/**
 * Finds a pair of numbers in a sorted array that sum up to a target value.
 * Uses the two-pointer technique for efficient searching.
 * 
 * @param {number[]} arr - The sorted array of numbers to search through.
 * @param {number} target - The target sum to find.
 * @returns {number[]|null} - Returns an array containing the pair if found, or null if not found.
 */
function findPairWithSum(arr, target) {
  // Initialize two pointers: one at the start and one at the end of the array
  let left = 0;
  let right = arr.length - 1;

  // Continue searching while the left pointer is less than the right pointer
  while (left < right) {
    console.log(`Checking pair: ${arr[left]} and ${arr[right]}`);

    // Calculate the sum of the current pair
    const sum = arr[left] + arr[right];

    if (sum === target) {
      // If the sum equals the target, we've found our pair
      console.log(`Found pair: ${arr[left]} + ${arr[right]} = ${target}`);
      return [arr[left], arr[right]];
    } else if (sum < target) {
      // If the sum is less than the target, we need a larger sum
      // So, we move the left pointer to the right to increase the sum
      console.log(`Sum ${sum} is less than target ${target}, moving left pointer`);
      left++;
    } else {
      // If the sum is greater than the target, we need a smaller sum
      // So, we move the right pointer to the left to decrease the sum
      console.log(`Sum ${sum} is greater than target ${target}, moving right pointer`);
      right--;
    }
  }

  // If we've exhausted all possibilities without finding a pair, return null
  console.log("No pair found");
  return null;
}

// Example usage
const sortedArray = [1, 3, 5, 7, 9, 11];
const targetSum = 14;
findPairWithSum(sortedArray, targetSum);

/**
 * Finds the maximum sum of a subarray of size k in the given array.
 * @param {number[]} arr - The input array of numbers.
 * @param {number} k - The size of the subarray.
 * @returns {number|null} The maximum sum of a subarray of size k, or null if the array length is less than k.
 */
function maxSubarraySum(arr, k) {
  // Check if the array length is less than k
  if (arr.length < k) {
    console.log("Array length is less than k");
    return null;
  }

  let maxSum = 0;
  let windowSum = 0;

  // Calculate sum of first window
  for (let i = 0; i < k; i++) {
    windowSum += arr[i];
  }
  maxSum = windowSum;

  console.log(`Initial window sum: ${windowSum}, Window: [${arr.slice(0, k)}]`);

  // Slide the window and update the maximum sum
  for (let i = k; i < arr.length; i++) {
    // Remove the first element of the previous window and add the last element of the new window
    windowSum = windowSum - arr[i - k] + arr[i];
    console.log(`New window sum: ${windowSum}, Window: [${arr.slice(i - k + 1, i + 1)}]`);

    // Update maxSum if the current window sum is greater
    if (windowSum > maxSum) {
      maxSum = windowSum;
      console.log(`New max sum found: ${maxSum}, Window: [${arr.slice(i - k + 1, i + 1)}]`);
    }
  }

  console.log(`Final max sum: ${maxSum}`);
  return maxSum;
}

// Example usage
const array = [1, 4, 2, 10, 23, 3, 1, 0, 20];
const k = 4;
maxSubarraySum(array, k);

/**
 * Finds the first non-repeating character in a given string.
 * @param {string} str - The input string to search.
 * @returns {string|null} The first non-repeating character, or null if not found.
 */
function firstNonRepeatingChar(str) {
  const charCount = new Map();

  // Count occurrences of each character
  for (let char of str) {
    charCount.set(char, (charCount.get(char) || 0) + 1);
    console.log(`Character ${char} count: ${charCount.get(char)}`);
  }

  // Find the first character with count 1
  for (let char of str) {
    if (charCount.get(char) === 1) {
      console.log(`First non-repeating character found: ${char}`);
      return char;
    }
  }

  console.log("No non-repeating character found");
  return null;
}

// Example usage
const inputString = "aabccdeff";
firstNonRepeatingChar(inputString);

// Create a new Map
const fruitInventory = new Map();

// Set key-value pairs
fruitInventory.set('apple', 5);
fruitInventory.set('banana', 3);
fruitInventory.set('orange', 2);

console.log('Initial inventory:', fruitInventory);

// Get a value using a key
console.log('Number of apples:', fruitInventory.get('apple'));

// Check if a key exists
console.log('Do we have pears?', fruitInventory.has('pear'));

// Update a value
fruitInventory.set('banana', fruitInventory.get('banana') + 2);
console.log('Updated banana count:', fruitInventory.get('banana'));

// Delete a key-value pair
fruitInventory.delete('orange');
console.log('Inventory after removing oranges:', fruitInventory);

// Iterate over the map
console.log('Current inventory:');
fruitInventory.forEach((count, fruit) => {
  console.log(`${fruit}: ${count}`);
});

// Get the size of the map
console.log('Number of fruit types:', fruitInventory.size);

