Solutions

Prerequisites

Before attempting this problem, you should be comfortable with:

Hash Set - Used for O(1) lookup to efficiently check if an element's successor exists
Array Traversal - Iterating through arrays and understanding linear search complexity
Sorting - Understanding how sorting brings related elements together for optimized approaches

1. Search with Array

Intuition

For each element x in the array, we need to check whether x + 1 also exists in the array. The straightforward approach is to scan through the entire array for each element to verify if its successor is present. While this works correctly, it requires a linear search for every element.

Algorithm

Initialize a counter to 0.
For each element x in the array, iterate through the array to check if x + 1 exists.
If x + 1 is found, increment the counter.
Return the final count.

class Solution:
    def countElements(self, arr: List[int]) -> int:
        count = 0
        for x in arr:
            if x + 1 in arr:
                count += 1
        return count

class Solution {
    public int countElements(int[] arr) {
        int count = 0;
        for (int x : arr) {
            if (integerInArray(arr, x + 1)) {
                count++;
            }
        }
        return count;
    }

    public boolean integerInArray(int[] arr, int target) {
        for (int x : arr) {
            if (x == target) {
                return true;
            }
        }
        return false;
    }
}

class Solution {
public:
    int countElements(vector<int>& arr) {
        int count = 0;
        for (auto x : arr) {
            if (integerInArray(arr, x + 1)) {
                count++;
            }
        }
        return count;
    }

    bool integerInArray(vector<int>& arr, int target) {
        for (auto x : arr) {
            if (x == target) {
                return true;
            }
        }
        return false;
    }
};

class Solution {
    /**
     * @param {number[]} arr
     * @return {number}
     */
    countElements(arr) {
        let count = 0;
        for (const x of arr) {
            if (arr.includes(x + 1)) {
                count++;
            }
        }
        return count;
    }
}

public class Solution {
    public int CountElements(int[] arr) {
        int count = 0;
        foreach (int x in arr) {
            if (IntegerInArray(arr, x + 1)) {
                count++;
            }
        }
        return count;
    }

    private bool IntegerInArray(int[] arr, int target) {
        foreach (int x in arr) {
            if (x == target) {
                return true;
            }
        }
        return false;
    }
}

func countElements(arr []int) int {
    count := 0
    for _, x := range arr {
        if integerInArray(arr, x+1) {
            count++
        }
    }
    return count
}

func integerInArray(arr []int, target int) bool {
    for _, x := range arr {
        if x == target {
            return true
        }
    }
    return false
}

class Solution {
    fun countElements(arr: IntArray): Int {
        var count = 0
        for (x in arr) {
            if (integerInArray(arr, x + 1)) {
                count++
            }
        }
        return count
    }

    private fun integerInArray(arr: IntArray, target: Int): Boolean {
        for (x in arr) {
            if (x == target) {
                return true
            }
        }
        return false
    }
}

class Solution {
    func countElements(_ arr: [Int]) -> Int {
        var count = 0
        for x in arr {
            if arr.contains(x + 1) {
                count += 1
            }
        }
        return count
    }
}

Time & Space Complexity

Time complexity: $O(N^2)$
Space complexity: $O(1)$ constant space

Where $N$ is the length of the input array arr.

2. Search with HashSet

Intuition

The brute force approach is slow because checking if x + 1 exists requires scanning the entire array. A hash set provides O(1) lookup time, so we can first store all elements in a set, then check for each element's successor in constant time.

Algorithm

Insert all elements from the array into a hash set.
Initialize a counter to 0.
For each element x in the array, check if x + 1 exists in the hash set.
If it does, increment the counter.
Return the final count.

class Solution:
    def countElements(self, arr: List[int]) -> int:
        hash_set = set(arr)
        count = 0
        for x in arr:
            if x + 1 in hash_set:
                count += 1
        return count

class Solution {
    public int countElements(int[] arr) {
        Set<Integer> hashSet = new HashSet<>();
        for (int x : arr) {
            hashSet.add(x);
        }
        int count = 0;
        for (int x : arr) {
            if (hashSet.contains(x + 1)) {
                count++;
            }
        }
        return count;
    }
}

class Solution {
public:
    int countElements(vector<int>& arr) {
        unordered_set<int> hashSet(arr.begin(), arr.end());
        int count = 0;
        for (int x : arr) {
            if (hashSet.find(x + 1) != hashSet.end()) {
                count++;
            }
        }
        return count;
    }
};

class Solution {
    /**
     * @param {number[]} arr
     * @return {number}
     */
    countElements(arr) {
        const hashSet = new Set(arr);
        let count = 0;
        for (const x of arr) {
            if (hashSet.has(x + 1)) {
                count++;
            }
        }
        return count;
    }
}

public class Solution {
    public int CountElements(int[] arr) {
        HashSet<int> hashSet = new HashSet<int>(arr);
        int count = 0;
        foreach (int x in arr) {
            if (hashSet.Contains(x + 1)) {
                count++;
            }
        }
        return count;
    }
}

func countElements(arr []int) int {
    hashSet := make(map[int]bool)
    for _, x := range arr {
        hashSet[x] = true
    }
    count := 0
    for _, x := range arr {
        if hashSet[x+1] {
            count++
        }
    }
    return count
}

class Solution {
    fun countElements(arr: IntArray): Int {
        val hashSet = arr.toHashSet()
        var count = 0
        for (x in arr) {
            if (hashSet.contains(x + 1)) {
                count++
            }
        }
        return count
    }
}

class Solution {
    func countElements(_ arr: [Int]) -> Int {
        let hashSet = Set(arr)
        var count = 0
        for x in arr {
            if hashSet.contains(x + 1) {
                count += 1
            }
        }
        return count
    }
}

Time & Space Complexity

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

Where $N$ is the length of the input array arr.

