CF 102697011 - Ski Sum

Rating: -
Tags: -
Solve time: 53s
Verified: yes

Solution

Problem Understanding

The task describes a ski resort where trails are separated into four difficulty categories: easy, difficult, very difficult, and expert-only. The input gives the number of trails in each category, and the goal is simply to calculate how many trails exist in total. The answer is the sum of the four provided counts.

The constraints are small because only four integers are read. There is no need for advanced data structures, searching, or simulation. Even a constant-time solution is enough, since the amount of work never grows with a large input size. The main requirement is correctness in handling the input format and summing all categories exactly once.

The main edge cases come from forgetting that every category contributes to the answer. A solution that only adds some categories may pass many random tests but fail on simple boundary cases.

For example, with:

Input:
0 0 0 1

Output:
1

The only trail is in the expert-only category. Ignoring that value would incorrectly produce zero.

Another case is:

Input:
5 0 0 0

Output:
5

Here all trails are easy trails. A solution that assumes every category is non-zero would still need to correctly handle the zero values.

Approaches

The brute-force idea is to enumerate trails and count them one by one. However, the input already gives the number of trails in each category, so constructing individual trail objects would add unnecessary work. If the four numbers were large, such an approach would perform a number of operations proportional to the total number of trails, while the answer only requires four additions.

The key observation is that the categories are already aggregated. There is no hidden relationship between trails, and no ordering or filtering is required. The total number of trails is directly obtained by adding the four counts. The brute-force approach works because counting individual trails would eventually produce the correct total, but it ignores the information already present in the input. The observation that each value is already a partial sum lets us reduce the entire problem to constant time.

Approach	Time Complexity	Space Complexity	Verdict
Brute Force	O(total number of trails)	O(1)	Unnecessary
Optimal	O(1)	O(1)	Accepted

Algorithm Walkthrough

Read the four integers representing the numbers of trails in the four difficulty categories.
Add the four values together because every trail belongs to exactly one category, so the sum of the categories is the total number of trails.
Print the resulting total.

Why it works: the algorithm relies on the invariant that every trail is counted exactly once in the input. Since the categories do not overlap, adding their sizes neither misses any trails nor counts any trail multiple times. The printed sum must equal the total number of trails.

Python Solution

import sys
input = sys.stdin.readline

def solve():
    a, b, c, d = map(int, input().split())
    print(a + b + c + d)

if __name__ == "__main__":
    solve()

The program reads the single input line and stores the four category counts. The addition is performed directly because no intermediate structure is needed.

There are no boundary issues with indexing, loops, or overflow in Python. The important implementation detail is that all four numbers must be included in the final expression. Missing one category is the only realistic source of a wrong answer.

Worked Examples

For the input:

20 16 13 6

the execution is:

Step	Easy	Difficult	Very difficult	Expert-only	Total
Read values	20	16	13	6
Add easy and difficult	20	16			36
Add very difficult			13		49
Add expert-only				6	55

The trace shows that each category contributes independently. The final value is the complete trail count.

For the input:

0 0 0 1

the execution is:

Step	Easy	Difficult	Very difficult	Expert-only	Total
Read values	0	0	0	1
Sum all categories	0	0	0	1	1

This example confirms that zero-sized categories are valid and must still be included in the calculation.

Complexity Analysis

Measure	Complexity	Explanation
Time	O(1)	Only four integers are read and added.
Space	O(1)	The program stores only four numbers.

The solution uses a fixed amount of work regardless of the input values, so it easily satisfies the limits.

Test Cases

import sys
import io

def solve():
    a, b, c, d = map(int, input().split())
    print(a + b + c + d)

def run(inp: str) -> str:
    old_stdin = sys.stdin
    old_stdout = sys.stdout
    try:
        sys.stdin = io.StringIO(inp)
        out = io.StringIO()
        sys.stdout = out
        solve()
        return out.getvalue()
    finally:
        sys.stdin = old_stdin
        sys.stdout = old_stdout

assert run("20 16 13 6\n") == "55\n", "sample 1"
assert run("0 0 0 1\n") == "1\n", "single expert trail"
assert run("5 0 0 0\n") == "5\n", "only easy trails"
assert run("1000000000 1000000000 1000000000 1000000000\n") == "4000000000\n", "large values"
assert run("7 3 9 1\n") == "20\n", "mixed categories"

Test input	Expected output	What it validates
`20 16 13 6`	`55`	Provided sample behavior
`0 0 0 1`	`1`	Handles zero categories
`5 0 0 0`	`5`	Handles a single non-zero category
`1000000000 1000000000 1000000000 1000000000`	`4000000000`	Handles large integer values
`7 3 9 1`	`20`	Checks normal mixed input

Edge Cases

When three categories contain zero trails, the algorithm still works because it adds every category without making assumptions about their values. For:

Input:
0 0 0 1

the four values are added as 0 + 0 + 0 + 1, producing 1.

When all trails belong to one category, the same logic applies. For:

Input:
5 0 0 0

the result is 5, because the three zero categories do not change the sum.

Large values also require attention because a careless implementation in languages with limited integer ranges could overflow. Python integers automatically expand to store large values, so:

Input:
1000000000 1000000000 1000000000 1000000000

correctly produces:

4000000000

The algorithm handles every case through the same invariant: each input number is one disjoint part of the total, and adding all four parts gives the complete answer.