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Algorithms & Data Structures Overview

This section covers fundamental algorithms and data structures essential for technical interviews and competitive programming.

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What You’ll Learn

This comprehensive guide covers:
  • Sorting Algorithms: Comparison-based and non-comparison-based sorting techniques
  • Search Algorithms: Binary search and its variations
  • Dynamic Programming: Problem-solving patterns and optimization techniques
  • Graph Algorithms: Traversal, shortest paths, and connectivity
  • Data Structures: Arrays, linked lists, stacks, queues, trees, and graphs

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Time Complexity Overview

Understanding algorithm efficiency is crucial:
Complexity ClassAlgorithms
O(n²)Bubble Sort, Selection Sort, Insertion Sort
O(n log n)Quick Sort, Merge Sort, Heap Sort
O(n^1.3)Shell Sort
O(n)Counting Sort, Bucket Sort, Radix Sort

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Stability in Sorting

Stable algorithms maintain the relative order of equal elements:
  • ✅ Stable: Bubble Sort, Insertion Sort, Merge Sort, Radix Sort
  • ❌ Unstable: Selection Sort, Quick Sort, Shell Sort, Heap Sort
Stability Definition: After sorting, two equal keys maintain their original order. For example, if we have two records with the same key value, a stable algorithm ensures the one that appeared first in the input will appear first in the output.

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Algorithm Categories

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Comparison-Based Sorts

  1. Bubble Sort: Repeatedly swap adjacent elements if they’re in wrong order
  2. Selection Sort: Find minimum element and place it at the beginning
  3. Insertion Sort: Build sorted array one element at a time
  4. Heap Sort: Use max heap to extract elements in order
  5. Merge Sort: Divide array into halves, sort recursively, then merge
  6. Quick Sort: Select pivot, partition around it, recursively sort partitions

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Non-Comparison Sorts

  1. Counting Sort: Count occurrences of each element
  2. Bucket Sort: Distribute elements into buckets, sort each bucket
  3. Radix Sort: Sort by individual digits/characters

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Special Algorithms

  1. Shell Sort: Generalized insertion sort with gap sequences

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Common Data Structures

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Linear Structures

  • Arrays: Fixed-size, contiguous memory
  • Linked Lists: Dynamic size, non-contiguous nodes
  • Stacks: LIFO (Last In First Out) operations
  • Queues: FIFO (First In First Out) operations

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Tree Structures

  • Binary Trees: Each node has at most two children
  • Binary Search Trees: Left subtree < root < right subtree
  • Heaps: Complete binary tree with heap property

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Graph Structures

  • Adjacency Matrix: 2D array representation
  • Adjacency List: Array of lists representation

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Problem-Solving Patterns

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Two Pointers

Useful for array/string problems requiring O(n) time: 
int left = 0, right = n - 1;
while (left < right) {
    // Process elements
    if (condition) left++;
    else right--;
}

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Sliding Window

For subarray/substring problems: 
for (int i = 0, j = 0; i < n; i++) {
    // Expand window
    while (condition) {
        // Shrink window
        j++;
    }
}

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Monotonic Stack

Find next greater/smaller element: 
Stack<Integer> stack = new Stack<>();
for (int i = 0; i < n; i++) {
    while (!stack.isEmpty() && nums[stack.peek()] < nums[i]) {
        // Process elements
        stack.pop();
    }
    stack.push(i);
}

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Interview Tips

Time Complexity

Always analyze and state the time complexity of your solution

Space Complexity

Consider space-time tradeoffs and optimize when possible

Edge Cases

Test with empty inputs, single elements, and boundary conditions

Code Quality

Write clean, readable code with meaningful variable names

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Common Pitfalls

  • Off-by-one errors: Carefully check loop boundaries
  • Integer overflow: Use long for large number operations
  • Null pointer exceptions: Always validate input
  • Infinite loops: Ensure loop conditions eventually become false

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Next Steps

Explore each topic in depth:

Sorting Algorithms

Learn all major sorting algorithms with implementations

Binary Search

Master binary search and its variations

Dynamic Programming

Solve optimization problems efficiently

Graph Theory

Understand graph algorithms and applications

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