HDU 3435 A new Graph Game
题意:又是这类求环总和的最小值,一个点只能在一个环上
思路:KM完美匹配求解,不过这题点有1000,理论上n^3算法是过不了的,不过也没有更好的方法了,用费用流来做的话也是n^3,而且常数还更大
代码:
#include <cstdio> #include <cstring> #include <cmath> #include <algorithm> using namespace std; const int MAXNODE = 1005; typedef int Type; const Type INF = 0x3f3f3f3f; struct KM { int n; Type g[MAXNODE][MAXNODE]; Type Lx[MAXNODE], Ly[MAXNODE], slack[MAXNODE]; int left[MAXNODE]; bool S[MAXNODE], T[MAXNODE]; void init(int n) { this->n = n; for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) g[i][j] = -INF; } void add_Edge(int u, int v, Type val) { g[u][v] = max(g[u][v], val); } bool dfs(int i) { S[i] = true; for (int j = 0; j < n; j++) { if (T[j]) continue; Type tmp = Lx[i] + Ly[j] - g[i][j]; if (!tmp) { T[j] = true; if (left[j] == -1 || dfs(left[j])) { left[j] = i; return true; } } else slack[j] = min(slack[j], tmp); } return false; } void update() { Type a = INF; for (int i = 0; i < n; i++) if (!T[i]) a = min(a, slack[i]); for (int i = 0; i < n; i++) { if (S[i]) Lx[i] -= a; if (T[i]) Ly[i] += a; } } void km() { for (int i = 0; i < n; i++) { left[i] = -1; Lx[i] = -INF; Ly[i] = 0; for (int j = 0; j < n; j++) Lx[i] = max(Lx[i], g[i][j]); } for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) slack[j] = INF; while (1) { for (int j = 0; j < n; j++) S[j] = T[j] = false; if (dfs(i)) break; else update(); } } int ans = 0; for (int i = 0; i < n; i++) { if (g[left[i]][i] == -INF) { printf("NO\n"); return; } ans += g[left[i]][i]; } printf("%d\n", -ans); } } gao; int t, n, m; int main() { int cas = 0; scanf("%d", &t); while (t--) { scanf("%d%d", &n, &m); gao.init(n); int u, v, w; while (m--) { scanf("%d%d%d", &u, &v, &w); u--; v--; gao.add_Edge(u, v, -w); gao.add_Edge(v, u, -w); } printf("Case %d: ", ++cas); gao.km(); } return 0; }