Problem Statement: You are given a starting number of 1. Your task is to reach a target number, t, using two available operations: operator_add: Adds a fixed number, x, to the current number. operator_multiply: Multiplies the current number by a fixed number, y. The objective is to reach the target number, t, by using these operations sequentially. Among all possible ways to reach t, pick the sequence that Maximizes the number of times operator 2 is applied Minimizes the number of times operator 1 is applied among all sequences that maximize usage of operator 2 Constraints: 1 ≤ t ≤ 10^20 1 ≤ x ≤ 1000 2 ≤ y ≤ 1000 Input Format: Three integers: t, x, and y. Output Format: If a solution exists: A list of strings where each string represents an operation followed by the number of times it is applied. The solution should be compact in the sense that consecutive occurrences of the same operator collapse to 1 element in the list. This means that if an element in the list correspond to "operator_add", then the next one should correspond to "operator_multiply" and vice versa. For example, if you want to apply the sequence "operation_add, operation_add, operation_multiply, operation_multiply, operation_multiply, operation_add", then the output should be: ["operator_add 2", "operator_multiply 3", "operator_add 1"]. If no solution exists: A list with one element: "no_solution". Examples: Input 1: t = 54, x = 1, y = 3 Output 1: ["operator_add 1", "operator_multiply 3"] Explanation: Starting from 1, add 1 once to get 2, then multiply the result by 3 thrice (2*3^3 = 54) to get 54. The sequence thus results in the target number. Using operator 2 at least 4 times will result in a number bigger than 54 (3^4 > 54). Hence operator 2 can maximally be used three times. For operator 2 being used three times, operator 1 needs to be used at least once because 3^3 is not equal to 54. Therefore it minimizes the usage of operator 1. Input 2: t = 3 x = 4 y = 4 Output 2: ["no_solution"] Explanation: Both operators increase the number and applying any operator once already results in a number that is too big. [execution time limit] 4 seconds (py3) [memory limit] 1 GB [input] integer64 t Target number: the number you want to reach by sequentially applying the operators. [input] integer64 x By how much you increase the current result if you apply operator1. [input] integer64 y By how much you multiply the current result if you apply operator2. [output] array.string List of strings where element i equals "operator_add" or "operator_multiply" followed by how many times you want to apply it. In case there is no solution, output is ["no_solution"].

You want to buy a billboard featuring the name of your company. The price of the billboard is the sum of the price of the letters in your company name. For example, the price of company name "aga" is two times the price of letter "a" plus the price of letter "g". You don't know the price per letter, but you do know the prices of other company names. Can you derive the price of your company name? A company name only contains letters from the alphabet. There are 26 different letters and they are all lower case. You are given: your_company_name: a string representing the name of your company other_company_names: a list of strings where each element is the name of another company other_company_prices: a list of real numbers where other_company_prices[i] is the price of other_company_names[i] Return the price of your company name if it can be derived, otherwise return -1 Constraints: The length of a company name is maximally 100 len(other_company_names) = len(other_company_prices) <= 100 For each price in other_company_prices: -10^6 <= price <= 10^6 Sample Input: your_company_name = "aabc" other_company_names = ["ab", "ac", "bd"] other_company_prices = [99.5, 1000.2, 2000.8] Sample Output: 1099.7 Explanation: The letters in "aabc" is the union of the letters in "ab" and "ac", hence the price is the sum. Sample Input: your_company_name = "d" other_company_names = ["aab", "acc"] other_company_prices = [500, 6000] Sample Output: -1 Explanation: The letter d doesn't appear in any other company name and therefore we cannot derive its price. [execution time limit] 4 seconds (py3) [memory limit] 1 GB [input] string your_company_name String representing the name of your company [input] array.string other_company_names List containing the names of other companies. [input] array.float other_company_prices List where element i contains the prices of other_company_names[i] [output] float Price of your company