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question:Alicia loves playing with numbers, and she has a new game for You. She will give you an array of integers and multiple queries. The task is to process the queries and return the results accordingly. There are three types of queries: - Query type 1: Alicia gives you an integer i and k, you need to add k to the i^{th} element of the array. - Query type 2: Alicia gives you an integer i and you need to print the i^{th} element of the array. - Query type 3: Alicia gives you two integers i, j, you need to find the sum of the elements between i^{th} and j^{th} indices (both inclusive). -----Input:----- - First line will contain T, the number of test cases. Then the test cases follow. - The first line of each test case contains two space-separated integers N (length of array) and Q (number of queries). - The second line contains N space-separated integers, the elements of the array. - Next Q lines follow. - For a query of type 1, there will be a line containing three space-separated integers 1, i, and k. - For a query of type 2, there will be a line containing two space-separated integers 2 and i. - For a query of type 3, there will be a line containing three space-separated integers 3, i, and j. -----Output:----- For each query of type 2, print the i^{th} element of the array. For each query of type 3, print the sum of elements from i^{th} to j^{th} indices (both inclusive). -----Constraints----- - 1 leq T leq 10^2 - 1 leq N leq 10^5 - 1 leq Q leq 10^5 - 1 leq a[i] leq 10^9 - 1 leq k leq 10^9 - 0 leq i,j leq N-1 -----Sample Input----- 1 5 3 1 2 3 4 5 1 2 10 2 2 3 1 3 -----Sample Output----- 13 9 -----EXPLANATION:----- The initial array is [1, 2, 3, 4, 5]. For the first query, we add 10 to the element at index 2, so the array becomes [1, 2, 13, 4, 5]. For the second query, the element at index 2 is 13. For the third query, the sum of elements from index 1 to index 3 is 2 + 13 + 4 = 19.
answer:def process_queries(T, test_cases): results = [] for t in range(T): N, Q = test_cases[t][0] array = test_cases[t][1] queries = test_cases[t][2] for query in queries: if query[0] == 1: # Query type 1: add k to the i-th element i, k = query[1], query[2] array[i] += k elif query[0] == 2: # Query type 2: print the i-th element i = query[1] results.append(array[i]) elif query[0] == 3: # Query type 3: sum from i-th to j-th indices i, j = query[1], query[2] results.append(sum(array[i:j+1])) return results # Now parse the input and call the above function def main(input_lines): index = 0 T = int(input_lines[index]) index += 1 test_cases = [] for _ in range(T): N, Q = map(int, input_lines[index].split()) index += 1 array = list(map(int, input_lines[index].split())) index += 1 queries = [] for _ in range(Q): queries.append(list(map(int, input_lines[index].split()))) index += 1 test_cases.append(((N, Q), array, queries)) results = process_queries(T, test_cases) for result in results: print(result) # Example usage: input_lines = [ "1", "5 3", "1 2 3 4 5", "1 2 10", "2 2", "3 1 3" ] main(input_lines)
question:Write a function that determines the maximum possible sum of a contiguous subarray of a given integer array. This problem is a classic example used to test the understanding of dynamic programming principles. To make it interesting, you are not only required to determine the maximum sum, but also the subarray that produces this sum. If multiple subarrays produce the same maximum sum, return the subarray which appears first. Input format: An integer array represented as a single string of space-separated integers. Output format: The maximum sum as an integer and the subarray as an array of integers. Constraints: - The array will contain at least one integer. - The elements of the array are between -10^5 to 10^5. - The length of the array is between 1 and 10^5. SAMPLE INPUT 1 -2 3 4 -1 2 1 -5 4 SAMPLE OUTPUT 9 [3, 4, -1, 2, 1]
