Unique Encryptions in Nexus Prime

| Problem Statement
In the futuristic city of Nexus Prime, a tech organization stores large amounts of encrypted data files. Each file's content is scrambled using different arrangements of letters to create unique encryption patterns. Dr. Axiom, the lead engineer, needs to figure out how many different ways a file can be scrambled (encrypted). As the size of the files grows, Dr. Axiom must find a fast way to count all possible unique arrangements of characters in the file.

Your task is to help Dr. Axiom by writing a program that, given a string s (representing the encrypted file), calculates how many unique ways the letters in the string can be rearranged. Return the answer modulo 10^9+7 to manage large numbers.

For example, if the string is "hidden code", there are many possible ways to rearrange the letters, like "hidden code", "ihdden code", "diden hode", "denh codei", and more. Your goal is to find out how many such unique arrangements exist.

Input Format

The first and only line consists of a single string S which represents the contents of the encrypted file. The string consists of lowercase English letters and spaces "'. There is a single space between consecutive words. Show More

Counting Repeated Game Scores

During a school sports day event, students record their scores, However, some students accidentally recorded the same score multiple times. Your task is to help the event organizer identify all scores that are repeated and determine the indices where each duplicate occurs.

You are given an integer N, representing the number of students, followed by a list of the ir scores. For each score that is repeated, output the score, followed by the letter 'T, and then the indices where the score appears. If no duplicates are found, return -1.

Input Format

The first line contains an integer N - the number of students.
The next N lines each contain an integer, representing a score recorded by a student.

| Output Format

For each score that appears more than once, print the score, followed by the letter'l', and then the indices where the score appears, separated by spaces. If no scores are repeated, output -1. Show More

Ruest for Mystic Numbers

Problem Statement

the land of Numeria, the ancient sages have discovered a magical property in me numbers that they call "Mystic Numbers". These numbers hold special wers that can influence the harmony of the universe. You, as an apprentice to e sages, have been tasked with identifying these MysticNumbers.

The sages define a Mystic Number as follows:
1. It must b e an even number.
2. When the digits of the number are repeatedly summed until a single- digit number is obtained, this single-digit result must be even.

You are given two boundaries, N1 and N2, which represent a range of numbers. your quest is to find all the Mystic Numbers within this range and report them back to the sages.

Input Format

The input contains two space-separated integers N1 and N2 denoting the two
poundaries range of numbers.

Output Format

Print a list of all Mystic Numbers between N1 and N2.

Constraints

1<= N1, N2 ≤ 10^9 Show More

Will We Meet

In the bustling town of Skyline Street, Jatin and Mano, two childhood friends, often challenge each other to exciting games. One day, they came up with a unique adventure-"The Climb of Heights."

Skyline Street consists of N buildings, each with a unique height, forming a magnificent skyline. The friends decide to start from their respective buildings and see if they can meet on a taller building by following a simple rule:

They can only move to the right (towards buildings with greater heights than their current one).
Once they reach a taller building, they continue the journey until no taller building exists in front of them.

Excited by the challenge, they come to you, the town's wise strategist, to predict their meeting point. Given a list H representing the heights of the buildings and multiple queries where Jatin and Mano start from different buildings, your task is to determine the leftmost building where they can meet. If no such meeting point exists, return -1.

Can you help Jatin and Mano navigate their way through Skyline Street and find out if they can meet atop a grand building?

|Input Format

The first line of input contains two integers N and 'O' representing the number of buildings in the city and 'O' the number of queries.

The second line of input contains N space-separated integers representing the heights of the buildings.

The next Q lines of input contain 2 space-separated integers J and M representing the starting positions of Jatin and Mano. Show More

Homework

The distance between 2 points (x y1) and (x2 y2) on a 2D plane is defined as But Paul, the math teacher, defined the distance between 2 points (x1, y1) and (x2,y2) on a 2D plane as min(|z1-z2l, [y/1 - val) in his class. As homework, he gave N points to the students and asked Min smallest distance between all possible pairs of points according to his new definition. You are given N poin ts on a 2D plane.

Help the students to complete the homework.
Calculate the Mh smallest distance according to Paul's new definition of distance.
Notes
- Assume #based indexing.
- All N points are unique.
- Mth smallest distance stands for Mth element you get by arranging all possible distances in increasing order.

Function description
Complete the function homework. This function takes the following 3 parameters and returns the required answer, an integer, the Mth smallest distance:
- N: Represents an integer denoting total points
- Points: Represents an array of pairs representing points on a 2D plane
- M. Represents the required smallest distance Show More

The city of Hackerland can be represented using a grid with n rows and m columns containing an empty cell represented by a '*' and a blocked cell represented by a #. Traveling is allowed only through empty cells. The people of Hackerland are required to travel from a starting cell defined by the character 'S' to an ending cell represented by a character 'E'.

