CF 5A - Chat Servers Outgoing Traffic

Rating: 1000
Tags: implementation
Solve time: 1m 9s
Verified: yes

Solution

Problem Understanding

We are given a sequence of chat server events. A user can join the chat, leave the chat, or send a message. Every time someone sends a message, the server delivers that message to every user currently inside the chat, including the sender.

The cost of one message delivery is the length of the message text. If there are k users in the chat and the message length is l, then the server produces k * l bytes of outgoing traffic for that event.

The task is to process all commands and compute the total traffic generated.

The input is small. There are at most 100 lines, and each line has length at most 100 characters. Even a straightforward simulation easily fits inside the limits. We do not need advanced data structures or optimization tricks. A linear scan over the input is enough.

The main challenge is parsing the commands correctly. There are three formats:

+name
-name
sender:message

The first character immediately tells us whether this is an add operation, remove operation, or message.

A subtle detail is that the sender does not matter for the traffic calculation. The server sends the message to everyone currently online, regardless of who wrote it. Only two values matter:

current number of users
message length

Another easy mistake is calculating the message length incorrectly. The length includes only the text after the colon, not the sender name or the colon itself.

Consider this example:

+Mike
Mike:hello

The message length is 5, not 10.

Another edge case is an empty message:

+Mike
Mike:

The message length is 0, so the traffic added is also 0, even though one user receives it.

A careless implementation might split incorrectly or assume every message contains at least one character after the colon.

One more situation that often causes bugs is updating the user count in the wrong order.

+Mike
-Mike
Mike:hello

This input is invalid according to the guarantees, because Mike is no longer in the chat. The statement guarantees such cases never happen, which lets us focus purely on simulation instead of validation.

Approaches

The brute-force idea is to explicitly track all online users in a set. Whenever a message appears, we could iterate through every user currently online and add the message length once per user.

That approach is correct because the server really does send one copy to every participant. If there are k users, iterating over all k users simulates the real process exactly.

The issue is that we do unnecessary work. The problem only asks for the total number of bytes sent, not who received them. Iterating through all users just to count them repeats information we already know.

The key observation is that every recipient receives exactly the same message. Instead of simulating each delivery separately, we can multiply:

traffic added = online_users * message_length

This reduces each message operation from iterating over all users to a constant-time calculation.

With at most 100 commands, even the brute-force solution would pass comfortably. Still, the optimized version is cleaner and expresses the real structure of the problem directly.

Approach	Time Complexity	Space Complexity	Verdict
Brute Force	O(n²)	O(n)	Accepted
Optimal	O(n)	O(1)	Accepted

Here, n is the number of commands.

Algorithm Walkthrough

Initialize two variables:

users = 0 for the current number of people in the chat, and answer = 0 for the total outgoing traffic. 2. Read the input line by line until EOF. 3. If a line starts with '+', increase users by 1.

A new person joined the chat, so future messages will be delivered to one more recipient. 4. If a line starts with '-', decrease users by 1.

That user left the chat, so future messages will reach one fewer person. 5. Otherwise, the line represents a message.

Find the position of the colon ':'. Everything after it is the message text. 6. Compute the message length as:

len(line_after_colon) 7. Add:

users * message_length

to answer.

Every online user receives one copy of the message, so the total bytes sent are exactly this product. 8. After processing all lines, print answer.

Why it works

The algorithm maintains one invariant throughout execution:

users = number of people currently inside the chat

The add and remove operations update this value exactly according to the commands. Whenever a message appears, every current participant receives exactly one copy of the message. Since the message length is l and there are users participants, the traffic added by that event is exactly users * l.

Because every command is processed in order and every message contribution is counted exactly once, the final sum is the correct total outgoing traffic.

Python Solution

import sys
input = sys.stdin.readline

users = 0
answer = 0

for line in sys.stdin:
    line = line.rstrip('\n')

    if line[0] == '+':
        users += 1

    elif line[0] == '-':
        users -= 1

    else:
        colon = line.find(':')
        message = line[colon + 1:]
        answer += users * len(message)

print(answer)

The solution directly follows the simulation described earlier.

