Given a number n, print all primes smaller than or equal to n. It is also given that n is a small number.

Example:

Input : n =10
Output : 2 3 5 7


Input : n = 20
Output: 2 3 5 7 11 13 17 19

Sieve of Eratosthenes

Given a number n, print all primes smaller than or equal to n. It is also given that n is a small number.

Example:

Input : n =10
Output : 2 3 5 7


Input : n = 20
Output: 2 3 5 7 11 13 17 19

The sieve of Eratosthenes is one of the most efficient ways to find all primes smaller than n when n is smaller than 10 million or so.

Following is the algorithm to find all the prime numbers less than or equal to a given integer n by the Eratosthene’s method:
When the algorithm terminates, all the numbers in the list that are not marked are prime.

Explanation with Example:

Let us take an example when n = 100. So, we need to print all prime numbers smaller than or equal to 100.


We create a list of all numbers from 2 to 100.

According to the algorithm we will mark all the numbers which are divisible by 2 and are greater than or equal to the square of it.

Now we move to our next unmarked number 3 and mark all the numbers which are multiples of 3 and are greater than or equal to the square of it.

We move to our next unmarked number 5 and mark all multiples of 5 and are greater than or equal to the square of it.

We continue this process, and our final table will look like below:

So, the prime numbers are the unmarked ones: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

FOR A2SV

🎯 Problem of the Day: Sort Colors

Problem Denoscription
You are given an array nums with \( n \) objects colored red, white, or blue. Sort the array in-place so that objects of the same color are adjacent, with the colors in the order red, white, and blue.
- Represent the colors using integers:
- 0 → Red
- 1 → White
- 2 → Blue

⚠️ Note: You must not use the library's sort function.

---

Example 1
Input:

nums = [2,0,2,1,1,0]

Output:

[0,0,1,1,2,2]

Example 2
Input:

nums = [2,0,1]

Output:

[0,1,2]

---

📝 Practice Questions for A2SV Preparation
1. Core Problem:
- Solve LeetCode 75: Sort Colors () using Dutch National Flag Algorithm for \( O(n) \) time complexity.

2. Related Problems:
- LeetCode 215 : Kth Largest Element in an Array
- LeetCode 347 : Top K Frequent Elements
- LeetCode 56 : Merge Intervals

3. Challenge Problem:
- LeetCode 88: Merge Sorted Array

---

💡 Tip: Use a two-pointer or three-pointer approach to keep track of boundaries for the different colors! Try to optimize your solution to \( O(n) \) in both time and space.

🧠 Share your solution and discuss your approach with the community! 🌟

Question: Can You Make This String a Palindrome?

A palindrome is a string that reads the same forwards and backwards. Given a string, determine if it's possible to rearrange the characters to form a palindrome.

Examples:

1. Input: "civic"

• Output: True

• Explanation: The string is already a palindrome.

2. Input: "ivicc"

• Output: True

• Explanation: Rearranging the characters can form the palindrome "civic".

3. Input: "hello"

• Output: False

• Explanation: No rearrangement can form a palindrome.

4. Input: "aabbcc"

• Output: True

• Explanation: Rearranging the characters can form the palindrome "abcba".

5. Input: "racecar"

• Output: True

• Explanation: The string is already a palindrome.

Challenge:
Write a function that takes a string as input and returns True if the string can be rearranged to form a palindrome, and False otherwise.

Question: Count Substrings with Same Start and End Character

Given a string s consisting only of lowercase English letters, your task is to find the number of substrings that start and end with the same character.

▎Examples:

1. Input: "abcba"
Output: 7
Explanation: The substrings are: "a", "b", "c", "b", "a", "bcb", and "abcba".

2. Input: "abacada"
Output: 9
Explanation: The substrings are: "a", "b", "a", "c", "a", "d", "aba", "aca", and "abaca".

3. Input: "a"
Output: 1
Explanation: The only substring is "a".

4. Input: "zzzz"
Output: 10
Explanation: All substrings start and end with 'z': "z", "z", "z", "z", "zz", "zz", "zz", "zz", "zzz", and "zzzz".

▎Challenge:

Write a function that takes a string as input and returns the total count of substrings that start and end with the same character.

question from today interview question

Question: Maximum Sum Score of an Array

You are given a 0-indexed integer array nums of length n. The sum score of nums at an index i (where 0 <= i < n) is defined as the maximum of:

• The sum of the first i + 1 elements of nums.

• The sum of the last n - i elements of nums.

Your task is to return the maximum sum score of nums at any index.

▎Examples:

1. Input: nums = [4, 3, -2, 5]
Output: 10
Explanation:

• At index 0: max(4, 4 + 3 - 2 + 5) = max(4, 10) = 10.

• At index 1: max(4 + 3, 3 - 2 + 5) = max(7, 6) = 7.

• At index 2: max(4 + 3 - 2, -2 + 5) = max(5, 3) = 5.

• At index 3: max(4 + 3 - 2 + 5, 5) = max(10, 5) = 10.

• The maximum sum score of nums is 10.

2. Input: nums = [-3, -5]
Output: -3
Explanation:

• At index 0: max(-3, -3 - 5) = max(-3, -8) = -3.

• At index 1: max(-3 - 5, -5) = max(-8, -5) = -5.

• The maximum sum score of nums is -3.

▎Challenge:

Write a function maximumSumScore(nums) that takes an integer array as input and returns the maximum sum score.

if u want help dm me.

i will respond as soon as possible