UVA 10249 - The Grand Dinner（网络流 or 贪心）

UVA 10249 - The Grand Dinner

题目链接

题意：给定几队队员，几张桌子，每队有一个人数，每个桌子也有一个容量上限，要求一种安排方案，使得没有同队人坐在一个桌子上，求方案

思路：明显贪心可以搞- -， 每次往容量最多的桌子塞就可以了。。不过这题既然出在网络流这章，还是用网络流也搞了下

源点连到每队，桌子连到汇点，容量就是容量，然后每队和每个桌子相连，容量为1，表示一个桌子只能做一个队员，然后跑一下最大流即可

代码：

网络流：

#include <cstdio>
#include <cstring>
#include <queue>
#include <algorithm>
using namespace std;

const int MAXNODE = 1005;
const int MAXEDGE = 1000005;

typedef int Type;
const Type INF = 0x3f3f3f3f;

struct Edge {
int u, v;
Type cap, flow;
Edge() {}
Edge(int u, int v, Type cap, Type flow) {
this->u = u;
this->v = v;
this->cap = cap;
this->flow = flow;
}
};

struct Dinic {
int n, m, s, t;
Edge edges[MAXEDGE];
int first[MAXNODE];
int next[MAXEDGE];
bool vis[MAXNODE];
Type d[MAXNODE];
int cur[MAXNODE];
vector<int> cut;

void init(int n) {
this->n = n;
memset(first, -1, sizeof(first));
m = 0;
}
void add_Edge(int u, int v, Type cap) {
edges[m] = Edge(u, v, cap, 0);
next[m] = first[u];
first[u] = m++;
edges[m] = Edge(v, u, 0, 0);
next[m] = first[v];
first[v] = m++;
}

bool bfs() {
memset(vis, false, sizeof(vis));
queue<int> Q;
Q.push(s);
d[s] = 0;
vis[s] = true;
while (!Q.empty()) {
int u = Q.front(); Q.pop();
for (int i = first[u]; i != -1; i = next[i]) {
Edge& e = edges[i];
if (!vis[e.v] && e.cap > e.flow) {
vis[e.v] = true;
d[e.v] = d[u] + 1;
Q.push(e.v);
}
}
}
return vis[t];
}

Type dfs(int u, Type a) {
if (u == t || a == 0) return a;
Type flow = 0, f;
for (int &i = cur[u]; i != -1; i = next[i]) {
Edge& e = edges[i];
if (d[u] + 1 == d[e.v] && (f = dfs(e.v, min(a, e.cap - e.flow))) > 0) {
e.flow += f;
edges[i^1].flow -= f;
flow += f;
a -= f;
if (a == 0) break;
}
}
return flow;
}

bool Maxflow(int s, int t, int tot) {
this->s = s; this->t = t;
Type flow = 0;
while (bfs()) {
for (int i = 0; i < n; i++)
cur[i] = first[i];
flow += dfs(s, INF);
}
return flow == tot;
}

void MinCut() {
cut.clear();
for (int i = 0; i < m; i += 2) {
if (vis[edges[i].u] && !vis[edges[i].v])
cut.push_back(i);
}
}
} gao;

const int N = 105;

int n, m, p
, t
;
vector<int> ans
;

int main() {
while (~scanf("%d%d", &n, &m) && n || m) {
gao.init(n + m + 2);
int sum = 0;
for (int i = 1; i <= n; i++) {
ans[i].clear();
scanf("%d", &p[i]);
sum += p[i];
gao.add_Edge(0, i, p[i]);
}
for (int i = 1; i <= m; i++) {
scanf("%d", &t[i]);
gao.add_Edge(n + i, n + m + 1, t[i]);
for (int j = 1; j <= n; j++)
gao.add_Edge(j, n + i, 1);
}
if (gao.Maxflow(0, n + m + 1, sum)) {
printf("1\n");
for (int i = 0; i < gao.m; i++) {
if (gao.edges[i].u >= 1 && gao.edges[i].u <= n && gao.edges[i].v >= n + 1 && gao.edges[i].v <= n + m && gao.edges[i].flow == 1) {
ans[gao.edges[i].u].push_back(gao.edges[i].v - n);
}
}
for (int i = 1; i <= n; i++) {
for (int j = 0; j < ans[i].size(); j++) {
printf("%d%c", ans[i][j], j == ans[i].size() - 1 ? '\n' : ' ');
}
}
} else printf("0\n");
}
return 0;
}

贪心:

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

const int N = 105;

int n, m, ans

;

struct State {
int num, id;
} p
, t
;

bool cmp(State a, State b) {
return a.num > b.num;
}

bool judge() {
for (int i = 1; i <= n; i++) {
int s = 1;
for (int j = 1; j <= p[i].num; j++) {
while (t[s].num == 0 && s <= m) s++;
if (s > m) return false;
ans[i][j] = t[s].id;
t[s++].num--;
}
}
return true;
}

int main() {
while (~scanf("%d%d", &n, &m) && n || m) {
for (int i = 1; i <= n; i++)
scanf("%d", &p[i].num);
for (int i = 1; i <= m; i++) {
scanf("%d", &t[i].num);
t[i].id = i;
}
sort(t + 1, t + m + 1, cmp);
if (!judge()) printf("0\n");
else {
printf("1\n");
for (int i = 1; i <= n; i++) {
printf("%d", ans[i][1]);
for (int j = 2; j <= p[i].num; j++)
printf(" %d", ans[i][j]);
printf("\n");
}
}
}
return 0;
}