Ultraviolet A 1349-optimal Bus Route Design (km perfect match)

Ultraviolet A 1349-optimal Bus Route Design

Question Link

Given some directed weighted edges, find and construct these edges into one ring with the minimum total weight.

Train of Thought: Since the ring inbound degree exit is 1, you can split each point into an inbound degree and an outbound degree, and then create a perfect match for a bipartite graph. Pay attention to this question, heavy edge

Code:

#include <cstdio>#include <cstring>#include <cmath>#include <algorithm>using namespace std;const int MAXNODE = 105;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();}}}void solve() {km();int ans = 0, flag = 0;for (int i = 0; i < n; i++) {if (g[left[i]][i] == -INF) {flag = 1;break;}ans += g[left[i]][i];}if (flag) printf("N\n");else printf("%d\n", -ans);}} gao;int n;int main() {while (~scanf("%d", &n) && n) {gao.init(n);int a, b;for (int i = 0; i < n; i ++) {while (scanf("%d", &a)) {if (a == 0) break;scanf("%d", &b);a--;gao.add_Edge(i, a, -b);}}gao.solve();}return 0;}

Ultraviolet A 1349-optimal Bus Route Design (km perfect match)