POJ 2135 Farm Tour and HDU 1853 Cyclic Tour (initial application of fee flow)

Source: Internet
Author: User
Tags min time limit
Farm Tour (portal)

Time limit:1000ms Memory limit:65536k
Total submissions:15477 accepted:5966 Description

When FJ's friends visit him on the farm, he likes to show them around. His farm comprises N (1<=n<=1000) n (1 fields numbered 1..N 1..N, the first of which contains he house and the Nth O F which contains the big barn. A Total m (1<=m<=10000) m (1 paths, that connect, the fields in various ways. Each path connects the different fields and have a nonzero length smaller than 35,000 35,000.

To show off his farm in the best-of-the-walks, he-a-tour-that-starts at his house, potentially travels through-some fields, a nd ends at the barn. Later, he returns (potentially through some fields) the back to his house again.

He wants his tour to being as short as possible, however he doesn ' t want-walk on any given path more than once. Calculate the shortest tour possible. FJ is sure this some tour exists for any given farm. Input

Line 1 1:two space-separated integers:n N and M M.

Lines 2 2. M+1 m+1:three space-separated integers that define a path:the starting field, the End field, and the path ' s length. Output

A single line containing the length of the shortest tour. Sample Input

4 5
1 2 1
2 3 1
3 4 1
1 3 2
2 4 2 Sample Output

6 Source

Usaco 2003 February Green

Test instructions

give you n n vertices, M m bars, solve the shortest path from 1 1 to n N and then from n N to 1 1, each of which is allowed to be accessed only once.

Thinking of solving problems

From 0 0 constructs an edge to 1 1, its capacity is 2 2, then constructs an n n to n+1 n+1 edge, the capacity also is 2, then the expense flow template goes one side, solves the 0 0 to n+1 n+1 the minimum expense flow.


#include <cstdio> #include <cstring> #include <cstdlib> #include <queue> #include <iostream&

#include <algorithm> #include <functional> using namespace std;
typedef pair<int,int > PII;
const int MAXN = 4e4 + 5;

const int INF = 0X3F3F3F3F; struct edge{int u, V, cap, flow, cost, NXT;}

E[MAXN << 1];

int HEAD[MAXN], tot;

    void Edge_init () {tot = 0;
Memset (Head,-1, sizeof (head));
    } void Add_edge (int u, int v, int cap, int cost) {e[tot].u = u;
    E[TOT].V = v;
    E[tot].cap = cap;
    E[tot].flow = 0;
    E[tot].cost = Cost;
    E[TOT].NXT = Head[u];

    Head[u] = tot + +;
    e[tot].u = v;
    E[TOT].V = u;
    E[tot].cap = 0;
    E[tot].flow = 0;
    E[tot].cost =-cost;
    E[TOT].NXT = Head[v];
HEAD[V] = tot + +;
    } bool SPFA (int start, int end) {queue<int>q;
    Memset (Vis, false, sizeof (VIS));
    memset (Pre,-1, sizeof (pre)); memset (Dis, 0x3f, sizeof (DIS));
    Dis[start] = 0;
    Vis[start] = true;
    Q.push (start);
        while (!q.empty ()) {int u = q.front ();
        Q.pop ();
        Vis[u] = false;
            for (int i = head[u]; ~i;i = e[i].nxt) {int v = E[I].V;
                if (E[i].cap-e[i].flow && dis[v] > Dis[u] + e[i].cost) {Dis[v] = Dis[u] + e[i].cost;
                PRE[V] = i;
                    if (!vis[v]) {Vis[v] = true;
                Q.push (v);
    }}}} if (pre[end] = = 1) return false;
return true;
    } PII min_flow (int s,int t) {int flow = 0;
    int cost = 0;
        while (SPFA (s, t)) {int Min = INF; for (int i = Pre[t];~i;i = pre[e[i].u]) {if (min > E[i].cap-e[i].flow) {min = e[i].cap-e[
            }} for (int i = pre[t]; ~i;i = pre[e[i].u]) {e[i].flow + = Min;
            e[i ^ 1].flow-= Min; Cost + = E[i].cost * Min;
    } flow + = Min;
} return Make_pair (flow, cost);

} int N, M;
        int main () {while (~scanf ("%d%d", &n, &m)) {int A, b, C;
        Edge_init ();
            for (int i = 0;i < M;i + +) {scanf ("%d%d%d", &a, &b, &c);
            Add_edge (A, B, 1, c);
        Add_edge (b, A, 1, c);
        } add_edge (0, 1, 2, 0);
        Add_edge (n, n + 1, 2, 0);
        PII AA = Min_flow (0, N + 1);
    printf ("%d\n", Aa.second);
} return 0;
Cyclic Tour (portal)

Time limit:1000/1000 MS (java/others

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