From 155c1823335f16df3400693012693d2da66613ee Mon Sep 17 00:00:00 2001
From: hanyixuanten <105723997+hanyixuanten@users.noreply.github.com>
Date: Mon, 28 Sep 2026 20:46:48 +0800
Subject: [PATCH] new file:   P3199.cpp

---
 P3199.cpp          | 58 ++++++++++++++++++++++++++++++++++
 solutions/P3199.md | 79 ++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 137 insertions(+)
 create mode 100644 P3199.cpp
 create mode 100644 solutions/P3199.md

diff --git a/P3199.cpp b/P3199.cpp
new file mode 100644
index 0000000..fd541f4
--- /dev/null
+++ b/P3199.cpp
@@ -0,0 +1,58 @@
+#include <bits/stdc++.h>
+using namespace std;
+int n, m;
+vector<pair<int, double>> fri[3005];
+int q[30000005];
+double d[3005];
+bool in[3005];
+int cnt[3005];
+int ql = 1, qr = 0;
+bool check(double minus)
+{
+    ql = 1, qr = 0;
+    memset(d, 0, sizeof d);
+    memset(cnt, 0, sizeof cnt);
+    for (int i = 1; i <= n; ++i)
+    {
+        q[++qr] = i;
+        in[i] = 1;
+    }
+    while (qr >= ql)
+    {
+        int now = q[ql++];
+        in[now] = 0;
+        for (pair<int, double> to : fri[now])
+        {
+            if (d[now] + to.second - minus < d[to.first])
+            {
+                d[to.first] = d[now] + to.second - minus, cnt[to.first]++;
+                if (!in[to.first])
+                    q[++qr] = to.first, in[to.first] = 1;
+            }
+            if (cnt[to.first] > n)
+                return 1;
+        }
+    }
+    return 0;
+}
+int main()
+{
+    scanf("%d%d", &n, &m);
+    for (int i = 1, u, v; i <= m; ++i)
+    {
+        double w;
+        scanf("%d%d%lf", &u, &v, &w);
+        fri[u].push_back({v, w});
+    }
+    double l = -1e7, r = 1e7;
+    while (r - l > 1e-9)
+    {
+        double mid = (l + r) / 2;
+        if (check(mid))
+            r = mid;
+        else
+            l = mid;
+    }
+    printf("%.8lf\n", l);
+    return 0;
+}
\ No newline at end of file
diff --git a/solutions/P3199.md b/solutions/P3199.md
new file mode 100644
index 0000000..14f77d8
--- /dev/null
+++ b/solutions/P3199.md
@@ -0,0 +1,79 @@
+# P3199 最小圈
+
+思路：找到最小圈相当于找到最小环。
+
+只须二分答案环的平均值的最小值 $mid$，并把每条边均减去 $mid$，使用 SPFA 判断负环即可。
+
+调试记录：
+
+- 二分范围错误
+  - 因为存在负边权，二分范围应该为 $-10^7$ 到 $10^7$
+- SPFA 判负环逻辑错误
+  - SPFA 判断负环用的是单个路径的长度 $> n$ 而非访问的点个数 $> n$
+- 初始入队点错误
+  - 存在圈且有一个点能到达其他所有点，不一定是点 $1$
+- 入队条件错误
+  - SPFA 入队的条件是未在队列中且进行了松弛操作
+- 队列长度不足
+  - 一个点可能多次入队，队列长度应该为 $n \times m$
+
+```cpp
+#include <bits/stdc++.h>
+using namespace std;
+int n, m;
+vector<pair<int, double>> fri[3005];
+int q[30000005];
+double d[3005];
+bool in[3005];
+int cnt[3005];
+int ql = 1, qr = 0;
+bool check(double minus)
+{
+    ql = 1, qr = 0;
+    memset(d, 0, sizeof d);
+    memset(cnt, 0, sizeof cnt);
+    for (int i = 1; i <= n; ++i)
+    {
+        q[++qr] = i;
+        in[i] = 1;
+    }
+    while (qr >= ql)
+    {
+        int now = q[ql++];
+        in[now] = 0;
+        for (pair<int, double> to : fri[now])
+        {
+            if (d[now] + to.second - minus < d[to.first])
+            {
+                d[to.first] = d[now] + to.second - minus, cnt[to.first]++;
+                if (!in[to.first])
+                    q[++qr] = to.first, in[to.first] = 1;
+            }
+            if (cnt[to.first] > n)
+                return 1;
+        }
+    }
+    return 0;
+}
+int main()
+{
+    scanf("%d%d", &n, &m);
+    for (int i = 1, u, v; i <= m; ++i)
+    {
+        double w;
+        scanf("%d%d%lf", &u, &v, &w);
+        fri[u].push_back({v, w});
+    }
+    double l = -1e7, r = 1e7;
+    while (r - l > 1e-9)
+    {
+        double mid = (l + r) / 2;
+        if (check(mid))
+            r = mid;
+        else
+            l = mid;
+    }
+    printf("%.8lf\n", l);
+    return 0;
+}
+```