分配甲、乙、丙、丁四人去完成五项任务,每人完成各项任务的时间如下表所示。由于任务数多于人数,故规定其中有一个人可完成两项任务,其余三人每人只完成一项任务。试确定总花费时间最少的分配任务方案。(只建立模型,不必求解)
人员\任务 | A | B | C | D | E |
---|---|---|---|---|---|
甲 | 9 | 2 | 4 | 15 | 9 |
乙 | 6 | 5 | 12 | 4 | 2 |
丙 | 11 | 7 | 13 | 4 | 17 |
丁 | 19 | 11 | 15 | 8 | 9 |
#include <bits/stdc++.h>
#define pii pair<int,int>
#define fi first
#define se second
using namespace std;
int a[10][10];
bool v[10];
struct sta {
int sum, two;
pii c;
vector<pii > one;
};
vector<sta> sch;
inline void per(int x) {
switch (x) {
case 1:
printf("甲");
break;
case 2:
printf("乙");
break;
case 3:
printf("丙");
break;
default:
printf("丁");
}
}
void dfs(int u, sta now) {
if (u == 5) {
if (!sch.empty() && sch.back().sum > now.sum)sch.clear();
if (sch.empty() || sch.back().sum == now.sum)
sch.push_back(now);
return;
}
if (!sch.empty() && sch.back().sum < now.sum)return;
vector<int> c;
for (int i = 1; i <= 5; i++)if (!v[i])c.push_back(i);
if (u == 4 && c.size() == 2) {
v[c[0]] = true, v[c[1]] = true;
sta nex = now;
nex.two = u;
nex.sum += a[u][c[0]] + a[u][c[1]];
nex.c = make_pair(c[0], c[1]);
dfs(u + 1, nex);
v[c[0]] = false, v[c[1]] = false;
return;
}
for (int i = 0; i < c.size(); i++) {
sta nex = now;
nex.sum += a[u][c[i]];
nex.one.emplace_back(u, c[i]);
v[c[i]] = true;
dfs(u + 1, nex);
v[c[i]] = false;
}
for (int i = 0; i < c.size(); i++)
for (int j = i + 1; j < c.size(); j++) {
v[c[i]] = true, v[c[j]] = true;
sta nex = now;
nex.two = u;
nex.sum += a[u][c[i]] + a[u][c[j]];
nex.c = make_pair(c[i], c[j]);
dfs(u + 1, nex);
v[c[i]] = false, v[c[j]] = false;
}
}
int main() {
for (int i = 1; i <= 4; i++)
for (int j = 1; j <= 5; j++)
scanf("%d", &a[i][j]);
sta now = {0, 0, {0, 0}, {}};
dfs(1, now);
printf("总最小花费时间为:%d\n", sch.back().sum);
for (int i = 0; i < sch.size(); i++) {
cout << "方案" << i + 1 << ":" << endl;
per(sch[i].two);
cout << "完成任务:" << (char) ('A' + sch[i].c.fi - 1) << "和"
<< (char) ('A' + sch[i].c.se - 1) << endl;
for (int j = 0; j < sch[i].one.size(); j++) {
per(sch[i].one[j].fi);
cout << "完成任务:" << (char) ('A' + sch[i].one[j].se - 1) << endl;
}
puts("");
}
return 0;
}
/*
9 2 4 15 9
6 5 12 4 2
11 7 13 4 17
19 11 15 8 9
*/
总最小花费时间为:25
方案1:
甲完成任务:B和C
乙完成任务:A
丙完成任务:D
丁完成任务:E