結果

問題 No.3078 Difference Sum Query
コンテスト
ユーザー qwewe
提出日時 2025-05-14 13:08:26
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 3,168 bytes
コンパイル時間 623 ms
コンパイル使用メモリ 67,568 KB
実行使用メモリ 7,848 KB
最終ジャッジ日時 2025-05-14 13:10:05
合計ジャッジ時間 4,943 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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ファイルパターン 結果
sample WA * 2
other WA * 26
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> // Include the iostream library for input/output operations
#include <ios>      // Include the ios library for I/O optimization functions

// Main function - the entry point of the program
int main() {
    // Optimize standard input/output operations for speed.
    // This is often beneficial in competitive programming to avoid Time Limit Exceeded verdicts.
    std::ios_base::sync_with_stdio(false); // Disable synchronization between C++ standard streams and C standard streams. This can speed up I/O.
    std::cin.tie(NULL); // Untie std::cin from std::cout. This prevents std::cout from being flushed automatically before std::cin operations, potentially speeding up input.

    int N; // Declare an integer variable N to store the number of vertices.
    int M; // Declare an integer variable M to store the number of edges. Although M's value is determined by N and not used in the calculation, it must be read according to the input format.
    
    // Read the number of vertices (N) and the number of edges (M) from standard input.
    std::cin >> N >> M; 

    // Analyze the problem constraints and properties:
    // 1. The problem states M = N * (N - 1) / 2. This is the formula for the number of edges in a complete graph with N vertices.
    //    A complete graph (denoted K_N) is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge.
    // 2. The problem states that all edge weights w_i are equal to 1.
    
    // The task is to find the minimum weight of a Hamiltonian cycle.
    // A Hamiltonian cycle is a cycle in the graph that visits each vertex exactly once and returns to the starting vertex.
    // In a graph with N vertices, any Hamiltonian cycle must consist of exactly N edges.
    // For example, if the cycle visits vertices in the order v1 -> v2 -> ... -> vN -> v1, it uses the edges (v1, v2), (v2, v3), ..., (v(N-1), vN), (vN, v1). There are N edges in total.
    
    // The total weight of a Hamiltonian cycle is the sum of the weights of the edges it contains.
    // Since the graph is K_N and all edge weights are 1, any edge used in any Hamiltonian cycle has weight 1.
    // Therefore, the total weight of any Hamiltonian cycle is the sum of N edge weights, each being 1.
    // Total weight = N * 1 = N.
    
    // The problem asks for the *minimum* weight. Since every possible Hamiltonian cycle in this graph has the same weight N, the minimum weight is simply N.
    // The problem statement guarantees that at least one such cycle exists. This is consistent with properties of complete graphs (K_N has Hamiltonian cycles for N >= 3; for N=2, the cycle 1-2-1 has length 2=N).
    
    // Consequently, the answer to the problem is N.
    // We do not need to read the details of the M edges provided in the input after the first line, as they are implicitly defined by the graph being K_N with unit weights. Reading them would be unnecessary work.

    // Output the calculated minimum weight, which is N, followed by a newline character.
    std::cout << N << "\n"; 

    // Return 0 to indicate that the program executed successfully.
    return 0; 
}
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