标签：i++ bsp color bool else font add style scanf
第一行2个正整数，分别为n和m
以下m行，每行3个数，表示边连接的信息，
若设边权为v，那么n≤3000,m≤10000,v≤50000
最小化平均值($01$分数规划)。
使用二分求解。对于一个猜测的$mid$,只需判断是否存在平均值小于$mid$的回路。
如何判断?
假设存在一个包含$k$条边的回路,回路上各边权值为$w_1$ ,$w_2$ ,$...$,$w_k$ ,那么平均值小于$midv意味着:
$$w_1 +w_2 +...+w_k <k×mid$$
即:
$$(w_1 -mid)+(w_2 -mid)+...+(w_k -mid)<0$$
换句话说,只要把边$(a,b)$的权$w(a,b)$改成$w(a,b)-mid$,再判断新图中是否有负环即可。
存在负环,那么之前的不等式满足,即存在着更小的平均值,$r=mid$;不存在,$l=mid$。
1 //It is made by Awson on 2017.10.9 2 #include <set> 3 #include <map> 4 #include <cmath> 5 #include <ctime> 6 #include <cmath> 7 #include <stack> 8 #include <queue> 9 #include <vector> 10 #include <string> 11 #include <cstdio> 12 #include <cstdlib> 13 #include <cstring> 14 #include <iostream> 15 #include <algorithm> 16 #define LL long long 17 #define Min(a, b) ((a) < (b) ? (a) : (b)) 18 #define Max(a, b) ((a) > (b) ? (a) : (b)) 19 #define sqr(x) ((x)*(x)) 20 using namespace std; 21 const double eps = 1e-9; 22 const int N = 3000; 23 const int M = 10000; 24 25 int n, m, u, v, c; 26 bool vis[N+5]; 27 double dist[N+5]; 28 struct tt { 29 int to, next; 30 double cost; 31 }edge[M+5]; 32 int path[N+5], top; 33 34 void add(int u, int v, double c) { 35 edge[++top].to = v; 36 edge[top].next = path[u]; 37 edge[top].cost = c; 38 path[u] = top; 39 } 40 bool dfs(int u, double dec) { 41 vis[u] = 1; 42 for (int i = path[u]; i; i = edge[i].next) 43 if (dist[edge[i].to] > dist[u]+edge[i].cost-dec) { 44 if (vis[edge[i].to]) return true; 45 dist[edge[i].to] = dist[u]+(double)edge[i].cost-dec; 46 if (dfs(edge[i].to, dec)) return true; 47 } 48 vis[u] = 0; 49 return false; 50 } 51 bool judge(double dec) { 52 for (int i = 1; i <= n; i++) { 53 memset(vis, 0, sizeof(vis)); 54 memset(dist, 0, sizeof(dist)); 55 if (dfs(i, dec)) return true; 56 } 57 return false; 58 } 59 void work() { 60 scanf("%d%d", &n, &m); 61 double L = 0, R = 0; 62 for (int i = 1; i <= m; i++) { 63 scanf("%d%d%d", &u, &v, &c); 64 add(u, v, c); 65 R = max(R, (double)c); 66 } 67 while (R-L >= eps) { 68 double mid = (L+R)/2.; 69 if (judge(mid)) R = mid; 70 else L =mid; 71 } 72 printf("%.8lf\n", (L+R)/2.); 73 } 74 int main() { 75 work(); 76 return 0; 77 }
标签：i++ bsp color bool else font add style scanf
原文地址：http://www.cnblogs.com/NaVi-Awson/p/7641518.html