The variable users stores how many people are currently online. Since add and remove commands always come in valid order, incrementing and decrementing this counter is enough. We do not actually need to store usernames.

For message lines, the important part is extracting only the message text. The sender name should not contribute to the byte count. Using find(':') gives the separator position, and slicing from colon + 1 extracts the actual message.

Using rstrip('\n') removes the trailing newline added by input reading. Without this, the newline character would incorrectly increase the message length by one.

The algorithm processes each line exactly once and performs only constant-time work per command.

Worked Examples

Example 1

Input:

+Mike
Mike:hello
+Kate
+Dmitry
-Dmitry
Kate:hi
-Kate

Command	Users Before	Message Length	Traffic Added	Users After	Total
+Mike	0	-	0	1	0
Mike:hello	1	5	5	1	5
+Kate	1	-	0	2	5
+Dmitry	2	-	0	3	5
-Dmitry	3	-	0	2	5
Kate:hi	2	2	4	2	9
-Kate	2	-	0	1	9

The trace shows that only message commands contribute to the answer. The second message has length 2 and is delivered to 2 users, adding 4.

Example 2

Input:

+Ann
+Bob
Ann:
-Bob
Ann:abc

Command	Users Before	Message Length	Traffic Added	Users After	Total
+Ann	0	-	0	1	0
+Bob	1	-	0	2	0
Ann:	2	0	0	2	0
-Bob	2	-	0	1	0
Ann:abc	1	3	3	1	3

This example demonstrates the empty-message edge case. The command Ann: produces zero traffic because the message text has length 0.

Complexity Analysis

Measure	Complexity	Explanation
Time	O(n)	Each command is processed once
Space	O(1)	Only counters are stored

The constraints are tiny, so this solution easily fits within the limits. Even with the maximum 100 commands, the runtime is effectively instantaneous.

Test Cases

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

def solve():
    users = 0
    answer = 0

    for line in sys.stdin:
        line = line.rstrip('\n')

        if line[0] == '+':
            users += 1

        elif line[0] == '-':
            users -= 1

        else:
            colon = line.find(':')
            message = line[colon + 1:]
            answer += users * len(message)

    print(answer)

def run(inp: str) -> str:
    backup_stdin = sys.stdin
    backup_stdout = sys.stdout

    sys.stdin = io.StringIO(inp)
    sys.stdout = io.StringIO()

    solve()

    output = sys.stdout.getvalue().strip()

    sys.stdin = backup_stdin
    sys.stdout = backup_stdout

    return output

# provided sample
assert run(
"""+Mike
Mike:hello
+Kate
+Dmitry
-Dmitry
Kate:hi
-Kate
"""
) == "9", "sample 1"

# single user, single message
assert run(
"""+A
A:test
"""
) == "4", "basic case"

# empty message
assert run(
"""+Ann
+Bob
Ann:
"""
) == "0", "empty message"

# multiple users receive same message
assert run(
"""+A
+B
+C
A:abc
"""
) == "9", "3 users * length 3"

# user leaves before next message
assert run(
"""+A
+B
-B
A:hello
"""
) == "5", "correct user count after removal"

Test input	Expected output	What it validates
One user sends one message	4	Basic message calculation
Empty message text	0	Correct handling of zero-length messages
Three users receive `"abc"`	9	Multiplication by current user count
User removed before message	5	Correct update order for joins and leaves

Edge Cases

Consider the empty-message case:

+Ann
+Bob
Ann:

After the first two commands, users = 2. The message text after the colon is an empty string, so its length is 0.

The algorithm computes:

2 * 0 = 0

The final answer remains 0, which is correct.

Now consider message parsing carefully:

+Mike
Mike:hello

The full line length is larger than 5, but only the substring after : counts. The algorithm finds the colon position and extracts "hello" only.

The contribution becomes:

1 * 5 = 5

A careless implementation using the whole line length would produce the wrong answer.

Finally, consider joins and leaves changing the recipient count:

+A
+B
-B
A:abc

After +A, users become 1.

After +B, users become 2.

After -B, users return to 1.

When "abc" is sent, only one participant is online, so the traffic added is:

1 * 3 = 3

The algorithm handles this correctly because the user counter is updated immediately after each command.