Readme.md

---

🚀 Week 9 - Day 1

Welcome to Day 1 of Week 9! Today, we explored some exciting problem-solving exercises across two sessions. Here’s a structured breakdown of everything we covered.

---

📚 Session 1: Problem-Solving with Arrays

🔥 Question 1: Divide Array Into Equal Pairs

Goal: Check if an array can be divided into equal pairs.
Solution:

• Sort the array.
• Count pairs of consecutive elements.
• Verify if the count matches half the array length.
  Code:

function Question1() {
  let nums = [3, 2, 3, 2, 2, 2];
  nums.sort((a, b) => a - b);
  let pair = 0;

  for (let i = 0; i < nums.length; i += 2) {
    if (nums[i] == nums[i + 1]) pair++;
  }

  return pair == nums.length / 2;
}

---

🔢 Question 2: Count Pairs and Remaining Elements

Goal: Count pairs of identical numbers and find the leftover.
Solution:

• Sort the array.
• Count pairs and calculate remaining elements.
  Code:

function Question2() {
  let nums = [1, 3, 2, 1, 3, 2, 2];
  let pairs = 0;
  nums.sort((a, b) => a - b);
  for (let i = 0; i < nums.length; ) {
    if (nums[i] == nums[i + 1]) {
      pairs++;
      i += 2;
    } else i++;
  }
  let arr = new Array(2);
  arr[0] = pairs;
  arr[1] = nums.length - 2 * pairs;
  return arr;
}

---

🔗 Question 3: Pairs with Divisible Indices

Goal: Count pairs of identical numbers where the product of their indices is divisible by k.
Code:

function Question3() {
  let nums = [3, 1, 2, 2, 2, 1, 3], k = 2;
  let pair = 0;
  for (let i = 0; i < nums.length; i++) {
    for (let j = i + 1; j < nums.length; j++) {
      if (nums[i] == nums[j] && ((i * j) % k) == 0) {
        pair++;
      }
    }
  }
  return pair;
}

---

🏔️ Question 4: Count Hills and Valleys

Goal: Identify and count hills and valleys in an array.
Code:

function Question4() {
  let nums = [2, 4, 1, 1, 6, 5];
  let count = 0;

  for (let i = 1; i < nums.length - 1; i++) {
    if (nums[i] == nums[i - 1]) continue;
    let next = i + 1;
    let prev = i - 1;
    while (nums[i] == nums[next]) next++;
    while (nums[i] == nums[prev]) prev--;
    if (next >= nums.length || prev < 0) continue;
    if (nums[i] > nums[prev] && nums[i] > nums[next]) count++;
    if (nums[i] < nums[prev] && nums[i] < nums[next]) count++;
  }
  console.log("Valleys and Hills are  ", count);
}

---

🎯 Session 2: Array Operations

🧮 Question 1: Generate and Print Array

Goal: Create an array of a given size with random numbers.
Code:

function Question1() {
  let size = 5;
  let arr = new Array(size);

  for (let i = 0; i < size; i++) {
    arr[i] = Math.floor(Math.random() * 100);
  }
  console.log("Array: ", arr);
}

---

➕ Question 2: Sum of Array Elements

Goal: Calculate the sum of all elements in an array.
Code:

function Question2() {
  let arr = [10, 20, 30, 40, 50];
  let sum = 0;
  for (let i = 0; i < arr.length; i++) {
    sum += arr[i];
  }
  console.log(sum);
}

---

🔝 Question 3: Find Maximum Element

Goal: Find the largest number in the array.
Code:

function Question3() {
  let arr = [10, 20, 30, 40, 50];
  let max = arr[0];
  for (let i = 1; i < arr.length; i++) {
    if (arr[i] > arr[0]) max = arr[i];
  }
  console.log("Maximum element: ", max);
}

---

🥇🥈 Question 4: Find First and Second Maximum

Goal: Identify the two largest elements in an array.
Code:

function Question4() {
  arr = [10, 20, 30, 40, 50];
  let max = arr[0] > arr[1] ? arr[0] : arr[1];
  let max2 = arr[0] < arr[1] ? arr[0] : arr[1];

  for (let i = 2; i < arr.length; i++) {
    if (arr[i] > max) {
      max2 = max;
      max = arr[i];
    }
    if (arr[i] > max && arr[i] > max2) max2 = arr[i];
  }

  console.log("1st Max element is ", max);
  console.log("2nd Max element is ", max2);
}

---

💡 Key Takeaways

• Sorted arrays simplify operations like counting pairs or finding max elements.
• Nested loops can efficiently solve complex conditions (e.g., divisible indices).
• Arrays are versatile for implementing diverse algorithms.

---

📝 Notes

1. Sorting arrays before operations often reduces complexity.
2. Use modular arithmetic for pair-based problems.
3. Practice identifying edge cases like duplicate values or array boundaries.

---

🌟 Next Steps

• Review today’s exercises and optimize the algorithms further.
• Explore additional scenarios for valleys and hills.
• Try dynamic input for all problems.

---

Keep Coding & Keep Growing! 🚀