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question:A company is organizing a corporate event and needs to distribute gift bags among its employees. Each gift bag has a weight restriction, and the company wants to ensure that the selected gifts do not exceed this weight limit while maximizing the total value of the gifts. You are given a list of gifts, where each gift has a specific weight and value. Determine the maximum total value of gifts that can be placed in a gift bag without exceeding the weight restriction. -----Constraints----- - The number of gifts, n, is an integer between 1 and 100 (inclusive). - Each gift's weight and value are integers between 1 and 1000 (inclusive). - The weight limit of the gift bag, W, is an integer between 1 and 10000 (inclusive). -----Input----- Input is given from Standard Input in the following format: n W weight1 value1 weight2 value2 ... weightn valuen -----Output----- Print the maximum total value of the gifts that can be placed in the gift bag without exceeding the weight restriction. -----Sample Input----- 4 10 5 60 3 50 4 70 2 30 -----Sample Output----- 150 Here, the optimal choice is to select the gifts with weights 5, 3, and 2, which gives a total value of 60 + 50 + 30 = 140.
answer:def knapsack(n, W, items): Returns the maximum total value of gifts that can be placed in the gift bag without exceeding the weight restriction. :param n: Number of gifts :param W: Weight limit of the gift bag :param items: List of tuples, where each tuple contains weight and value of a gift :return: Maximum total value dp = [[0] * (W + 1) for _ in range(n + 1)] for i in range(1, n + 1): weight, value = items[i - 1] for w in range(W + 1): if weight <= w: dp[i][w] = max(dp[i - 1][w], dp[i - 1][w - weight] + value) else: dp[i][w] = dp[i - 1][w] return dp[n][W] def main(): import sys input = sys.stdin.read data = input().split() n = int(data[0]) W = int(data[1]) items = [(int(data[i * 2 + 2]), int(data[i * 2 + 3])) for i in range(n)] print(knapsack(n, W, items)) if __name__ == "__main__": main()
question:You are given two arrays of integers `A` and `B`, both of size `n`. Your task is to determine if you can obtain array `B` by removing some (possibly zero) elements from array `A` without changing the order of the remaining elements in `A`. Input The first line contains an integer `n` (1 ≤ n ≤ 1000) — the size of arrays `A` and `B`. The next line contains `n` integers a1, a2, ..., an (1 ≤ ai ≤ 1000) — the elements of array `A`. The next line contains `n` integers b1, b2, ..., bn (1 ≤ bi ≤ 1000) — the elements of array `B`. Output Print "YES" if array `B` can be obtained from array `A` by removing some elements without changing the order of the remaining elements. Otherwise, print "NO". Examples Input 5 1 2 3 4 5 2 4 5 Output YES Input 6 1 2 3 4 5 6 1 3 6 5 Output NO Input 4 4 3 2 1 4 3 2 1 Output YES
answer:def can_obtain_b_from_a(n, A, B): Determines if array B can be obtained from array A by removing some elements without changing the order of the remaining elements. :param n: integer, size of arrays A and B :param A: list of integers, array A :param B: list of integers, array B :return: string "YES" if B can be obtained from A, otherwise "NO" i, j = 0, 0 while i < len(A) and j < len(B): if A[i] == B[j]: j += 1 i += 1 if j == len(B): return "YES" else: return "NO"
question:You are managing a warehouse and need to ensure that products are stored and organized efficiently. The warehouse can be represented as a grid of cells, where each cell can either be empty or contain a product. Each type of product has a unique identifier (a positive integer). Your task is to process a series of operations on the grid. The operations include adding products, removing products, and querying the warehouse to check the current configuration and quantity of specific products. Consider the warehouse grid is of size m x n. **Operations:** 1. **Add Product:** This operation adds a product to a specified cell in the grid. If the cell already contains a product, it will be replaced by the new product. Format: `ADD x y id` (Add product with id `id` to cell at coordinates `(x, y)`) 2. **Remove Product:** This operation removes the product from a specified cell in the grid. Format: `REMOVE x y` (Remove product from cell at coordinates `(x, y)`) 3. **Query Product Quantity:** This operation queries the number of cells in the grid that contain a product with a specific identifier. Format: `QUERY id` (Return the number of cells containing product with id `id`) Write a program to handle these operations efficiently. # Input: - The first line contains two integers, `m` and `n` (1 ≤ m, n ≤ 100), representing the dimensions of the warehouse grid. - The second line contains a single integer `k` (1 ≤ k ≤ 1000), representing the number of operations. - The next `k` lines describe the operations in the format specified above. # Output: For each `QUERY` operation, output the result on a new line. # Example **Input:** ``` 3 3 7 ADD 1 1 2 ADD 2 2 3 ADD 3 3 2 REMOVE 1 1 QUERY 2 QUERY 3 QUERY 4 ``` **Output:** ``` 1 1 0 ``` # Explanation 1. After the operations "ADD 1 1 2" and "ADD 3 3 2", there are two cells containing the product with id `2`: `(1, 1)` and `(3, 3)`. 2. The operation "REMOVE 1 1" leaves only one cell containing the product with id `2`: `(3, 3)`. 3. The "QUERY 2" operation results in `1` since there's only one cell with product id `2`. 4. The "QUERY 3" operation results in `1` since there's one cell with product id `3`. 5. The "QUERY 4" operation results in `0` since no cells contain the product id `4`.
answer:def manage_warehouse(operations, m, n): Manages warehouse operations and returns results for QUERY operations. Parameters: operations (list of str): A list of operations to process. m (int): Number of rows in the warehouse grid. n (int): Number of columns in the warehouse grid. Returns: list of int: Results of QUERY operations. warehouse = [[0] * n for _ in range(m)] product_count = {} results = [] for op in operations: parts = op.split() command = parts[0] if command == "ADD": x, y, id = int(parts[1]) - 1, int(parts[2]) - 1, int(parts[3]) if warehouse[x][y] != 0: old_id = warehouse[x][y] product_count[old_id] -= 1 if product_count[old_id] == 0: del product_count[old_id] warehouse[x][y] = id product_count[id] = product_count.get(id, 0) + 1 elif command == "REMOVE": x, y = int(parts[1]) - 1, int(parts[2]) - 1 if warehouse[x][y] != 0: product_id = warehouse[x][y] product_count[product_id] -= 1 if product_count[product_id] == 0: del product_count[product_id] warehouse[x][y] = 0 elif command == "QUERY": id = int(parts[1]) results.append(product_count.get(id, 0)) return results
question:Write a function that receives a string representing a mathematical expression and checks if the parentheses in the expression are balanced. A balanced string is one where each opening parenthesis '(' has a corresponding closing parenthesis ')', and they are properly nested. The function should follow these constraints: - Return `True` if the parentheses are balanced, and `False` otherwise. - The string can contain other characters besides parentheses. - Ignore non-parenthesis characters when evaluating the balance of the parentheses. - An empty string is considered balanced. Examples: - `"(a + b) * (c + d)"` -> `True` - `"((a + b) * (c + d)"` -> `False` - `"((a+b))"` -> `True` - `"a + b) * c + d("` -> `False` - `""` -> `True`
answer:def is_balanced(expression): Returns True if the parentheses in the expression are balanced, False otherwise. stack = [] for char in expression: if char == '(': stack.append(char) elif char == ')': if not stack: return False stack.pop() return len(stack) == 0