CF 102697017 - Chem Lab: Cross the Charges

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Solve time: 3m 37s
Verified: yes

Solution

Problem Understanding

The problem models a chemistry rule called “crossing the charges”. Two ions have charges represented by two integers. To find the molecular coefficients, the values are crossed over, meaning the first ion receives the second ion’s charge and the second ion receives the first ion’s charge.

The input contains two integers representing the original charges. The output should contain the two coefficients after applying the crossing operation.

The constraints are small because the only operation needed is moving two values. No searching, iteration, or data structure is required. Any algorithm more complicated than constant time is unnecessary.

The only edge case worth considering is when both charges are the same. For example:

Input:

5 5

Output:

5 5

A solution that tries to remove duplicates or assumes the values must change would fail here. Crossing two equal charges leaves the pair unchanged.

Approaches

A direct approach is to read the two numbers, store them, and print them in reverse order. The operation is correct because the definition of crossing the charges is exactly a swap.

There is no meaningful brute force solution because there are no choices to explore. Any method that performs extra work only adds complexity without solving a harder problem.

The entire task reduces to exchanging two variables.

Approach	Time Complexity	Space Complexity	Verdict
Direct swap	O(1)	O(1)	Accepted

Algorithm Walkthrough

Read the two charge values from the input.
Output the second value first and the first value second, because crossing the charges swaps their positions.

Why it works:

The required transformation is a permutation of two elements. A swap preserves both original values and places each one in the other ion’s coefficient position, which exactly matches the definition of the crossing operation.

Python Solution

import sys
input = sys.stdin.readline

a, b = map(int, input().split())
print(b, a)

The program reads both charges in one line and stores them as integers. The output statement reverses their order, which performs the required crossing.

No loops, arrays, or extra variables are needed because the input size is fixed at two values. Python integers are also more than sufficient for the arithmetic involved, since the program never performs calculations on the values.

Worked Examples

For the input:

2 3

the internal state is:

Step	a	b	Output
Read input	2	3
Swap positions	3	2	3 2

The result shows that the second charge becomes the first coefficient.

For the input:

7 7

the state is:

Step	a	b	Output
Read input	7	7
Swap positions	7	7	7 7

Equal values remain unchanged after crossing.

Complexity Analysis

Measure	Complexity	Explanation
Time	O(1)	Only two integers are read and printed.
Space	O(1)	Only the two input values are stored.

The solution uses the minimum possible amount of work and easily fits within the given limits.

Test Cases

import sys
import io

def solve(inp: str) -> str:
    sys.stdin = io.StringIO(inp)
    input = sys.stdin.readline
    a, b = map(int, input().split())
    return f"{b} {a}\n"

assert solve("2 3\n") == "3 2\n", "sample"
assert solve("4 3\n") == "3 4\n", "different charges"
assert solve("5 5\n") == "5 5\n", "equal charges"
assert solve("1 1000000000\n") == "1000000000 1\n", "large values"

Test input	Expected output	What it validates
`2 3`	`3 2`	Basic swapping behavior
`4 3`	`3 4`	Values are placed in the opposite positions
`5 5`	`5 5`	Equal charges remain unchanged
`1 1000000000`	`1000000000 1`	Large integer handling

Edge Cases

When both charges are identical, swapping them produces the same output. For input:

8 8

the algorithm reads a = 8 and b = 8, then prints b a, resulting in:

8 8

A correct implementation does not need a special condition because the normal swap already handles this case.

When one value is much larger than the other, the same rule applies. For input:

1 999999999

the program prints:

999999999 1

The algorithm only changes positions, so the magnitude of the charges has no effect on correctness.