#include <iostream> #include <vector> using namespace std; const int MAXN = 100; int n, m; int color[MAXN]; // 记录每个节点的颜色 bool g[MAXN][MAXN]; // 邻接矩阵 vector<int> adj[MAXN]; // 邻接表 void dfs(int u, int c) { color[u] = c; for (int v : adj[u]) { if (color[v] == 0) { // 如果未被染色,染成另一种颜色 dfs(v, 3 - c); } else if (color[v] == c) { // 如果相邻节点颜色相同,无法着色 cout << "Impossible to color the graph with " << m << " colors." << endl; exit(0); } } } int main() { // 读入邻接矩阵 cin >> n; for (int i = 1; i <= n; i++) { for (int j = 1; j <= n; j++) { cin >> g[i][j]; if (g[i][j]) { adj[i].push_back(j); } } } // 深度优先搜索染色 m = 1; for (int u = 1; u <= n; u++) { if (color[u] == 0) { dfs(u, 1); m = max(m, color[u]); } } // 输出结果 cout << "The graph can be colored with " << m << " colors." << endl; cout << "Coloring result: "; for (int u = 1; u <= n; u++) { cout << color[u] << " "; } cout << endl; return 0; }图图着色
时间: 2024-04-25 11:26:35 浏览: 20
这段代码实现了图的着色,采用了深度优先搜索的方法。在搜索过程中,用颜色数组记录每个节点的颜色,初始值为0。如果一个节点未被染色,就将它染成另一种颜色(用1和2代表两种颜色),然后继续对它的邻居节点进行染色。如果一个节点已经被染色,并且它的颜色与相邻节点的颜色相同,说明无法用m种颜色对该图进行着色。最后输出着色结果和需要的最少颜色数。
该算法的时间复杂度为O(n^2),其中n为节点数。实际上,采用邻接表存储图的话,时间复杂度可以降为O(n+m),其中m为边数。
相关问题
#include <iostream>#include <ctime>#include <cstdlib>using namespace std;const int MAXN = 500; // 需要排序的数组大小const int MAXV = 2000; // 随机数的最大值// 直接插入排序void insertSort(int a[], int
Sure, I can help you with that. The code you provided is written in C++ and it seems to be implementing the insertion sort algorithm. Insertion sort is a simple sorting algorithm that works by repeatedly inserting elements into a sorted portion of the array.
Here's the complete implementation of the insertion sort algorithm based on the code you provided:
```cpp
#include <iostream>
#include <ctime>
#include <cstdlib>
using namespace std;
const int MAXN = 500; // Size of the array to be sorted
const int MAXV = 2000; // Maximum value for random numbers
// Function to generate random numbers
void generateRandomArray(int a[], int n) {
srand(time(0));
for (int i = 0; i < n; i++) {
a[i] = rand() % MAXV;
}
}
// Function to print the array
void printArray(int a[], int n) {
for (int i = 0; i < n; i++) {
cout << a[i] << " ";
}
cout << endl;
}
// Insertion sort implementation
void insertionSort(int a[], int n) {
for (int i = 1; i < n; i++) {
int key = a[i];
int j = i - 1;
while (j >= 0 && a[j] > key) {
a[j + 1] = a[j];
j--;
}
a[j + 1] = key;
}
}
int main() {
int arr[MAXN];
// Generate random array
generateRandomArray(arr, MAXN);
cout << "Original array: ";
printArray(arr, MAXN);
// Sort the array using insertion sort
insertionSort(arr, MAXN);
cout << "Sorted array: ";
printArray(arr, MAXN);
return 0;
}
```
This code generates a random array of size `MAXN` with values ranging from 0 to `MAXV`. It then sorts the array using the insertion sort algorithm and prints the original and sorted arrays.
Let me know if you have any further questions or if there's anything else I can assist you with!
#include<cstdio> #include<cstdlib> #include<cstring> #include<cmath> #include<ctime> #include<iostream> #include<algorithm> #include<map> #include<stack> #include<queue> #include<vector> #include<set> #include<string> #define dd double #define ll long long dd PI = acos(-1); using namespace std; const ll MAXN = 1e5 + 5; const ll INF = 1e9 + 5; ll n; struct node { ll x, y; }s[5000]; ll dp[MAXN] = { 0 }; int main() { //ios::sync_with_stdio(false); ll n, m; cin >> n >> m; for (ll i = 1; i <= n; i++) { cin >> s[i].x >> s[i].y; } for (ll i = 1; i <= n; i++) { for (ll j = m; j >= s[i].x; j--) { dp[j] = max(dp[j], dp[j - s[i].x] + s[i].y); } } cout << dp[m] << endl; }
这是一段动态规划求解背包问题的代码,用来求解一个容量为m的背包能够装下的最大价值。具体实现过程为:
1. 定义一个结构体node,用来存储物品的重量和价值。
2. 读入物品数量n和背包容量m,然后读入每个物品的重量和价值。
3. 使用二重循环,遍历每一个物品,然后从大到小枚举背包容量j,更新dp[j]的值,表示容量为j的背包能够装下的最大价值。
4. 最后输出dp[m]的值,即容量为m的背包能够装下的最大价值。
值得注意的是,这段代码中还定义了一些常量和宏定义,如MAXN、INF等,以及一些头文件和命名空间的使用。
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