
- Increment the count of that number in the map.
Return the res.

class Solution:
    def numIdenticalPairs(self, nums: List[int]) -> int:
        count = defaultdict(int)
        res = 0
        for num in nums:
            res += count[num]
            count[num] += 1
        return res

public class Solution {
    public int numIdenticalPairs(int[] nums) {
        Map<Integer, Integer> count = new HashMap<>();
        int res = 0;
        for (int num : nums) {
            res += count.getOrDefault(num, 0);
            count.put(num, count.getOrDefault(num, 0) + 1);
        }
        return res;
    }
}

class Solution {
public:
    int numIdenticalPairs(vector<int>& nums) {
        unordered_map<int, int> count;
        int res = 0;
        for (int num : nums) {
            res += count[num];
            count[num]++;
        }
        return res;
    }
};

class Solution {
    /**
     * @param {number[]} nums
     * @return {number}
     */
    numIdenticalPairs(nums) {
        const count = {};
        let res = 0;
        for (const num of nums) {
            res += count[num] || 0;
            count[num] = (count[num] || 0) + 1;
        }
        return res;
    }
}

public class Solution {
    public int NumIdenticalPairs(int[] nums) {
        var count = new Dictionary<int, int>();
        int res = 0;
        foreach (int num in nums) {
            if (count.ContainsKey(num)) {
                res += count[num];
                count[num]++;
            } else {
                count[num] = 1;
            }
        }
        return res;
    }
}

class Solution {
    fun numIdenticalPairs(nums: IntArray): Int {
        val count = mutableMapOf<Int, Int>()
        var res = 0
        for (num in nums) {
            res += count.getOrDefault(num, 0)
            count[num] = count.getOrDefault(num, 0) + 1
        }
        return res
    }
}

class Solution {
    func numIdenticalPairs(_ nums: [Int]) -> Int {
        var count = [Int: Int]()
        var res = 0
        for num in nums {
            res += count[num] ?? 0
            count[num, default: 0] += 1
        }
        return res
    }
}

impl Solution {
    pub fn num_identical_pairs(nums: Vec<i32>) -> i32 {
        let mut count = HashMap::new();
        let mut res = 0;
        for &num in &nums {
            res += *count.get(&num).unwrap_or(&0);
            *count.entry(num).or_insert(0) += 1;
        }
        res
    }
}

Time & Space Complexity

Time complexity: $O(n)$
Space complexity: $O(n)$

Common Pitfalls

Double Counting Pairs

A good pair requires i < j, meaning each pair should only be counted once. When using nested loops, ensure the inner loop starts from i + 1 rather than 0. Similarly, when using the mathematical formula c * (c - 1) / 2, this already accounts for unique pairs and should not be doubled.

Integer Overflow in Pair Calculation

When using the formula c * (c - 1) / 2 to calculate the number of pairs for a frequency c, the multiplication can overflow for large values if using 32-bit integers. In languages with fixed-size integers, ensure you use an appropriate data type or perform the division before the multiplication becomes too large.