DFS
数据结构:栈
空间:O(h)使用空间具有绝对优势
回溯+剪枝 隐藏栈维护路径
排列数字
https://www.acwing.com/problem/content/844/
# include <iostream>
using namespace std;
const int N = 10;
int n, path[N];
bool st[N];
void dfs(int u)
{
if (u == n) // 枚举到第n个位置
{
for (int i = 0; i < n; i ++) cout << path[i] << ' ';
cout << endl;
return;
}
for (int i = 1; i <= n; i ++)
{
if (!st[i])
{
path[u] = i;
st[i] = true;
dfs(u + 1);
path[u] = 0;
st[i] = false;
}
}
}
int main()
{
cin >> n;
dfs(0); // 从第0个位置开始枚举
return 0;
}
N皇后问题
https://www.acwing.com/problem/content/845/
# include <iostream>
using namespace std;
const int N = 10;
int n;
char g[N][N];
bool col[N], dg[N], udg[N];
void dfs(int u)
{
if (u == n)
{
for (int i = 0; i < n; i ++) cout << g[i] << endl;
cout << endl;
return;
}
for (int i = 0; i < n; i ++)
{
if (!col[i] && !dg[u + i] && !udg[n - u + i])
{
g[u][i] = 'Q';
col[i] = dg[u + i] = udg[n - u + i] = true;
dfs(u + 1);
col[i] = dg[u + i] = udg[n - u + i] = false;
g[u][i] = '.';
}
}
}
int main()
{
cin >> n;
for (int i = 0; i < n; i ++)
for (int j = 0; j < n; j ++) g[i][j] = '.';
dfs(0);
}
BFS
数据结构:队列
空间:O(2^n)最短路径