CF 493A - Vasya and Football

CF 493A - Vasya and Football

Rating: 1300
Tags: implementation
Solve time: 1m 38s
Verified: yes

Solution

Problem Understanding

We are given the names of the home and away teams, followed by a chronological list of card events during a football match.

Each event specifies the minute, which team the player belongs to, the player's jersey number, and whether the referee gives a yellow card or a red card.

A player is sent off in two situations. The first is receiving a direct red card. The second is receiving a yellow card when they already have one yellow card, since the second yellow automatically becomes a red-card dismissal.

The output must contain every player's first dismissal, in chronological order. If a player has already been sent off, any later cards for that player must be ignored. A player can appear in the output at most once.

The constraints are very small. There are at most 90 events, matching the length of a football match. Even a quadratic solution would perform comfortably within the limits. The challenge is not efficiency but correctly simulating the rules and handling all corner cases.

Several situations can easily cause incorrect answers.

A player may receive a direct red card and later receive another card in the input. That later event must be ignored because we only care about the first dismissal.

Example:

HOME
AWAY
2
10 h 7 r
20 h 7 y

Correct output:

HOME 7 10

A careless implementation might print the same player twice.

A second yellow card counts as a dismissal immediately.

Example:

HOME
AWAY
2
15 a 9 y
30 a 9 y

Correct output:

AWAY 9 30

If we only count yellow cards and never convert the second one into a red card, we miss the dismissal.

Players from different teams may share the same jersey number.

Example:

HOME
AWAY
2
10 h 10 r
20 a 10 r

Correct output:

HOME 10 10
AWAY 10 20

Tracking players only by number would incorrectly merge these two distinct players.

Approaches

The most straightforward solution is to simulate the match exactly as described.

For every event, we need to know how many yellow cards a player has already received and whether they have already been sent off. When a yellow card arrives, we increase the yellow-card count. If the count reaches two, we record a dismissal. When a direct red card arrives, we immediately record a dismissal.

A very naive implementation could repeatedly scan all previous events whenever a new event arrives to determine a player's current state. With at most 90 events, this would require roughly $90^2 = 8100$ operations, which is still easily fast enough.

The cleaner approach is to store each player's current state in a dictionary. Since a player is uniquely identified by both team and jersey number, we use the pair (team, number) as the key.

The key observation is that every event only affects one player. We never need to recompute information from earlier events. By maintaining the current yellow-card count and dismissal status for each player, every event can be processed in constant time.

Approach	Time Complexity	Space Complexity	Verdict
Brute Force	O(n²)	O(n)	Accepted
Optimal	O(n)	O(n)	Accepted

Algorithm Walkthrough

1. Read the home-team name and away-team name.
2. Read the number of events.
3. Create a dictionary storing the number of yellow cards for each player.
4. Create a set containing players who have already been sent off.
5. Process events in the order they appear. Since the input is already chronological, this automatically preserves the required output order.
6. For each event, build a unique player identifier (team_side, jersey_number).
7. If the player is already in the dismissed set, ignore the event and continue. A player can only be sent off once.
8. If the card is a direct red card:

a. Print the team name, player number, and current minute.

b. Mark the player as dismissed. 9. If the card is a yellow card:

a. Increase that player's yellow-card count.

b. If the count becomes two, print the team name, player number, and current minute.

c. Mark the player as dismissed. 10. After all events are processed, all required dismissals have been reported in chronological order.

Why it works

The algorithm maintains two pieces of information for every player: how many yellow cards they have received so far and whether they have already been dismissed.

Before processing an event, the stored state exactly matches all previous events. When a yellow card arrives, increasing the yellow count correctly reflects the new match state. A player is dismissed precisely when their second yellow card is received or when a direct red card is shown. Once dismissed, the player is added to the dismissed set, causing all future events for that player to be ignored.

Because events are processed chronologically, every dismissal is output at the exact minute when it first occurs, and the output order is automatically correct.

Python Solution

import sys
input = sys.stdin.readline

home = input().strip()
away = input().strip()

n = int(input())

yellow = {}
sent_off = set()

out = []

for _ in range(n):
    t, side, num, card = input().split()
    t = int(t)
    num = int(num)

    player = (side, num)

    if player in sent_off:
        continue

    team_name = home if side == "h" else away

    if card == "r":
        out.append(f"{team_name} {num} {t}")
        sent_off.add(player)
    else:
        yellow[player] = yellow.get(player, 0) + 1

        if yellow[player] == 2:
            out.append(f"{team_name} {num} {t}")
            sent_off.add(player)

sys.stdout.write("\n".join(out))

The dictionary yellow stores the current yellow-card count for each player. The key is (side, num) because player numbers are only unique within a team.

The set sent_off prevents duplicate dismissals. This is the most important implementation detail. Once a player receives a red card, whether direct or through a second yellow, every later event involving that player must be ignored.

The input is already sorted by time, so appending dismissals to out immediately produces the required chronological order. No additional sorting is needed.

