結果

問題 No.3074 Divide Points Fairly
ユーザー qwewe
提出日時 2025-05-14 13:05:10
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 4,147 bytes
コンパイル時間 760 ms
コンパイル使用メモリ 70,680 KB
実行使用メモリ 7,848 KB
最終ジャッジ日時 2025-05-14 13:07:03
合計ジャッジ時間 9,569 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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ファイルパターン 結果
sample WA * 3
other WA * 42
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <iostream> // Required for input/output operations (cin, cout)
#include <vector> // Include vector header, although not strictly used in the final logic
#include <string> // Include string header, although not strictly used in the final logic

// The main function where the program execution begins
int main() {
    // Optimize standard input/output streams for faster performance.
    // std::ios_base::sync_with_stdio(false) disables synchronization between C++ standard streams and C's stdio library.
    // std::cin.tie(NULL) unties cin from cout, meaning that standard input operations will not force a flush of the standard output buffer.
    // These optimizations are common in competitive programming to speed up I/O heavy tasks.
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(NULL);

    int N; // Variable to store the number of clauses in the formula
    // Read the integer N from standard input. N represents the number of constraints (clauses).
    std::cin >> N;

    // Variables to temporarily store the bounds a_i and b_i for each clause.
    // Use 'long long' data type because the problem states that the variable indices a_i and b_i 
    // can be as large as 5 * 10^15 (5000000000000000), which exceeds the maximum value 
    // representable by a standard 32-bit integer type (int). 'long long' typically provides 64 bits.
    long long a, b; 
    
    // Loop N times to read all the clause definitions specified in the input.
    // Each clause is defined by a pair of integers a_i and b_i, representing the start and end
    // indices of the variables included in the disjunction for that clause.
    // According to the problem statement's input format, we must read these N pairs.
    // Even though the specific values of a_i and b_i do not affect the final "Yes/No" decision
    // in this particular problem, reading them is necessary to consume the input correctly.
    for (int i = 0; i < N; ++i) {
        // Read the pair of long long integers for the i-th clause.
        std::cin >> a >> b;
    }

    // Analysis of the problem:
    // The problem asks if there exists a truth assignment (True/False) for K = 5 * 10^15 variables 
    // x_1, x_2, ..., x_K such that the given Boolean formula f evaluates to True.
    // The formula f is a conjunction (AND operation, denoted by ^ or wedge symbol) of N clauses:
    // f = C_1 AND C_2 AND ... AND C_N 
    // Each clause C_i is a disjunction (OR operation, denoted by v or vee symbol) of variables 
    // whose indices j are in the range [a_i, b_i]:
    // C_i = (x_{a_i} OR x_{a_i+1} OR ... OR x_{b_i})
    
    // A key observation is that all variables appear only in their positive form (e.g., x_j). 
    // There are no negated variables (e.g., NOT x_j). This type of Boolean formula is known as a 
    // monotone formula.
    
    // Consider the truth assignment where *all* variables x_1, x_2, ..., x_K are set to TRUE.
    // Let's evaluate any clause C_i = (x_{a_i} OR ... OR x_{b_i}) under this assignment.
    // Since the problem guarantees 1 <= a_i <= b_i <= K, the range [a_i, b_i] contains at least one index j.
    // For any variable x_j in this clause, its value is TRUE under our chosen assignment.
    // In a disjunction (OR), if at least one operand is TRUE, the entire expression evaluates to TRUE.
    // Therefore, every clause C_i is TRUE under the all-TRUE assignment.
    
    // Now consider the entire formula f = C_1 AND C_2 AND ... AND C_N.
    // Since every clause C_i is TRUE, their conjunction (AND) is also TRUE.
    // This demonstrates that the assignment where all variables are TRUE is a satisfying assignment.
    
    // The problem asks if *there exists* such an assignment. Since we found one (the all-TRUE assignment),
    // the answer to the problem is always "Yes", regardless of the specific values of N, a_i, and b_i 
    // (as long as they satisfy the given constraints).

    // Print "Yes" to standard output, indicating that the formula is satisfiable.
    std::cout << "Yes" << std::endl;

    // Return 0 to signal successful execution of the main function.
    return 0;
}
0