谢尔宾斯基三角形（英语：Sierpinski triangle）是一种分形，由波兰数学家谢尔宾斯基在1915年提出。它是自相似集的例子。它的豪斯多夫维是log(3)/log(2) ≈ 1.585。
今天我们来学学如何用代码生成任意第n图形
对于这个图形，显然我们知道它的每个子结构都是相同的，所以具有递归的性质
所以我们把握好递归边界，递归分治往下画就行了
代码：
#include <iostream> #include <vector> #include <string> #include <algorithm> #include <cstdio> #include <cstring> #include <ctime> #include <cstdlib> #include <set> #include <map> #include <cctype> #include <list> #include <cmath> #include <bitset> #include <queue> #include <stack> #include <sstream> #include <functional> #include <cassert> using namespace std; #define tmax(a, b) if (b > a) a = b #define tmin(a, b) if (b < a) a = b char inc() { char _[10]; scanf("%s", _); return _[0]; } int ini() { int _; scanf("%d", &_); return _; } long long inll() { long long _; scanf("%I64d", &_); return _; } double ind() { double _; scanf("%lf", &_); return _; } string ins() { string _; cin >> _; return _; } int inl(char _[]) { if (!fgets(_, (int)1e8, stdin)) return -1; int i = strlen(_); if (_[i - 1] == '\n') _[--i] = 0; return i; } typedef pair<int, int> pii; typedef pair<char, char> pcc; typedef long long LL; const int inf = 0x3f3f3f3f; const LL lnf = 0x3f3f3f3f3f3f3f3f; const double pi = 3.14159265358979323846; const double eps = 1e-8; const int mod = 100007; const int maxn = 1e3+ 10; char mp[maxn][maxn]; void Draw(int n, int x, int y) { if (n == 1) { mp[x][y + 1] = mp[x][y + 2] = '_'; mp[x][y] = mp[x - 1][y + 1] = '/'; mp[x - 1][y + 2] = mp[x][y + 3] = '\\'; return; } int w = 1 << n; int h = w >> 1; Draw(n - 1, x, y); Draw(n - 1, x, y + w); Draw(n - 1, x - h, y + w / 2); } int main() { int CAS = 0; //std::ios::sync_with_stdio(0); //std::cin.tie(0); #ifdef NIGHT_13 freopen("in.txt", "r", stdin); freopen("out.txt", "w", stdout); int time_night_13 = clock(); #endif // NIGHT_13 int n = ini(); Draw(n, (1 << n) - 1 , 0); for (int i = 0, st = 1 << n; i < 1 << n; ++i, ++st) { for (int j = 0; j <= st; ++j) { printf("%c", mp[i][j] ? mp[i][j] : ' '); } puts(""); } #ifdef NIGHT_13 fprintf(stderr, "\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n"); fprintf(stderr, "\t Time: %dms", (int)clock() - time_night_13); fprintf(stderr, "\n...........................................\n\n"); #endif // NIGHT_13 return 0; } 运行效果： -------------------n = 1-------------------------- /\ /__\ -------------------n = 2-------------------------- /\ /__\ /\ /\ /__\/__\ -------------------n = 3-------------------------- /\ /__\ /\ /\ /__\/__\ /\ /\ /__\ /__\ /\ /\ /\ /\ /__\/__\/__\/__\ -------------------n = 4-------------------------- /\ /__\ /\ /\ /__\/__\ /\ /\ /__\ /__\ /\ /\ /\ /\ /__\/__\/__\/__\ /\ /\ /__\ /__\ /\ /\ /\ /\ /__\/__\ /__\/__\ /\ /\ /\ /\ /__\ /__\ /__\ /__\ /\ /\ /\ /\ /\ /\ /\ /\ /__\/__\/__\/__\/__\/__\/__\/__\ -------------------n = 5-------------------------- /\ /__\ /\ /\ /__\/__\ /\ /\ /__\ /__\ /\ /\ /\ /\ /__\/__\/__\/__\ /\ /\ /__\ /__\ /\ /\ /\ /\ /__\/__\ /__\/__\ /\ /\ /\ /\ /__\ /__\ /__\ /__\ /\ /\ /\ /\ /\ /\ /\ /\ /__\/__\/__\/__\/__\/__\/__\/__\ /\ /\ /__\ /__\ /\ /\ /\ /\ /__\/__\ /__\/__\ /\ /\ /\ /\ /__\ /__\ /__\ /__\ /\ /\ /\ /\ /\ /\ /\ /\ /__\/__\/__\/__\ /__\/__\/__\/__\ /\ /\ /\ /\ /__\ /__\ /__\ /__\ /\ /\ /\ /\ /\ /\ /\ /\ /__\/__\ /__\/__\ /__\/__\ /__\/__\ /\ /\ /\ /\ /\ /\ /\ /\ /__\ /__\ /__\ /__\ /__\ /__\ /__\ /__\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\