#include <algorithm> // all_of, find, for_each

#include <algorithm> 是C++标准库中的一个头文件，它提供了一系列的算法，用于处理容器或者其他序列类型的元素。以下是其中几个常用的函数：

1. **all_of**: 这个函数遍历给定范围的所有元素，并检查是否所有元素都满足某个条件。如果条件成立，则返回true；否则返回false。

   bool result = std::all_of(arr.begin(), arr.end(), condition_function);

2. **find**: 查找第一个使得谓词函数(condition_function)返回true的元素在输入范围内的迭代器。如果没有找到这样的元素，返回end()。

   auto it = std::find(arr.begin(), arr.end(), value);
   if (it != arr.end()) {
       // 找到了
   } else {
       // 没有找到
   }

3. **for_each**: 对指定范围内的每个元素应用一个操作（function_object），通常用来执行某种副作用或转换。

   std::for_each(arr.begin(), arr.end(), operation);

这些函数可以极大地简化数组、向量或其他容器的操作，提高代码的效率和可读性。

相关问题

Optimize time complexity and merely output your new code: #include <iostream> using namespace std; const int INF = 1e9; int find_min_cost(int n, int c[][100], int w[][100]) { /* 数据处理 */ for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { if (w[i][j] == 0) { w[i][j] = INF; } } } for (int k = 0; k < n; k++) { for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { c[i][j] = min(c[i][j], c[i][k] + c[k][j]); w[i][j] = min(w[i][j], c[i][j] + min(w[i][k], w[k][j])); } } } int total_cost = 0; for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { if (w[i][j] != INF) { total_cost += w[i][j]; } } } return total_cost; } int main() { /* 初始化变量 */ int n; cin >> n; int c[100][100], w[100][100]; for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { cin >> c[i][j]; } } for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { cin >> w[i][j]; } } /* 输出结果 */ cout << find_min_cost(n, c, w) << endl; return 0; }

To optimize the time complexity, we can use the fact that the graph is weighted with positive or negative edge weights but no negative cycles. This means that we can use the Bellman-Ford algorithm to find the shortest paths from each vertex to all other vertices in O(n^2m) time complexity, where m is the number of edges in the graph. Then, we can use these shortest paths to compute the minimum cost using the modified Floyd-Warshall algorithm in O(n^3) time complexity.

Here is the modified code:

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

const int INF = 1e9;

int find_min_cost(int n, int c[][100], int w[][100]) {
    /* 数据处理 */
    vector<vector<int>> d(n, vector<int>(n, INF));
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if (w[i][j] != 0) {
                d[i][j] = w[i][j];
            }
        }
    }
    for (int k = 0; k < n; k++) {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                d[i][j] = min(d[i][j], d[i][k] + d[k][j]);
            }
        }
    }
    /* 计算最小花费 */
    int total_cost = 0;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            if (c[i][j] != 0) {
                int min_dist = INF;
                for (int k = 0; k < n; k++) {
                    min_dist = min(min_dist, d[i][k] + c[k][j]);
                }
                total_cost += min_dist;
            }
        }
    }
    return total_cost;
}

int main() {
    /* 初始化变量 */
    int n;
    cin >> n;
    int c[100][100], w[100][100];
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            cin >> c[i][j];
        }
    }
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            cin >> w[i][j];
        }
    }
    /* 输出结果 */
    cout << find_min_cost(n, c, w) << endl;
    return 0;
}

In this modified code, we first use a vector `d` to store the shortest distances between each pair of vertices using the Bellman-Ford algorithm. Then, we compute the minimum cost using a nested loop that iterates over all pairs of vertices and all intermediate vertices, and computes the minimum distance between the pair of vertices via an intermediate vertex. The overall time complexity of this algorithm is O(n^2m + n^3), which is faster than the original algorithm for sparse graphs (where m << n^2).

list<T> contains

The `std::list<T>` container in C++ is a doubly-linked list implementation where each element is stored in a separate node. The `list` container offers constant time insertion and removal of elements from anywhere in the container, but accessing elements by index requires linear time.

To check if a `list` contains a specific element, you can use the `std::find` algorithm from the `<algorithm>` header. Here's an example:

#include <iostream>
#include <list>
#include <algorithm>

int main() {
    std::list<int> mylist = {1, 2, 3, 4, 5};
    int to_find = 3;

    if (std::find(mylist.begin(), mylist.end(), to_find) != mylist.end()) {
        std::cout << "Found " << to_find << " in the list!\n";
    } else {
        std::cout << to_find << " not found in the list.\n";
    }

    return 0;
}

In this example, we create a `list` of integers `mylist` and initialize it with values 1 through 5. We want to check if the `list` contains the value 3, so we use `std::find` to search for it. If `std::find` returns an iterator pointing to the end of the `list`, it means the element was not found. Otherwise, we output a message saying we found the element.