From 031882ce27e4991ec9ab4d2dbd9230362afc3b10 Mon Sep 17 00:00:00 2001
From: Wenyuan Huang <157926136+whuang369@users.noreply.github.com>
Date: Sat, 17 Oct 2026 03:09:48 -0500
Subject: [PATCH] Fix #194: define R in problem 101 statement and fix its
 sample

R is the upper bound on the number of OR gates in the hidden circuit (the
interactor rejects inputs with more than R '|'), but the statement called it
"R external switches" and never said what it bounds. Without the bound the
problem is unsolvable within the query limit: an arbitrary T for N = 8000
needs 8000 bits, while log2 C(8000, 120) ~ 894 matches the 900-query
full-score threshold.

The sample was also invalid: its wiring broke i < Ui < Vi and the
"exactly one" rule, and its queries had length 5 instead of 2N+1 = 7 (the
interactor answers Wrong Answer [4]). Replace it with a valid wiring; the
two replies and the final accept were checked against interactor.cpp.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
---
 algorithmic/problems/101/statement.txt | 24 +++++++++++++-----------
 1 file changed, 13 insertions(+), 11 deletions(-)

diff --git a/algorithmic/problems/101/statement.txt b/algorithmic/problems/101/statement.txt
index d06c41911..4464b050b 100644
--- a/algorithmic/problems/101/statement.txt
+++ b/algorithmic/problems/101/statement.txt
@@ -1,8 +1,9 @@
 Problem Name: Circuit
 
 Description:
-You are given a circuit board consisting of N component slots and R external switches.  
+You are given a circuit board consisting of N component slots.  
 Each slot contains either an AND gate (&) or an OR gate (|). The actual type of each slot is hidden.  
+Every slot was supposed to contain an AND gate, but at most R slots mistakenly contain an OR gate instead.  
 Your task is to determine the true type of every slot by interacting with the judge.
 
 Specifications of the Circuit Board:
@@ -25,7 +26,7 @@ Specifications of the Circuit Board:
 - The output of the circuit is defined as the output of switch 0.
 
 Interaction:
-At the beginning of the interaction, the judge prints N and R, followed by N lines each containing Ui Vi.  
+At the beginning of the interaction, the judge prints N and R (the maximum number of OR gates in the hidden circuit), followed by N lines each containing Ui Vi.  
 This describes the wiring of the board. Then your program must interact as follows:
 
 1. Query:  
@@ -41,6 +42,7 @@ This describes the wiring of the board. Then your program must interact as follo
 Constraints:
 - 1 ≤ N ≤ 8000  
 - 1 ≤ R ≤ min(N, 120)  
+- The hidden circuit contains at most R OR gates (|)  
 - i < Ui < Vi ≤ 2N for all 0 ≤ i < N  
 - For each j=1..2N, exactly one i satisfies Ui=j or Vi=j  
 - At most 5000 queries may be made. Exceeding this limit results in Wrong Answer.
@@ -58,27 +60,27 @@ Sample Interaction:
 
 Suppose the input file contains:
 3 2
-3 4
-2 4
-0 1
+1 4
+2 3
+5 6
 &&|
 
 The judge first outputs:
 3 2
-3 4
-2 4
-0 1
+1 4
+2 3
+5 6
 
-(Here the hidden true circuit is T = "&&|".)
+(Here the hidden true circuit is T = "&&|". It has 1 OR gate, which does not exceed R = 2.)
 
 Then the interaction may proceed as follows (lines beginning with '#' are explanations):
 
-? 01001
+? 0001110
 # Player asks a query with binary string s.
 1
 # Judge replies that the circuit output is 1.
 
-? 11111
+? 1111111
 # Another query.
 0
 # Judge replies with 0.