用c++
时间: 2023-07-01 15:15:19 浏览: 60
好的,这是使用 C++ 实现任务分配问题分支限界算法的代码:
```c++
#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
#include <ctime>
using namespace std;
// 随机生成任务成本矩阵
vector<vector<int>> generate_cost_matrix(int n) {
vector<vector<int>> cost_matrix(n, vector<int>(n));
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
cost_matrix[i][j] = rand() % 10 + 1;
}
}
return cost_matrix;
}
// 计算状态的限界值
int calculate_bound(const vector<int>& state, const vector<vector<int>>& cost_matrix) {
// 已分配的任务成本总和
int bound = 0;
for (int i = 0; i < state.size(); i++) {
if (state[i] != -1) {
bound += cost_matrix[i][state[i]];
}
}
// 剩余未分配任务的最小成本估计
for (int i = state.size(); i < cost_matrix.size(); i++) {
int min_cost = INT_MAX;
for (int j = 0; j < state.size(); j++) {
if (find(state.begin(), state.end(), j) == state.end()) {
min_cost = min(min_cost, cost_matrix[i][j]);
}
}
bound += min_cost;
}
return bound;
}
// 扩展状态
vector<pair<int, vector<int>>> expand_state(const vector<int>& state, const vector<vector<int>>& cost_matrix) {
vector<pair<int, vector<int>>> states;
for (int i = state.size(); i < cost_matrix.size(); i++) {
for (int j = 0; j < state.size(); j++) {
if (find(state.begin(), state.end(), j) == state.end()) {
vector<int> new_state(state);
new_state.push_back(j);
int bound = calculate_bound(new_state, cost_matrix);
states.push_back(make_pair(bound, new_state));
}
}
}
return states;
}
// 任务分配问题求解
int task_assignment(int n) {
vector<vector<int>> cost_matrix = generate_cost_matrix(n);
vector<int> initial_state(n, -1);
priority_queue<pair<int, vector<int>>, vector<pair<int, vector<int>>>, greater<pair<int, vector<int>>>> queue;
queue.push(make_pair(calculate_bound(initial_state, cost_matrix), initial_state));
while (!queue.empty()) {
int bound = queue.top().first;
vector<int> state = queue.top().second;
queue.pop();
if (state.size() == n) {
// 找到可行解
int cost = 0;
for (int i = 0; i < n; i++) {
cost += cost_matrix[i][state[i]];
}
return cost;
}
vector<pair<int, vector<int>>> new_states = expand_state(state, cost_matrix);
for (auto new_state : new_states) {
if (new_state.first < bound) {
queue.push(new_state);
}
}
}
return -1;
}
int main() {
srand(time(0));
for (int n = 3; n <= 9; n++) {
int cost = task_assignment(n);
cout << "n = " << n << ", cost = " << cost << endl;
}
return 0;
}
```
这里使用了 STL 中的 vector、queue、algorithm 等容器和算法来实现任务分配问题的分支限界算法。和 Python 版本的实现类似,我们也是使用优先队列来维护待扩展状态,其中每个元素都是一个 pair 类型的二元组 (bound, state),表示该状态的限界值和状态本身。在队列中,优先按照 bound 的大小进行排序,每次取出 bound 最小的状态进行扩展。同时,为了方便计算限界值,我们将未分配任务的人员编号设为 -1。
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