Another subtle point is checking for dismissal after incrementing the yellow count. A player is dismissed exactly when the count becomes two. Checking for values greater than or equal to two would also work, but checking for equality matches the rules more precisely.

Worked Examples

Sample 1

Input:

MC
CSKA
9
28 a 3 y
62 h 25 y
66 h 42 y
70 h 25 y
77 a 4 y
79 a 25 y
82 h 42 r
89 h 16 y
90 a 13 r

Minute	Player	Card	Yellow Count After Event	Dismissed?	Output
28	a,3	y	1	No
62	h,25	y	1	No
66	h,42	y	1	No
70	h,25	y	2	Yes	MC 25 70
77	a,4	y	1	No
79	a,25	y	1	No
82	h,42	r	1	Yes	MC 42 82
89	h,16	y	1	No
90	a,13	r	0	Yes	CSKA 13 90

Output:

MC 25 70
MC 42 82
CSKA 13 90

This example demonstrates both dismissal mechanisms. Player 25 is sent off through a second yellow card, while players 42 and 13 receive direct red cards.

Custom Example

Input:

HOME
AWAY
5
10 h 7 r
20 h 7 y
30 a 7 y
40 a 7 y
50 a 7 r

Minute	Player	Card	Yellow Count After Event	Dismissed?	Output
10	h,7	r	0	Yes	HOME 7 10
20	h,7	y	Ignored	Already sent off
30	a,7	y	1	No
40	a,7	y	2	Yes	AWAY 7 40
50	a,7	r	Ignored	Already sent off

Output:

HOME 7 10
AWAY 7 40

This trace shows both important corner cases. Players from different teams may share the same number, and events after a dismissal must be ignored.

Complexity Analysis

Measure	Complexity	Explanation
Time	O(n)	Each event is processed once with constant-time dictionary and set operations
Space	O(n)	At most one dictionary entry and one set entry per player appearing in the input

With at most 90 events, the running time is tiny. The solution easily fits within the time and memory limits.

Test Cases

# helper: run solution on input string, return output string
import sys
import io

def run(inp: str) -> str:
    sys.stdin = io.StringIO(inp)

    input = sys.stdin.readline

    home = input().strip()
    away = input().strip()
    n = int(input())

    yellow = {}
    sent_off = set()
    out = []

    for _ in range(n):
        t, side, num, card = input().split()
        t = int(t)
        num = int(num)

        player = (side, num)

        if player in sent_off:
            continue

        team = home if side == "h" else away

        if card == "r":
            out.append(f"{team} {num} {t}")
            sent_off.add(player)
        else:
            yellow[player] = yellow.get(player, 0) + 1
            if yellow[player] == 2:
                out.append(f"{team} {num} {t}")
                sent_off.add(player)

    return "\n".join(out)

# provided sample
assert run(
"""MC
CSKA
9
28 a 3 y
62 h 25 y
66 h 42 y
70 h 25 y
77 a 4 y
79 a 25 y
82 h 42 r
89 h 16 y
90 a 13 r
"""
) == """MC 25 70
MC 42 82
CSKA 13 90"""

# minimum input, single yellow
assert run(
"""A
B
1
1 h 1 y
"""
) == ""

# second yellow causes dismissal
assert run(
"""A
B
2
10 h 5 y
20 h 5 y
"""
) == "A 5 20"

# same number on different teams
assert run(
"""A
B
2
10 h 10 r
20 a 10 r
"""
) == """A 10 10
B 10 20"""

# events after dismissal ignored
assert run(
"""A
B
3
10 h 7 r
20 h 7 y
30 h 7 r
"""
) == "A 7 10"

Test input	Expected output	What it validates
Single yellow card	Empty output	No dismissal occurs
Two yellows	Dismissal on second yellow	Automatic red-card rule
Same jersey number on both teams	Two separate outputs	Player identity includes team
Cards after dismissal	One output only	Later events must be ignored

Edge Cases

Direct red followed by later events

Input:

HOME
AWAY
2
10 h 7 r
20 h 7 y

At minute 10, player (h, 7) receives a direct red card and enters the dismissed set. At minute 20, the algorithm sees that the player is already dismissed and skips the event.

Output:

HOME 7 10

The player appears exactly once.

Second yellow card dismissal

Input:

HOME
AWAY
2
15 a 9 y
30 a 9 y

After the first event, the yellow count becomes 1. After the second event, the yellow count becomes 2, triggering a dismissal and adding the player to the dismissed set.

Output:

AWAY 9 30

The dismissal occurs at the correct minute.

Same jersey number on different teams

Input:

HOME
AWAY
2
10 h 10 r
20 a 10 r

The algorithm stores players as (side, number). Thus (h, 10) and (a, 10) are distinct keys.

The first event dismisses the home player. The second event dismisses the away player.

Output:

HOME 10 10
AWAY 10 20

No collision occurs between players who share the same jersey number but belong to different teams.