// Clear the entire map
fruitInventory.clear();
console.log('Inventory after clearing:', fruitInventory);

/**
 * Calculates the nth Fibonacci number using dynamic programming.
 * @param {number} n - The position of the Fibonacci number to calculate.
 * @returns {number} The nth Fibonacci number.
 */
function fibonacci(n) {
  // Initialize an array to store Fibonacci numbers
  const fib = new Array(n + 1);

  // Base cases
  fib[0] = 0;
  fib[1] = 1;

  console.log(`F(0) = ${fib[0]}`);
  console.log(`F(1) = ${fib[1]}`);

  // Calculate Fibonacci numbers iteratively
  for (let i = 2; i <= n; i++) {
    fib[i] = fib[i - 1] + fib[i - 2];
    console.log(`F(${i}) = ${fib[i]}`);
  }

  return fib[n];
}

// Example usage
const n = 10;
console.log(`The ${n}th Fibonacci number is:`, fibonacci(n));

/**
 * Performs a binary search on a sorted array.
 * @param {number[]} arr - The sorted array to search.
 * @param {number} target - The value to find.
 * @returns {number} The index of the target if found, or -1 if not found.
 */
function binarySearch(arr, target) {
  let left = 0;
  let right = arr.length - 1;

  while (left <= right) {
    const mid = Math.floor((left + right) / 2);
    console.log(`Searching in range [${left}, ${right}], mid = ${mid}`);

    if (arr[mid] === target) {
      console.log(`Target ${target} found at index ${mid}`);
      return mid;
    } else if (arr[mid] < target) {
      console.log(`${arr[mid]} < ${target}, searching right half`);
      left = mid + 1;
    } else {
      console.log(`${arr[mid]} > ${target}, searching left half`);
      right = mid - 1;
    }
  }

  console.log(`Target ${target} not found in the array`);
  return -1;
}

// Example usage
const sortedArray = [1, 3, 5, 7, 9, 11, 13, 15];
const target = 7;
binarySearch(sortedArray, target);

class Graph {
  constructor() {
    this.adjacencyList = {};
  }

  addVertex(vertex) {
    if (!this.adjacencyList[vertex]) this.adjacencyList[vertex] = [];
  }

  addEdge(v1, v2) {
    this.adjacencyList[v1].push(v2);
    this.adjacencyList[v2].push(v1);
  }

  dfs(start) {
    const result = [];
    const visited = {};
    const adjacencyList = this.adjacencyList;

    (function dfsHelper(vertex) {
      if (!vertex) return null;
      visited[vertex] = true;
      result.push(vertex);
      console.log(`Visiting vertex: ${vertex}`);

      adjacencyList[vertex].forEach(neighbor => {
        if (!visited[neighbor]) {
          console.log(`Exploring neighbor: ${neighbor} of vertex: ${vertex}`);
          return dfsHelper(neighbor);
        } else {
          console.log(`Neighbor: ${neighbor} already visited`);
        }
      });
    })(start);

    return result;
  }
}

// Example usage
const graph = new Graph();
['A', 'B', 'C', 'D', 'E', 'F'].forEach(vertex => graph.addVertex(vertex));
graph.addEdge('A', 'B');
graph.addEdge('A', 'C');
graph.addEdge('B', 'D');
graph.addEdge('C', 'E');
graph.addEdge('D', 'E');
graph.addEdge('D', 'F');
graph.addEdge('E', 'F');

console.log(graph.dfs('A'));

class Graph {
  // ... (same constructor, addVertex, and addEdge methods as above)

  bfs(start) {
    const queue = [start];
    const result = [];
    const visited = {};
    visited[start] = true;

    while (queue.length) {
      let vertex = queue.shift();
      result.push(vertex);
      console.log(`Visiting vertex: ${vertex}`);

      this.adjacencyList[vertex].forEach(neighbor => {
        if (!visited[neighbor]) {
          visited[neighbor] = true;
          queue.push(neighbor);
          console.log(`Adding neighbor: ${neighbor} to queue`);
        } else {
          console.log(`Neighbor: ${neighbor} already visited`);
        }
      });
    }

    return result;
  }
}

// Example usage (using the same graph as in DFS example)
console.log(graph.bfs('A'));

class MinHeap {
  constructor() {
    this.heap = [];
  }

  getParentIndex(i) {
    return Math.floor((i - 1) / 2);
  }

  getLeftChildIndex(i) {
    return 2 * i + 1;
  }

  getRightChildIndex(i) {
    return 2 * i + 2;
  }

  swap(i1, i2) {
    [this.heap[i1], this.heap[i2]] = [this.heap[i2], this.heap[i1]];
  }

  insert(key) {
    this.heap.push(key);
    this.heapifyUp(this.heap.length - 1);
  }

