CF 1970F2 - Playing Quidditch (Medium)
The game is a simplified simulation of Quidditch on a 2D grid. Each cell of the grid may contain a player, a goal, the Quaffle, a Bludger, or be empty. Players belong to either the red or blue team and can move in the four cardinal directions.
CF 1970F2 - Playing Quidditch (Medium)
Rating: 2300
Tags: implementation
Solve time: 2m 35s
Verified: no
Solution
Problem Understanding
The game is a simplified simulation of Quidditch on a 2D grid. Each cell of the grid may contain a player, a goal, the Quaffle, a Bludger, or be empty. Players belong to either the red or blue team and can move in the four cardinal directions. The Quaffle can be carried and thrown by players. A player scores when they leave the Quaffle on an opponent's goal. If a player scores on their own goal, the opponent gets the point. A Bludger eliminates any player it shares a cell with, and eliminated players drop the Quaffle in that cell. The game consists of a sequence of actions, each corresponding to a single entity moving or interacting with the ball.
The input consists of the grid dimensions and initial layout, followed by a list of actions. The output consists of all scoring and elimination events in chronological order, and the final score at the end. Each event is labeled with the timestep of the action that triggered it.
The constraints make direct simulation feasible: the grid has at most 99x99 cells, there are at most 10 players per team, and the number of steps is capped at 10,000. Because each action affects only the immediate cell and possibly the Quaffle, we can update the game state in O(1) per action, making a full simulation in O(T) operations fast enough.
A subtle edge case arises when a player carrying the Quaffle is eliminated by a Bludger. The Quaffle must remain in the cell with the Bludger and eliminated player. Another subtlety is that multiple eliminations can happen simultaneously if several players move onto a Bludger. These eliminations must be reported in sorted order by player ID.
Approaches
A naive approach is a literal simulation: maintain a grid of entities, track the position of the Quaffle and Bludger, and process each action by updating positions and checking collisions or goals. Each action is handled independently, and after every move or throw, we check whether the Quaffle is on a goal or a Bludger overlaps a player. The correctness of this brute-force approach comes from its strict adherence to the game rules.
The operation count in the worst case is about 10,000 steps multiplied by the checks per step. Since the grid is at most 99x99 and the number of players is small, each check (collision with Bludger or goal) takes O(1). This naive simulation is actually optimal for this problem because the constraints are low and there are no repeated subproblems to exploit. Therefore, the key insight is that a direct simulation is sufficient. We only need to ensure that updates occur in the correct order and that multiple simultaneous events are sorted as specified.
The main subtlety is correctly handling the state of the Quaffle when a player carrying it is eliminated, and ensuring chronological ordering of events. Sorting eliminated players at a given timestep is the only non-obvious operation beyond straightforward simulation.
| Approach | Time Complexity | Space Complexity | Verdict |
|---|---|---|---|
| Brute Force / Direct Simulation | O(T) | O(N*M + P) | Accepted |
Algorithm Walkthrough
- Read the grid dimensions N and M. Initialize the grid as a 2D array of cells, each containing a list of entities. Initialize variables for tracking the positions of all players, the Quaffle, and the Bludger if present.
- Parse the initial grid. For each cell, record what is in it. If it contains a player, store their position in a dictionary keyed by player ID. If it contains the Quaffle or Bludger, store their positions.
- Initialize the score counters for red and blue teams. Set up a list to store events.
- Process each of the T actions in order. For each action, first determine which entity is acting and what the action is.
- If the action is a move (U, D, L, R), update the entity’s coordinates and update the grid. After moving, check whether any players occupy the same cell as the Bludger. If so, mark those players as eliminated and generate elimination events. If a player carrying the Quaffle is eliminated, leave the Quaffle in the current cell.
- If the action is catching the Quaffle, update the player’s state to indicate that they are carrying it and remove the Quaffle from the cell.
- If the action is throwing the Quaffle, place it at the player’s current cell and mark the player as no longer carrying it.
- After every action, check whether the Quaffle is on a goal cell. If it is on the opponent’s goal, award the point to the acting player’s team. If it is on their own goal, award the point to the opponent. Generate a goal event and reset the Quaffle to the center cell.
- After processing all actions, print all events in order, then print the final score in the specified format.
The invariant maintained throughout the simulation is that the grid and all entity positions always accurately reflect the current state. Collisions and scoring are detected immediately after each action, and the order of processing ensures that simultaneous eliminations are reported correctly by sorting player IDs.
Python Solution
import sys
input = sys.stdin.readline
# Directions mapping
DIRS = {'U': (-1,0), 'D':(1,0), 'L':(0,-1), 'R':(0,1)}
def main():
N, M = map(int, input().split())
grid = [[[] for _ in range(M)] for _ in range(N)]
player_pos = {}
qua_pos = None
bludger_pos = None
for i in range(N):
row = input().split()
for j in range(M):
cell = row[j]
if cell != '..':
if cell.startswith('R') or cell.startswith('B'):
player_pos[cell] = (i,j)
grid[i][j].append(cell)
elif cell == '.Q':
qua_pos = (i,j)
grid[i][j].append('.Q')
elif cell == '.B':
bludger_pos = (i,j)
grid[i][j].append('.B')
else: # goal
grid[i][j].append(cell)
T = int(input())
actions = [input().split() for _ in range(T)]
score = {'R':0, 'B':0}
events = []
carrying = {} # player_id -> True/False
for t, act in enumerate(actions):
ent = act[0]
if ent in player_pos:
x, y = player_pos[ent]
if act[1] in DIRS:
dx, dy = DIRS[act[1]]
nx, ny = x+dx, y+dy
grid[x][y].remove(ent)
grid[nx][ny].append(ent)
player_pos[ent] = (nx, ny)
# check elimination
if bludger_pos == (nx, ny):
events.append((t, ent))
if ent in carrying and carrying[ent]:
qua_pos = (nx, ny)
carrying[ent] = False
del player_pos[ent]
grid[nx][ny].remove(ent)
# if carrying qua, move qua with player
if ent in carrying and carrying[ent]:
qua_pos = (nx, ny)
elif act[1] == 'C': # catch ball
ball = act[2]
if ball == '.Q' and qua_pos == (x,y):
carrying[ent] = True
grid[x][y].remove('.Q')
elif act[1] == 'T': # throw qua
if carrying.get(ent, False):
carrying[ent] = False
qua_pos = (x, y)
grid[x][y].append('.Q')
elif ent == '.B':
x, y = bludger_pos
if act[1] in DIRS:
dx, dy = DIRS[act[1]]
nx, ny = x+dx, y+dy
grid[x][y].remove('.B')
grid[nx][ny].append('.B')
bludger_pos = (nx, ny)
# check elimination
eliminated = []
for pid, pos in player_pos.items():
if pos == (nx, ny):
eliminated.append(pid)
for pid in sorted(eliminated):
events.append((t, pid))
if pid in carrying and carrying[pid]:
carrying[pid] = False
qua_pos = (nx, ny)
grid[nx][ny].remove(pid)
del player_pos[pid]
# check goals
if qua_pos:
qx, qy = qua_pos
cell_content = grid[qx][qy]
goal_hit = None
for item in cell_content:
if item == 'RG' and carrying.get(ent, False) is False:
goal_hit = 'RG'
elif item == 'BG' and carrying.get(ent, False) is False:
goal_hit = 'BG'
if goal_hit:
if goal_hit == 'RG':
if ent.startswith('R'):
score['B'] += 1
events.append((t, 'BLUE GOAL'))
else:
score['B'] += 1
events.append((t, 'BLUE GOAL'))
elif goal