The people can jump a length of any integer k in all four directions from a given cell i.e. up, down, left, and right. However, if the jump length kis greater than 1, the next jump must be made in the same direction, For example, a hacker is allowed to jump 3 units towards the right, followed by 1 unit towards the right, and then 3 units towards the left. They however cannot jump 3 units towards the right followed by 1 unit towards the left as direction change is not allowed if the previous jump was of length greater than 1. Note that the last jump in any jump sequence is always of length 1.

The jump can be made over a blocked cell as well as long as both starting and ending cells are empty.

Given the map of Hackerland as a 2g matrix grid, that contains exactly one 'S' and 'E' each, find the minimum number of jumps required to travel from Sto E. Report -1 if it is not possible to reach E from S.

Example
Suppose n = 5, m = 6 and grid = ["S **** #". ******** ******* ******** " ***** E") Show More

Given an array of strings, each of the same length, and a target string, construct the target string using characters from the strings in the given array such that the indices of the characters in the order in which they are used form a strictly increasing sequence. Here the index of a character is the
position at which it appears in the string. Note that it is acceptable to use multiple characte rs from the same string.

Determine the number of ways to construct the target string. One construction is different from another if either the sequences of indices they use are different or the sequences are the same but there exists a character at some index such that it is chosen from a different string in these constructions. Since the answer can be very large, return the value modulo (10^9 + 7).

Consider an example with n = 3 strings, each of length 3. Let the array of strings be words = ["adc", "aec", "efg"], and the target string target = "ac". There are 4 ways to reach the target:

1. Select the 15t character of "adc" and the 3rd character of "adc".
2. Select the 1st character of "adc" and the 3rd character of "aec".
3. Select the 15t character of "aec" and the 3rd character of "adc".
4. Select the 1st character of "aec" and the 3rd character of "aec". Show More

A pixel color RGB is defined as a 24 bit integer. Each 8 bit integer (1 byte) represents either red, green or blue color. Each 8 bit integer has an integer value between 0 (Low intensity) and 255 (High intensity)

For the distance between two pixels having RGB values (r1, g1, b1) and (r2, 82, b2), it is calculated as follows:

d = square_root( (r1-r2)^2+ (g1-g2)^2+ (b1- b2)^2)

Given a 24-bi t binary string describing a pixel, identify which of these five colors the pixel is closest to using the Euclidean distance calculation. Then return the closest pure color: Red, Green, Blue, Black, White. Show More

Company's software team utilizes several algorithms to maintain data integrity, one of which targets the encoding of symmetrical names. Symmetrical names are unique in that they read identically in both directions, similar to palindromes in language parlance.

The chief aim of the algorithm is to rearrange the characters in the original symmetrical name according to these criteria:
- The rearra nged name is a reshuffled version of the original symmetrical name.
- The restructured name should be symmetrical as well.
- This restructured name should be lexicographically smallest among all its symmetric permutations.

Given an initial symmetrical name that contains only lowercase English characters, compute the encoded name.

A string s is considered to be lexicographically smaller than the string t of the same length if the first character in s that differs from that in t is smaller, For example, "abcd" is lexicographically smaller
than "abdc" but larger than "abad"

Note that the output encoded name could match the original name if it's already the smallest lexicographically.

Example
The original string is letters = "babab".
This can be reversed to give "abbba", which is a symmetric rearrangement of the original symmetrical name and is the smallest possible reverse order,

It satisfies all the requirements so return the string abbba. Show More

Company is focused on using sophisticated algorithms to optimize inventory turnover within its warehouse network. In this case, you're given a task related to a specific operation with an array of
inventory levels.

Formally, you are given an array of positive integers, inventoryLevels, of size n. Additionally, you have two positive integers x and y, with x being equal to or smaller than y. You can apply an inventory operation on inventoryLevels any number of times, potentially not at all.

The inventory operation involves selecting two distinct indices i and j within the array (0 < i, j< n), incrementing the value at index / in inventoryLevels by x, and decreasing the value at index j in
inventoryLevels by y.

Find the maximum possible value for the smallest level in inventoryLevels after the operations are performed.

Note: It is possible that while performing operations, elements become negative. However, after the completion of all the operations on inventoryLevels, each value should within the array
should be greater than 0.

Example
n=3
InventoryLevels = [11, 1, 2]
X=2
y=3 Show More