# 在环中，白书P333UVa11090（bellman—ford负圈判定，二分查找）

1.通过本题详细理解了bellman—ford算法与dijkstra算法的原理以及具体操作细节差异。
2.本题是bellman—ford判断负圈的特殊形式。因为要判负圈，所以初始化d[]数组时的操作与原模板略有不同：

`````` queue<int> Q;
memset(inq, 0, sizeof(inq));
memset(cnt, 0, sizeof(cnt));
for(int i = 0; i < n; i++) { d[i] = 0; inq[0] = true; Q.push(i); }``````

3.二分查找算法应用（注意数据类型）。

``````if(!test(ub+1)) printf("No cycle found.\n");
else {
double L = 0, R = ub;
while(R - L > 1e-3) {
double M = L + (R-L)/2;
if(test(M)) R = M; else L = M;
}``````
``````// UVa11090 Going in Cycle!!
// Rujia Liu
#include<cstdio>
#include<cstring>
#include<queue>
using namespace std;

const int INF = 1000000000;
const int maxn = 1000;

struct Edge {
int from, to;
double dist;
};

struct BellmanFord {
int n, m;
vector<Edge> edges;
vector<int> G[maxn];
bool inq[maxn];     // 是否在队列中
double d[maxn];     // s到各个点的距离
int p[maxn];        // 最短路中的上一条弧
int cnt[maxn];      // 进队次数

void init(int n) {
this->n = n;
for(int i = 0; i < n; i++) G[i].clear();
edges.clear();
}

void AddEdge(int from, int to, double dist) {
edges.push_back((Edge){from, to, dist});
m = edges.size();
G[from].push_back(m-1);
}

bool negativeCycle() {
queue<int> Q;
memset(inq, 0, sizeof(inq));
memset(cnt, 0, sizeof(cnt));
for(int i = 0; i < n; i++) { d[i] = 0; inq[0] = true; Q.push(i); }

while(!Q.empty()) {
int u = Q.front(); Q.pop();
inq[u] = false;
for(int i = 0; i < G[u].size(); i++) {
Edge& e = edges[G[u][i]];
if(d[e.to] > d[u] + e.dist) {
d[e.to] = d[u] + e.dist;
p[e.to] = G[u][i];
if(!inq[e.to]) { Q.push(e.to); inq[e.to] = true; if(++cnt[e.to] > n) return true; }
}
}
}
return false;
}
};

BellmanFord solver;

bool test(double x) {
for(int i = 0; i < solver.m; i++)
solver.edges[i].dist -= x;
bool ret = solver.negativeCycle();
for(int i = 0; i < solver.m; i++)
solver.edges[i].dist += x;
return ret;
}

int main() {
int T;
scanf("%d", &T);
for(int kase = 1; kase <= T; kase++) {
int n, m;
scanf("%d%d", &n, &m);
solver.init(n);
int ub = 0;
while(m--) {
int u, v, w;
scanf("%d%d%d", &u, &v, &w); u--; v--; ub = max(ub, w);
}
printf("Case #%d: ", kase);

if(!test(ub+1)) printf("No cycle found.\n");
else {
double L = 0, R = ub;
while(R - L > 1e-3) {
double M = L + (R-L)/2;
if(test(M)) R = M; else L = M;
}
printf("%.2lf\n", L);
}
}
return 0;
}``````
原文作者：Bellman - ford算法
原文地址: https://blog.csdn.net/NCUscienceZ/article/details/78595894
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