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Bulgarian Informatics Group D · 2007–2026

270 independently explained problems: 54 Municipal, 54 Regional, 105 National Olympiad and 57 Autumn Tournament tasks. Start with the easier tasks and work upwards. Difficulty labels are learning estimates, not official ratings; Group D also includes challenging national-level problems. The six 2017 National tasks shared by Groups C and D use their existing permanent URLs. Years follow Arena’s competition-season labels. Source clarifications and special grader requirements are noted on affected tasks.

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Easy96

Counting 2

Digits 1

Arithmetic 1

Simulation 1

Sorting 2

Big integers 1

Counting 1

Number Theory 1

Strings 1

Arrays and counting 2

Simulation 1

Frequency counting 5

Grid simulation 1

Arithmetic indexing 1

Integer indexing 1

Sets and distinct values 1

Grid scanning 1

Sorting and checking 1

String conversion 1

Run counting 1

Arithmetic and greedy choice 1

Triangle inequalities 1

Combinatorial counting 1

Contribution counting 1

Geometry and boundary updates 1

Prefix sums 2

Arithmetic and digit scanning 1

String arithmetic 1

Digit sequences 1

Strings and positional weights 1

Character frequencies 1

String parsing 2

String scanning 2

Array scanning 2

Prime exponents 1

Permutations 1

Inverse permutations 1

Sequence scanning 1

Circular simulation 1

Digits and divisibility 1

Combinatorics 1

Number bases 1

Geometry enumeration 1

Digit frequency counting 1

Prefix sums and compact storage 1

Circular arrays 1

Periodic simulation 1

Digit arithmetic 1

Suffix maxima 1

Bounded enumeration 2

Sorting by elapsed time 1

Sequence simulation 2

Time simulation 1

Distinct graph neighbours 1

Coordinate geometry 1

Binary Search 1

Interval intersections 1

Calendar arithmetic 1

Geometric sums 1

Previous and next occurrence arrays 1

Precomputation 1

Sorting and simulation 1

Range queries 1

GCD and divisibility 1

Sequence generation 1

Grid rotation 1

Set intersection 1

LCM and arithmetic progressions 1

Euclidean algorithm 1

Window enumeration 1

Bijective base conversion 1

Frequency counting and sorting 1

Divisor enumeration 1

Two pointers on sorted arrays 1

Periodic prefix sums 1

Sorting distinct values 1

Numeral systems 1

Difference arrays 1

Digit sorting 1

Grid components 1

Sequence trend runs 1

Calendar simulation 1

Integer halving bounds 1

Medium142

Ranked Choice Simulation 1

Exhaustive search 2

Arrays and matrices 1

Number theory 1

Simulation 2

Sorting 1

Enumeration 1

Two Pointers 1

Number Theory 1

Strings and simulation 1

Big integers 1

Binary search 1

Binary Search 2

Strings 2

Arrays and counting 1

Sorting and greedy 1

Two pointers 1

Simulation 1

Rational Arithmetic 2

Combinatorial geometry 1

Invariants 1

Modular arithmetic 1

Arithmetic interval counting 1

Binary enumeration 1

Unbounded dynamic programming 1

Streaming digit sequence 1

Big integers 1

Digits and modular arithmetic 1

Fixed-event simulation 1

Frequency counting 2

Bounded-state simulation 1

Two-dimensional prefix sums 1

Prime factorization 3

Frequency inversion 1

Precomputation 1

Prefix and suffix maxima 1

Sorting and greedy 1

Bounding rectangles 1

String runs and simulation 1

Exact rational arithmetic 1

Permutation cycles 1

Partition dynamic programming 1

Sorting and runs 1

Greedy two pointers 1

Sorting and decimal subtraction 1

Boyer–Moore voting 1

Sieve and prefix sums 1

Functional graphs 1

Prime sieve and combinatorics 1

Packed presence bitmap 1

Counting formulas 1

Implicit sequence indexing 1

Constructive geometry 1

Big integer base conversion 1

Prime sieve and prefix sums 1

Geometry and indexing 1

Greedy interval traversal 1

Sorting by concatenation 1

Modular arithmetic and dates 1

Linear recurrence 1

Greedy representation 1

Two Pointers 2

Ordered set and streaming 1

Divisor enumeration 1

Cyclic shifts 1

Breadth-first search 1

Grid dynamic programming 2

Prime sieve 1

Area bounds and enumeration 1

Big integer arithmetic 1

Unbounded knapsack 1

Divisors and formulas 1

Local invariant updates 1

Divisor sieve and prefix sums 1

Sets and symmetry 1

Decimal arithmetic 1

Blocked-grid runs 1

Stacks and subset enumeration 1

Odd divisors 1

Prefix sums 2

Rectangle enumeration 1

Bitmask enumeration 1

Priority queue simulation 1

Big integer doubling 1

Prefix and suffix products 1

Greedy swaps 1

Date enumeration 1

Josephus formula 1

Hypothesis enumeration 1

Grid path invariants 1

Greedy 1

Big integer multiplication 1

Matrix exponentiation 1

String permutation 1

Sorting and two pointers 1

Digit arithmetic 1

Two pointers on positions 1

Stacks and dynamic programming 1

Dynamic programming 1

