分治画分形图 之 谢尔宾斯基三角形

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 = bchar 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--------------------------                               /\                              /__\                             /\  /\                            /__\/__\                           /\      /\                          /__\    /__\                         /\  /\  /\  /\                        /__\/__\/__\/__\                       /\              /\                      /__\            /__\                     /\  /\          /\  /\                    /__\/__\        /__\/__\                   /\      /\      /\      /\                  /__\    /__\    /__\    /__\                 /\  /\  /\  /\  /\  /\  /\  /\                /__\/__\/__\/__\/__\/__\/__\/__\               /\                              /\              /__\                            /__\             /\  /\                          /\  /\            /__\/__\                        /__\/__\           /\      /\                      /\      /\          /__\    /__\                    /__\    /__\         /\  /\  /\  /\                  /\  /\  /\  /\        /__\/__\/__\/__\                /__\/__\/__\/__\       /\              /\              /\              /\      /__\            /__\            /__\            /__\     /\  /\          /\  /\          /\  /\          /\  /\    /__\/__\        /__\/__\        /__\/__\        /__\/__\   /\      /\      /\      /\      /\      /\      /\      /\  /__\    /__\    /__\    /__\    /__\    /__\    /__\    /__\ /\  /\  /\  /\  /\  /\  /\  /\  /\  /\  /\  /\  /\  /\  /\  /\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\