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Mastering Array Problems on LeetCode: Common Patterns and Solutions

Solving array problems efficiently is crucial for coding interviews, especially on platforms like LeetCode. This guide explores key problem-solving patterns, effective strategies, and must-know algorithms, with C# examples to help beginners and intermediate developers build confidence.

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1. Common Array Problem Patterns

Recognizing patterns in array problems helps reduce brute-force solutions and improves efficiency. Below are some of the most common approaches:

1.1 Two-Pointer Technique

The two-pointer technique is used to reduce the time complexity of problems that involve searching or modifying an array in place.

Example: Two Sum (Sorted Array)

Problem: Find two numbers in a sorted array that add up to a given target.

Solution: Use two pointers, one at the beginning and one at the end.

public int[] TwoSumSorted(int[] numbers, int target) {
    int left = 0, right = numbers.Length - 1;
    while (left < right) {
        int sum = numbers[left] + numbers[right];
        if (sum == target) return new int[] { left + 1, right + 1 };
        else if (sum < target) left++;
        else right--;
    }
    return new int[] { -1, -1 }; // No solution
}

Time Complexity: O(n)

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1.2 Sliding Window

Sliding window is useful for problems involving subarrays or sequences.

Example: Longest Subarray with Sum K

Problem: Find the longest contiguous subarray that sums to k.

public int LongestSubarraySumK(int[] nums, int k) {
    int left = 0, sum = 0, maxLength = 0;
    for (int right = 0; right < nums.Length; right++) {
        sum += nums[right];
        while (sum > k && left <= right) {
            sum -= nums[left];
            left++;
        }
        if (sum == k) maxLength = Math.Max(maxLength, right - left + 1);
    }
    return maxLength;
}

Time Complexity: O(n)

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1.3 Prefix Sum

Prefix sum optimizes problems where multiple range queries are performed.

Example: Subarray Sum Equals K

Problem: Find the number of subarrays that sum to k.

public int SubarraySum(int[] nums, int k) {
    Dictionary<int, int> prefixSumMap = new Dictionary<int, int>();
    prefixSumMap[0] = 1; // Base case
    int sum = 0, count = 0;
    foreach (var num in nums) {
        sum += num;
        if (prefixSumMap.ContainsKey(sum - k))
            count += prefixSumMap[sum - k];
        if (!prefixSumMap.ContainsKey(sum))
            prefixSumMap[sum] = 0;
        prefixSumMap[sum]++;
    }
    return count;
}

Time Complexity: O(n)

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2. How to Think Like a Problem Solver

When tackling algorithm challenges, follow these steps:

2.1 Understand the Problem

• Read carefully and clarify edge cases.
• Identify constraints (e.g., array size, negative numbers, duplicates).

2.2 Plan Your Approach

• Recognize applicable patterns.
• Choose an efficient data structure (hash maps, heaps, etc.).
• Consider brute force first, then optimize.

2.3 Implement and Optimize

• Write clean, modular code.
• Test with edge cases.
• Analyze time and space complexity.

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3. Top 10 Must-Know Algorithms for Coding Interviews

Here are fundamental algorithms that every programmer should master:

3.1 Binary Search

Used for searching in sorted arrays.

public int BinarySearch(int[] arr, int target) {
    int left = 0, right = arr.Length - 1;
    while (left <= right) {
        int mid = left + (right - left) / 2;
        if (arr[mid] == target) return mid;
        else if (arr[mid] < target) left = mid + 1;
        else right = mid - 1;
    }
    return -1;
}

Time Complexity: O(log n)

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3.2 Sorting Algorithms

QuickSort (Divide & Conquer Approach)

public void QuickSort(int[] arr, int left, int right) {
    if (left >= right) return;
    int pivot = Partition(arr, left, right);
    QuickSort(arr, left, pivot - 1);
    QuickSort(arr, pivot + 1, right);
}

private int Partition(int[] arr, int left, int right) {
    int pivot = arr[right], i = left;
    for (int j = left; j < right; j++) {
        if (arr[j] < pivot) {
            (arr[i], arr[j]) = (arr[j], arr[i]);
            i++;
        }
    }
    (arr[i], arr[right]) = (arr[right], arr[i]);
    return i;
}

Time Complexity: O(n log n)

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3.3 Depth-First Search (DFS) & Breadth-First Search (BFS)

Used for tree and graph traversal.

DFS Example:

public void DFS(TreeNode root) {
    if (root == null) return;
    Console.WriteLine(root.val);
    DFS(root.left);
    DFS(root.right);
}

BFS Example:

public void BFS(TreeNode root) {
    Queue<TreeNode> queue = new Queue<TreeNode>();
    queue.Enqueue(root);
    while (queue.Count > 0) {
        TreeNode node = queue.Dequeue();
        Console.WriteLine(node.val);
        if (node.left != null) queue.Enqueue(node.left);
        if (node.right != null) queue.Enqueue(node.right);
    }
}

Time Complexity: O(n)

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Conclusion

Mastering array problems requires recognizing patterns, optimizing solutions, and understanding fundamental algorithms. With structured problem-solving techniques and efficient implementations, you can confidently tackle coding interviews and algorithm challenges on platforms like LeetCode. Keep practicing, analyzing different solutions, and refining your approach to become an expert problem solver! 🚀