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question:You are tasked with managing a robot in a grid-sized warehouse with obstacles, and your goal is to navigate the robot from a start position to a target position. The warehouse can be represented as a grid where each cell is either empty or contains an obstacle. The robot can move in four directions: up, down, left, and right, but it cannot move through obstacles. Your objective is to determine the minimum number of moves required for the robot to reach the target position from the start position. If it is not possible for the robot to reach the target, return -1. -----Input----- The first line of input contains three integers n, m and k (1 leq n, m leq 1000,1 leq k leq n cdot m) — the number of rows, the number of columns and the number of obstacles in the warehouse. The next k lines each contain two integers x_{i} and y_{i} (1 leq x_i leq n, 1 leq y_i leq m) — the row and column indices of the obstacles. The next line contains two integers x_s and y_s (1 leq x_s leq n, 1 leq y_s leq m) — the starting position of the robot. The final line contains two integers x_t and y_t (1 leq x_t leq n, 1 leq y_t leq m) — the target position of the robot. -----Output----- Print an integer representing the minimum number of moves required for the robot to reach the target position from the start position. If it is not possible, output -1. -----Examples----- Input 5 5 3 2 2 3 3 4 4 1 1 5 5 Output 8 Input 5 5 10 2 2 2 3 3 2 3 4 4 2 4 5 5 1 5 2 5 3 5 4 1 1 5 5 Output -1 -----Note----- For the first test, Starting from (1,1), the robot will take a path around the obstacles to reach (5,5) in minimum 8 moves. For the second test, The target position is not reachable due to the obstacles blocking all possible paths.

answer:from collections import deque def min_moves_to_target(n, m, k, obstacles, start, target): # Create the warehouse grid and mark obstacles grid = [[0] * m for _ in range(n)] for ox, oy in obstacles: grid[ox - 1][oy - 1] = 1 # Marking obstacle cells as 1 # Starting and target positions sx, sy = start tx, ty = target # Directions for moving in the grid directions = [(-1, 0), (1, 0), (0, -1), (0, 1)] # Up, Down, Left, Right # BFS queue initialized with starting position queue = deque([(sx - 1, sy - 1, 0)]) # (x, y, steps) visited = set() visited.add((sx - 1, sy - 1)) while queue: x, y, steps = queue.popleft() # Check if target is reached if (x, y) == (tx - 1, ty - 1): return steps # Explore all possible directions for dx, dy in directions: nx, ny = x + dx, y + dy if 0 <= nx < n and 0 <= ny < m and (nx, ny) not in visited and grid[nx][ny] == 0: visited.add((nx, ny)) queue.append((nx, ny, steps + 1)) # If target is not reachable, return -1 return -1

question:The king of Kingdom XYZ is planning to build a new road network within the kingdom. The kingdom consists of N cities, numbered from 1 to N, and M bidirectional roads connecting some pairs of cities. Each road has a certain length associated with it. Due to budget constraints, the king wants to ensure that the total length of the roads in the new network is minimized, but at the same time, the network should be designed such that every city is connected directly or indirectly through the roads. You, as the chief engineer, are tasked with creating this optimized road network. Specifically, you need to find the minimum possible total length of roads that are necessary to connect all the cities together. If it is not possible to connect all the cities, return -1. Input: - The first line contains two integers N and M, the number of cities and the number of roads respectively. - The next M lines each contain three integers u, v, and w representing a bidirectional road between cities u and v with length w. Output: - Output a single integer which is the minimum total length of roads required to connect all the cities, or -1 if it's not possible. Constraints: - 1 ≤ N ≤ 10^4 - 0 ≤ M ≤ 10^5 - 1 ≤ w ≤ 10^6 - Each road connects two different cities u and v (1 ≤ u, v ≤ N). SAMPLE INPUT 4 5 1 2 1 1 3 2 3 4 4 1 4 3 2 3 2 SAMPLE OUTPUT 6 Explanation: A minimum spanning tree (MST) of the given graph would be: - road between city 1 and city 2 with length 1, - road between city 2 and city 3 with length 2, - road between city 1 and city 4 with length 3. The total length of these roads is 1 + 2 + 3 = 6, which is the minimum total length required to ensure all cities are connected.

answer:def find_minimum_spanning_tree(N, M, roads): Returns the minimum possible total length of roads that connects all cities, or -1 if not possible to connect all cities. if M == 0: return -1 if N > 1 else 0 # No roads and more than one city means we can't connect all cities. from heapq import heappop, heappush # Start with a graph represented as adjacency list graph = {i: [] for i in range(1, N+1)} for u, v, w in roads: graph[u].append((w, v)) graph[v].append((w, u)) # Prim's Algorithm to find MST min_heap = [(0, 1)] # (cost, start_node) visited = set() total_cost = 0 while min_heap and len(visited) < N: cost, u = heappop(min_heap) if u not in visited: total_cost += cost visited.add(u) for next_cost, v in graph[u]: if v not in visited: heappush(min_heap, (next_cost, v)) return total_cost if len(visited) == N else -1

question:You own a school and have a list of students in your school, each student has a number of toys. You want to form groups such that every student in a group has the same number of toys. The challenge is to minimize the number of groups formed. Each student is represented by the number of toys they have. You need to determine the minimum number of groups required. Input format The first line of the input contains an integer N, the number of students. The next line contains N space-separated integers, each representing the number of toys a student has. Output format Print a single integer, the minimum number of groups required. Constraints 1 ≤ N ≤ 100,000 0 ≤ Number of toys per student ≤ 1,000,000 SAMPLE INPUT 5 1 2 2 3 3 SAMPLE OUTPUT 3

answer:def min_groups_required(n, toys): Determines the minimum number of groups such that each student in a group has the same number of toys. Args: n: Integer, the number of students. toys: List of integers, number of toys each student has. Returns: Integer, the minimum number of groups required. toy_count = {} # Count the frequency of each toys number for toy in toys: if toy in toy_count: toy_count[toy] += 1 else: toy_count[toy] = 1 # The number of unique keys in toy_count represents the number of groups required return len(toy_count)

question:A local bakery sells a variety of pastries and wants to analyze the sales performance of each type of pastry over a given number of days. For this, they have recorded the number of units sold for each pastry type daily. The bakery owner wants to calculate the total units sold for each type of pastry and determine which pastry type had the highest average sales per day. If there is a tie, you only need to print the lowest index pastry type. Write a program that processes the sales data and outputs the information as specified. Input: Each test case is formed as follow: - The first line contains a positive integer P, the number of pastry types (1 ≤ P ≤ 50). - The second line contains a positive integer D, the number of days the sales were tracked (1 ≤ D ≤ 30). - The next D lines each contain P integers separated by spaces, representing the number of units sold for each pastry type on that day. Each value T is such that 0 ≤ T ≤ 100. Output: For each test case, output two lines: 1. The first line contains P integers separated by spaces, where each integer is the total number of units sold for the corresponding pastry type. 2. The second line contains the index (1-based) of the pastry type with the highest average sales per day. Example: Input: 3 4 10 20 30 15 25 10 20 10 25 5 30 15 Output: 50 85 80 2

answer:def analyze_sales(P, D, sales): total_sales_per_pastry = [0] * P for day_sales in sales: for i in range(P): total_sales_per_pastry[i] += day_sales[i] average_sales_per_pastry = [total_sales_per_pastry[i] / D for i in range(P)] max_average_index = average_sales_per_pastry.index(max(average_sales_per_pastry)) + 1 return total_sales_per_pastry, max_average_index def format_output(total_sales_per_pastry, max_average_index): return ( ' '.join(map(str, total_sales_per_pastry)), str(max_average_index) )