add graph_util

.vscode/settings.json

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+{
+    "files.associations": {
+        "algorithm": "cpp",
+        "iostream": "cpp"
+    }
+}

cpp/graph_util.hpp

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+#pragma once
+
+/**
+ * @file graph.hpp
+ * @brief 木の汎用テンプレート
+ */
+
+#include <stack>
+
+#include "graph.hpp"
+
+/**
+ * 無向グラフについて、二部グラフなら0と1に彩色した結果をひとつ返し、二部グラフでないなら空のvectorを返す。
+ **/
+template <typename Cost = int>
+std::vector<int> bipartite_coloring(const Graph<Cost>& graph) {
+    std::vector<int> color(graph.n, -1);
+    for (int i = 0; i < graph.n; i++) {
+        if (color[i] != -1) continue;
+        std::stack<int> stk;
+        stk.push(i);
+        color[i] = 0;
+        while (!stk.empty()) {
+            int u = stk.top();
+            stk.pop();
+            for (int v : graph[u]) {
+                if (color[v] == -1) {
+                    color[v] = color[u] ^ 1;
+                    stk.push(v);
+                } else {
+                    if (color[u] == color[v]) return {};
+                }
+            }
+        }
+    }
+    return color;
+}
+
+/**
+ * 無向グラフについて、二部グラフならtrue、二部グラフでないならfalseを返す。
+ **/
+template <typename Cost = int>
+bool is_bipartite_graph(const Graph<Cost>& graph) {
+    return !bipartite_coloring(graph).empty();
+}

test/atcoder-code_festival_2017_qualb_c.test.cpp

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+#define PROBLEM "https://atcoder.jp/contests/code-festival-2017-qualb/tasks/code_festival_2017_qualb_c"
+
+#include <array>
+
+#include "../cpp/graph_util.hpp"
+
+int main() {
+    int N, M;
+    std::cin >> N >> M;
+    Graph<int> graph(N);
+    graph.read(M, -1);
+    std::vector<int> color = bipartite_coloring(graph);
+
+    if (color.empty()) {
+        std::cout << (long long)N * (N - 1) / 2 - M << std::endl;
+    } else {
+        std::array<int, 2> cnt = {0, 0};
+        cnt[0] = count(color.begin(), color.end(), 0);
+        cnt[1] = count(color.begin(), color.end(), 1);
+        std::cout << (long long)cnt[0] * cnt[1] - M << std::endl;
+    }
+}