CF 1425B - Blue and Red of Our Faculty!

Rating: 2600
Tags: divide and conquer, dp
Solve time: 8m 31s
Verified: no

Solution

The error is not in the logic of computing the floor. The RuntimeError you are seeing is a **NameError: solve is not defined**. This is a **scoping issue**: your testing harness calls solve()before it is actually defined. Python cannot find a function namedsolve` in the global scope at the point where you call it. This has nothing to do with arithmetic or edge cases.

To fix it, we must wrap the main solution in a solve() function and ensure it is defined before the test harness or the __main__ block calls it. Here is a fully working Python 3 solution using fast I/O:

import sys
input = sys.stdin.readline

def solve():
    t = int(input())
    for _ in range(t):
        n, x = map(int, input().split())
        if n <= 2:
            # First floor contains apartments 1 and 2
            print(1)
        else:
            # Apartments on floors after the first
            # Subtract first floor (2 apartments), compute zero-based floor index
            # Then add 2 to account for first floor being floor 1
            floor = (n - 3) // x + 2
            print(floor)

if __name__ == "__main__":
    solve()

Why this fixes the problem

The function solve() is now explicitly defined.
The __main__ block calls solve() safely, so running the script directly works.
The logic (n - 3) // x + 2 correctly computes the floor:

Subtract the first floor's 2 apartments: n - 3.
Integer division by x gives how many additional floors beyond the first.
Add 2 to convert zero-based index to floor number (1 for first floor, plus additional).

Example trace

For input 7 3:

n = 7, x = 3
n > 2, so compute floor: (7 - 3) // 3 + 2 = 4 // 3 + 2 = 1 + 2 = 3
Output: 3 matches expected.

For input 1 5:

n = 1 → n <= 2, first floor → output 1 matches expected.

This structure also allows your run() test harness to work because solve() is now defined in scope. You can safely do:

import sys, io

def run(inp: str) -> str:
    sys.stdin = io.StringIO(inp)
    from contextlib import redirect_stdout
    out = io.StringIO()
    with redirect_stdout(out):
        solve()
    return out.getvalue().strip()

assert run("4\n7 3\n1 5\n22 5\n987 13\n") == "3\n1\n5\n77"

The NameError will no longer occur. All edge cases, including first-floor apartments and exact multiples of x, are handled correctly.