CF 1409C - Yet Another Array Restoration

CF 1409C - Yet Another Array Restoration

Rating: 1200
Tags: brute force, math, number theory
Solve time: 7m 3s
Verified: no

Solution

The root cause of the failure here is the test harness is trying to call a solve() function that isn’t defined in the same context. In Python, if you define the main code in the global scope without wrapping it in a function, calling solve() later will always fail with NameError or RuntimeError. This is unrelated to the algorithm itself.

To fix it, we need a fully self-contained Python 3 solution where all logic is inside a function called solve() and fast I/O is used. The algorithm itself - sliding window over all (fret, note_index) pairs - is correct, so we keep that approach.

Here is the corrected, complete solution:

import sys
input = sys.stdin.readline

def solve():
    # read input
    a = list(map(int, input().split()))
    n = int(input())
    b = list(map(int, input().split()))

    # generate all possible frets for each note
    frets = []
    for i in range(n):
        for j in range(6):
            fret = b[i] - a[j]
            frets.append((fret, i))  # (fret_index, note_index)
    
    frets.sort()  # sort by fret number

    count = [0] * n  # how many times each note is in current window
    unique = 0       # number of unique notes in the window
    ans = float('inf')
    l = 0

    # sliding window to find minimal range covering all notes
    for r in range(len(frets)):
        fret, idx = frets[r]
        if count[idx] == 0:
            unique += 1
        count[idx] += 1

        # contract window from the left while all notes are covered
        while unique == n:
            ans = min(ans, frets[r][0] - frets[l][0])
            left_fret, left_idx = frets[l]
            count[left_idx] -= 1
            if count[left_idx] == 0:
                unique -= 1
            l += 1

    print(ans)

if __name__ == "__main__":
    solve()

Key points

1. The function solve() contains all the logic, so you can safely call it in a test harness.
2. Each note b[i] can be played on any string j with fret b[i] - a[j].
3. Sorting all (fret, note_index) pairs allows a sliding window to efficiently find the minimal fret difference that covers all notes.
4. count and unique track how many distinct notes are in the current window.
5. The result ans is the smallest difference of max and min fret in a valid window.

How to run a test

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()

# sample test
assert run("1 4 100 10 30 5\n6\n101 104 105 110 130 200\n") == "0", "sample 1"

This fixes the RuntimeError because solve() is now defined.

If you want, I can also walk through this sample step by step to show why the answer is 0 with the fret assignments. This often clarifies the sliding window logic for edge cases. Do you want me to do that?