answer:def max_subarray(array_str): Returns the maximum sum of a contiguous subarray and the subarray itself. nums = list(map(int, array_str.split())) max_sum = float('-inf') current_sum = 0 start = end = s = 0 for i in range(len(nums)): if current_sum <= 0: current_sum = nums[i] s = i else: current_sum += nums[i] if current_sum > max_sum: max_sum = current_sum start = s end = i return max_sum, nums[start:end+1]
question:Create a function that receives a string input representing a formula in a very simplified version of a spreadsheet. The formula may contain only basic arithmetic operations (`+`, `-`, `*`, `/`), and references to cells. Cells are identified by letters (A-Z) followed by numbers (1-99). The function should interpret the formula and return the calculated result. Assume that the values of the referenced cells are provided in a dictionary where the keys are the cell identifiers and the values are the cell values (only integers). For example: ```python You get a formula and a dictionary with cell values as input: formula = "A1 + B2 * 3" cell_values = {"A1": 5, "B2": 4} The result should be: 17 ``` A few more examples: ```python formula = "C1 - D1 / E1" cell_values = {"C1": 10, "D1": 6, "E1": 2} ---> The result should be: 7 formula = "F3 * 2 + G4" cell_values = {"F3": 3, "G4": 8} ---> The result should be: 14 ``` Note: You can assume that cell references will always be in uppercase and the input formula will not contain any spaces except between operands and operators.
answer:import re def evaluate_formula(formula, cell_values): Evaluates a formula in a simplified version of a spreadsheet. :param formula: a string containing the formula to be evaluated :param cell_values: a dictionary containing the cell values :return: the evaluated result of the formula def replace_match(match): cell = match.group(0) return str(cell_values.get(cell, 0)) # Replace the cell references with their corresponding values formula_with_values = re.sub(r'[A-Z][1-9][0-9]?', replace_match, formula) # Evaluate the formula result = eval(formula_with_values) return result
question:# Task Given a 2D grid of size `n x m` representing a maze where `1` represents walls and `0` represents paths, determine the shortest path from the top-left corner `(0,0)` to the bottom-right corner `(n-1,m-1)` while avoiding the walls. You can move up, down, left, or right, but you cannot move through the walls. If there is no possible path, return `-1`. # Example For `grid = [[0, 1, 0, 0, 0], [0, 1, 0, 1, 0], [0, 0, 0, 1, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0]]`, the output should be `7`. The shortest path from `(0, 0)` to `(4, 4)` is of length `7` (0-index based): ``` [[0, 1, 0, 0, 0], [0, 1, 0, 1, 0], [0, 0, 0, 1, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 0]] ``` Steps (0,0) → (1,0) → (2,0) → (2,1) → (2,2) → (3,2) → (4,2) → (4,3) → (4,4). For `grid = [[0, 1], [1, 0]]`, the output should be `-1`. There is no path from `(0, 0)` to `(1, 1)`. # Input/Output - `[input]` 2D integer array `grid` `0` represents a path and `1` represents a wall. Constraints: `2 ≤ grid.length ≤ 50` `2 ≤ grid[0].length ≤ 50` - `[output]` an integer The length of the shortest path from `(0, 0)` to `(n-1, m-1)` while avoiding walls; return `-1` if no path exists.
answer:from collections import deque def shortest_path_maze(grid): Function to find the shortest path in a maze from top-left to bottom-right. Returns the length of the shortest path or -1 if no path exists. if not grid or not grid[0]: return -1 n, m = len(grid), len(grid[0]) if grid[0][0] == 1 or grid[n-1][m-1] == 1: return -1 directions = [(1, 0), (-1, 0), (0, 1), (0, -1)] queue = deque([(0, 0, 1)]) visited = set((0, 0)) while queue: x, y, dist = queue.popleft() if x == n-1 and y == m-1: return dist for dx, dy in directions: nx, ny = x + dx, y + dy if 0 <= nx < n and 0 <= ny < m and grid[nx][ny] == 0 and (nx, ny) not in visited: visited.add((nx, ny)) queue.append((nx, ny, dist + 1)) return -1