3. Search with Sorted Array

Intuition

Sorting brings equal elements together and places consecutive values next to each other. After sorting, we can traverse the array once and track "runs" of identical values. When we encounter a new value that is exactly one more than the previous value, all elements in the previous run satisfy the condition.

Algorithm

Sort the array.
Initialize a counter and a run length tracker (starting at 1).
Iterate through the sorted array starting from index 1.
If the current element differs from the previous one:
- If the current element equals the previous element plus 1, add the run length to the counter.
- Reset the run length to 0.
Increment the run length for each element processed.
Return the final count.

class Solution:
    def countElements(self, arr: List[int]) -> int:
        arr.sort()
        count = 0
        run_length = 1
        for i in range(1, len(arr)):
            if arr[i - 1] != arr[i]:
                if arr[i - 1] + 1 == arr[i]:
                    count += run_length
                run_length = 0
            run_length += 1
        return count

class Solution {
    public int countElements(int[] arr) {
        Arrays.sort(arr);
        int count = 0;
        int runLength = 1;
        for (int i = 1; i < arr.length; i++) {
            if (arr[i - 1] != arr[i]) {
                if (arr[i - 1] + 1 == arr[i]) {
                    count += runLength;
                }
                runLength = 0;
            }
            runLength++;
        }
        return count;
    }
}

class Solution {
public:
    int countElements(vector<int>& arr) {
        std::sort(arr.begin(), arr.end());
        int count = 0;
        int runLength = 1;
        for (int i = 1; i < arr.size(); i++) {
            if (arr[i - 1] != arr[i]) {
                if (arr[i - 1] + 1 == arr[i]) {
                    count += runLength;
                }
                runLength = 0;
            }
            runLength++;
        }
        return count;
    }
};

class Solution {
    /**
     * @param {number[]} arr
     * @return {number}
     */
    countElements(arr) {
        arr.sort((a, b) => a - b);
        let count = 0;
        let runLength = 1;
        for (let i = 1; i < arr.length; i++) {
            if (arr[i - 1] !== arr[i]) {
                if (arr[i - 1] + 1 === arr[i]) {
                    count += runLength;
                }
                runLength = 0;
            }
            runLength++;
        }
        return count;
    }
}

public class Solution {
    public int CountElements(int[] arr) {
        Array.Sort(arr);
        int count = 0;
        int runLength = 1;
        for (int i = 1; i < arr.Length; i++) {
            if (arr[i - 1] != arr[i]) {
                if (arr[i - 1] + 1 == arr[i]) {
                    count += runLength;
                }
                runLength = 0;
            }
            runLength++;
        }
        return count;
    }
}

class Solution {
    fun countElements(arr: IntArray): Int {
        arr.sort()
        var count = 0
        var runLength = 1
        for (i in 1 until arr.size) {
            if (arr[i - 1] != arr[i]) {
                if (arr[i - 1] + 1 == arr[i]) {
                    count += runLength
                }
                runLength = 0
            }
            runLength++
        }
        return count
    }
}

class Solution {
    func countElements(_ arr: [Int]) -> Int {
        let sortedArr = arr.sorted()
        var count = 0
        var runLength = 1
        for i in 1..<sortedArr.count {
            if sortedArr[i - 1] != sortedArr[i] {
                if sortedArr[i - 1] + 1 == sortedArr[i] {
                    count += runLength
                }
                runLength = 0
            }
            runLength += 1
        }
        return count
    }
}

Time & Space Complexity

Time complexity: $O(N \log N)$
Space complexity: varies from $O(N)$ $O (N)$ to $O(1)$ $O (1)$
- The overall space complexity is dependent on the space complexity of the sorting algorithm you're using. The space complexity of sorting algorithms built into programming languages are generally anywhere from $O(N)$ to $O(1)$ .

Where $N$ is the length of the input array arr.

Common Pitfalls

Checking for x - 1 Instead of x + 1

The problem asks to count elements x where x + 1 exists in the array. A common mistake is checking for x - 1 instead, which counts elements that have a predecessor rather than a successor.

# Wrong: Checking for predecessor
if x - 1 in hash_set:
    count += 1

# Correct: Checking for successor
if x + 1 in hash_set:
    count += 1

Counting Unique Values Instead of All Occurrences

The problem asks to count every element x where x + 1 exists, including duplicates. Using a set for counting instead of iterating through the original array will miss duplicate elements.

# Wrong: Only counts unique values
hash_set = set(arr)
count = sum(1 for x in hash_set if x + 1 in hash_set)

# Correct: Count all occurrences including duplicates
hash_set = set(arr)
count = sum(1 for x in arr if x + 1 in hash_set)