  heapifyUp(i) {
    let currentIndex = i;
    while (this.heap[currentIndex] < this.heap[this.getParentIndex(currentIndex)]) {
      this.swap(currentIndex, this.getParentIndex(currentIndex));
      currentIndex = this.getParentIndex(currentIndex);
    }
  }

  extractMin() {
    if (this.heap.length === 0) return null;
    if (this.heap.length === 1) return this.heap.pop();

    const min = this.heap[0];
    this.heap[0] = this.heap.pop();
    this.heapifyDown(0);
    return min;
  }

  heapifyDown(i) {
    let smallest = i;
    const left = this.getLeftChildIndex(i);
    const right = this.getRightChildIndex(i);

    if (left < this.heap.length && this.heap[left] < this.heap[smallest]) {
      smallest = left;
    }

    if (right < this.heap.length && this.heap[right] < this.heap[smallest]) {
      smallest = right;
    }

    if (smallest !== i) {
      this.swap(i, smallest);
      this.heapifyDown(smallest);
    }
  }
}

// Example usage
const minHeap = new MinHeap();
[3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5].forEach(num => minHeap.insert(num));
console.log(minHeap.heap);
console.log(minHeap.extractMin());
console.log(minHeap.heap);

class TrieNode {
  constructor() {
    this.children = {};
    this.isEndOfWord = false;
  }
}

class Trie {
  constructor() {
    this.root = new TrieNode();
  }

  insert(word) {
    let current = this.root;
    for (let char of word) {
      if (!current.children[char]) {
        current.children[char] = new TrieNode();
      }
      current = current.children[char];
    }
    current.isEndOfWord = true;
    console.log(`Inserted word: ${word}`);
  }

  search(word) {
    let current = this.root;
    for (let char of word) {
      if (!current.children[char]) {
        console.log(`Word ${word} not found`);
        return false;
      }
      current = current.children[char];
    }
    console.log(`Word ${word} ${current.isEndOfWord ? 'found' : 'not found'}`);
    return current.isEndOfWord;
  }

  startsWith(prefix) {
    let current = this.root;
    for (let char of prefix) {
      if (!current.children[char]) {
        console.log(`No words start with ${prefix}`);
        return false;
      }
      current = current.children[char];
    }
    console.log(`Found words starting with ${prefix}`);
    return true;
  }
}

// Example usage
const trie = new Trie();
['apple', 'app', 'apricot', 'banana'].forEach(word => trie.insert(word));
trie.search('app');
trie.search('application');
trie.startsWith('app');
trie.startsWith('ban');

class UnionFind {
  constructor(size) {
    this.parent = Array(size).fill().map((_, i) => i);
    this.rank = Array(size).fill(0);
    this.count = size;
  }

  find(x) {
    if (this.parent[x] !== x) {
      this.parent[x] = this.find(this.parent[x]);
    }
    return this.parent[x];
  }

  union(x, y) {
    let rootX = this.find(x);
    let rootY = this.find(y);

    if (rootX === rootY) return;

    if (this.rank[rootX] < this.rank[rootY]) {
      [rootX, rootY] = [rootY, rootX];
    }
    this.parent[rootY] = rootX;
    if (this.rank[rootX] === this.rank[rootY]) {
      this.rank[rootX]++;
    }
    this.count--;

    console.log(`United ${x} and ${y}`);
  }

  connected(x, y) {
    return this.find(x) === this.find(y);
  }
}

// Example usage
const uf = new UnionFind(10);
uf.union(0, 1);
uf.union(2, 3);
uf.union(4, 5);
uf.union(6, 7);
uf.union(8, 9);
uf.union(0, 2);
uf.union(4, 6);
uf.union(0, 4);

console.log(uf.connected(1, 5)); // Should print: true
console.log(uf.connected(7, 9)); // Should print: false

class Graph {
  constructor() {
    this.adjacencyList = {};
  }

  addVertex(vertex) {
    if (!this.adjacencyList[vertex]) this.adjacencyList[vertex] = [];
  }

  addEdge(v1, v2) {
    this.adjacencyList[v1].push(v2);
  }

  topologicalSort() {
    const visited = {};
    const stack = [];

    const dfsHelper = (vertex) => {
      visited[vertex] = true;
      this.adjacencyList[vertex].forEach(neighbor => {
        if (!visited[neighbor]) {
          dfsHelper(neighbor);
        }
      });
      stack.push(vertex);
      console.log(`Added ${vertex} to stack`);
    };

    for (let vertex in this.adjacencyList) {
      if (!visited[vertex]) {
        dfsHelper(vertex);
      }
    }

    return stack.reverse();
  }
}

// Example usage
const graph = new Graph();
['A', 'B', 'C', 'D', 'E', 'F'].forEach(vertex => graph.addVertex(vertex));
graph.addEdge('A', 'C');
graph.addEdge('B', 'C');
graph.addEdge('B', 'D');
graph.addEdge('C', 'E');
graph.addEdge('D', 'F');
graph.addEdge('E', 'F');

console.log(graph.topologicalSort());