Sorting and sliding windows 1

Segmented multiple marking 1

Pair-sum preprocessing 1

Periodic indexing 1

Digit dynamic programming 1

Grid scanning 1

Positional digit counting 1

Integer binary search 1

Counting 1

Coprime directions and inclusion-exclusion 1

Multi-source BFS 1

Piecewise volume simulation 1

LCM and modular arithmetic 1

Decimal convolution 1

Number Theory 1

Divisor pairs and LCM 1

Greedy matching 1

Sorting and grouping 1

Graphs 1

Greedy stack simulation 1

Robot Without Reversing 12

Hard32

String algorithms 1

Prefix Sums 1

Number Theory 1

Bitmasks 1

Fenwick order statistics 1

Monotonic stack 1

Bitset dynamic programming 1

Digit constraints 1

Big integers and enumeration 1

Number Theory 1

Fibonacci enumeration 1

Geometry and arithmetic sums 1

Prime sieve 1

Exact rational arithmetic 1

Linear recurrence and counting 1

Greedy digit allocation 1

Flood fill and geometry 1

Suffix DP and lexicographic reconstruction 1

Simulation 1

Monotonic stacks and contributions 1

Greedy string repair 1

Exhaustive search and construction 1

Lexicographic unranking 1

Coordinate compression and BFS 1

Divisors and remainder pairing 1

Cached grid simulation 1

Dijkstra on a hexagonal grid 1

Digit DP and big integers 1

Grid Hamiltonian cycle 1

Divisors and packing 1

Geometry and sweep line 1

Minimum-cost bipartite matching 1

Try the problem yourself before reading the analysis. Solutions use C++17. Special grader headers and compiler requirements are explained on affected tasks.

GROUP D2020 · MediumHypothesis enumeration

Identify a Counterfeit Coin from Three Weighings

National Olympiad — National round (2020 season)

Submission name: scale.cpp

Solve in Editor →

Problem summary

One coin among A…L is lighter or heavier. From three equal-count pan weighings, identify the unique coin and weight direction, when possible.

Input

Three lines: left coin string,right coin string,outcome <,>,=. Here < means the right pan rises and > means it descends.

Output

Coin and lighter/heavier if unique, otherwise indefinitely.

Constraints

Twelve coins and three weighings, with equal coin counts on both pans.

Worked example

Input and output for the worked example discussed below.

Input

ABCD EFGH =
ABCI EFJK <
ABIJ EFGH =

Output

K lighter

Solution analysis

Enumerate all 24 hypotheses: each of twelve coins may have deviation −1 or +1. Genuine weights cancel because each weighing uses equal pan counts.
For one hypothesis compute left deviation minus right deviation. Positive means the right pan rises(<), negative means it descends(>), zero means balance. Retain only hypotheses matching all three.
In the sample only K lighter fits: its presence in the second right pan makes that pan rise, and the other two weighings balance. Multiple surviving identities or signs mean identification is indefinite.

Why it works

The enumeration contains every possible counterfeit identity and sign and rejects precisely inconsistent hypotheses.

Complexity: O(24Wℓ) time and O(Wℓ) space for W=3 and pan length at most 12, all fixed constants here.

Watch out. Interpret symbols as the stated right-pan direction, not numeric less-than of left-pan weight. The sign must also be unique.

Commented C++17 solution

An independently written complete program with standard headers.

// The enumeration contains every possible counterfeit identity and sign and rejects precisely inconsistent
// hypotheses.
#include<algorithm>
#include<array>
#include<iostream>
#include<string>
#include<utility>
#include<vector>
using namespace std;
struct Weighing{
    string left,right;
    char outcome;
};
int main(){
    array<Weighing,3>tests;
    for(Weighing&test:tests){
        cin>>test.left>>test.right>>test.outcome;
    }
    vector<pair<char,int>>possible;
    for(char coin='A';coin<='L';coin++){
        for(int sign:{-1,1}){
            bool valid=true;
            for(const Weighing&test:tests){
                int delta=sign*
                    (int(count(test.left.begin(),test.left.end(),coin))-
                        int(count(test.right.begin(),test.right.end(),coin)));
                char result=delta>0?'<':delta<0?'>':'=';
                valid=valid&&result==test.outcome;
            }
            if(valid){
                possible.push_back({coin,sign});
            }
        }
    }
    if(possible.size()==1){
        cout<<possible[0].first<<' '<<(possible[0].second<0?"lighter":"heavier")<<'\n';
    }
    else{
        cout<<"indefinitely\n";
    }
}

Source: Arena Olimpiici ↗

Intermediate.Put your skills to the test.

Identify a Counterfeit Coin from Three Weighings

Problem summary

Input

Output

Constraints

Worked example

Input

Output

Solution analysis

Why it works

Commented C++17 solution

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