Add problems (#71)

* new problems

* file name upd

Author: YanagiOrigami

algorithmic/problems/182/checker.cc

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+#include "testlib.h"
+#include <vector>
+
+using namespace std;
+
+int main(int argc, char* argv[]) {
+    // 初始化 testlib
+    registerTestlibCmd(argc, argv);
+
+    // 1. 读取输入数据 (Input)
+    int N = inf.readInt();
+    int M = inf.readInt();
+
+    // 存储边列表，用于验证覆盖
+    vector<pair<int, int>> edges;
+    edges.reserve(M);
+    for (int i = 0; i < M; i++) {
+        int u = inf.readInt();
+        int v = inf.readInt();
+        edges.push_back({u, v});
+    }
+
+    // 2. 读取标准答案 (Answer)
+    // 修改处：ans 文件中只包含一个整数 K* (最优/参考解的大小)
+    int K_optimal = ans.readInt();
+
+    // 3. 读取选手输出 (Output) 并统计 K
+    vector<int> user_sol(N + 1); // 1-based indexing
+    int K_user = 0;
+
+    for (int i = 1; i <= N; i++) {
+        // 读取 0 或 1
+        int val = ouf.readInt(0, 1, format("x_%d", i)); 
+        user_sol[i] = val;
+        if (val == 1) {
+            K_user++;
+        }
+    }
+
+    // 4. 验证选手的解是否有效 (Validity Check)
+    for (int i = 0; i < M; i++) {
+        int u = edges[i].first;
+        int v = edges[i].second;
+
+        // 如果一条边的两个端点都没被选中
+        if (user_sol[u] == 0 && user_sol[v] == 0) {
+            quitf(_wa, "Edge %d-%d is not covered (vertices %d and %d are both 0).", u, v, u, v);
+        }
+    }
+
+    // 5. 计算得分 (Scoring)
+    if (K_user == 0) {
+        if (M == 0) {
+             quitf(_ok, "Ratio: 1");
+        } else {
+             quitf(_wa, "Logic error: Valid solution found with size 0 for non-empty graph.");
+        }
+    }
+
+    double score = (double)K_optimal / K_user * 100.0;
+    double Ratio = (double)K_optimal / K_user;
+
+    // 6. 输出结果
+    quitf(_ok, "Valid Vertex Cover. K_user=%d, K_jury=%d, Ratio: %.4f", K_user, K_optimal, Ratio);
+
+    return 0;
+}

algorithmic/problems/182/config.yaml

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+type: default
+time: 2s
+memory: 512m
+subtasks:
+  - score: 100
+    n_cases: 3
+checker: checker.cc
+checker_type: testlib

algorithmic/problems/182/statement.txt

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+# Vertex Cover Challenge
+
+## Context
+
+You are given an undirected graph G = (V, E) with |V| = N vertices and |E| = M edges.
+You must select a subset of vertices S ⊆ V to form a Vertex Cover.
+
+A subset S is a valid vertex cover if and only if:
+  for every edge {u, v} ∈ E, at least one of its endpoints is in S.
+  (i.e., u ∈ S or v ∈ S or both).
+
+This is a heuristic optimization problem.
+You are NOT required to find the theoretically optimal solution.
+Instead, you should try to minimize the size of the set S (denoted as |S|).
+
+Let:
+  K* = the minimum vertex cover size (optimal solution).
+  K  = the size of the vertex cover found by your solution.
+
+The score is defined as:
+  Score = K* / K * 100
+
+Thus:
+- Score = 100.0 means you found an optimal vertex cover.
+- Larger K yields a smaller score.
+- Invalid solutions (where some edges are not covered) receive score = 0.
+
+The value K* is known to the judge but not to the contestant.
+
+## Input Format
+
+The first line contains two integers:
+  N M
+where:
+  2 ≤ N ≤ 10,000
+  1 ≤ M ≤ 500,000
+
+The next M lines each contain two integers:
+  u v
+representing an undirected edge {u, v},
+with 1 ≤ u, v ≤ N and u ≠ v.
+
+Multiple edges between the same pair of vertices may appear but imply the same constraint.
+
+## Output Format
+
+Output exactly N lines.
+
+The i-th line must contain one integer x_i ∈ {0, 1}:
+- 1 indicates that vertex i is included in the vertex cover (i ∈ S).
+- 0 indicates that vertex i is excluded from the vertex cover (i ∉ S).
+
+Requirements:
+- For any edge {u, v} ∈ E, it must be true that x_u = 1 OR x_v = 1.
+
+## Scoring
+
+Let:
+  K = Σ x_i (Total number of vertices selected, i.e., sum of 1s in output)
+  K* = Optimal minimum vertex cover size (hidden)
+
+If the solution is invalid (i.e., there exists an edge {u, v} where x_u=0 and x_v=0):
+  Score = 0
+
+Otherwise:
+  Score = K* / K * 100
+
+Higher score is better.
+
+## Example
+
+Input:
+4 3
+1 2
+2 3
+3 4
+
+Output:
+0
+1
+1
+0
+
+Explanation:
+The edges are {1,2}, {2,3}, {3,4}.
+The output selects vertices 2 and 3 (S={2, 3}).
+- Edge {1,2} is covered by 2.
+- Edge {2,3} is covered by 2 (and 3).
+- Edge {3,4} is covered by 3.
+All edges are covered.
+Total size K = 2.
+Assuming the optimal K* = 2, the Score = 2 / 2 * 100 = 100.0.
+
+## Constraints
+
+- 2 ≤ N ≤ 10,000
+- 1 ≤ M ≤ 500,000
+- Time Limit: 2.0s
+- Memory Limit: 512MB

algorithmic/problems/182/testdata/1.ans

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+5800