多联骨牌的生成办法,维基上只找到固定的骨牌fix,而free的没有找到。
于是只好写个set判重的简单枚举了。
旋转的操作,可以在坐标轴上画个点,以原点为轴心,逆时针旋转90度,新的点的坐标为(-y,x)。顺时针也差不多。
反转类似。
对于操作完的骨牌,还要进行标准化,取最小的横纵坐标为参考,求出新的坐标,以便于判断。
生成所有骨牌以后,预处理一下(一顿乱搞)就好了。
#include<bits/stdc++.h>
using namespace std; #define local const int maxn = ; struct Cell
{
int x,y;
Cell(int x = ,int y = ):x(x),y(y){}
bool operator < (const Cell & rhs) const {
return x < rhs.x||(x == rhs.x && y < rhs.y);
}
};
#define FOR_CELL(c, p) for(Polyomino::const_iterator c = (p).begin(); c != (p).end(); ++c) typedef set<Cell> Polyomino; inline void normalize(Polyomino *px){
int minx = px->begin()->x, miny = px->begin()->y;
Polyomino::const_iterator c;
for(c = px->begin(); c != px->end(); ++c) {
minx = min(minx, c->x);
miny = min(miny, c->y);
}
Polyomino pn;
for(c = px->begin(); c != px->end(); ++c){
pn.insert(Cell(c->x-minx,c->y-miny));
}
*px = pn;
} inline void Rotate(Polyomino & px) {
Polyomino p2;
Polyomino::const_iterator c;
for(c = px.begin(); c != px.end(); ++c)
p2.insert(Cell(c->y,-c->x));
px = p2;
normalize(&px);
} inline void flip(Polyomino &px) {
Polyomino p3;
Polyomino::const_iterator c;
for(c = px.begin(); c != px.end(); ++c)
p3.insert(Cell(-c->x,c->y));
normalize(&p3);
px = p3;
} set<Polyomino>poly[maxn]; void check(const Polyomino &p0,Cell& newCell){
Polyomino p = p0;
p.insert(newCell);
normalize(&p);
int n = p.size();
for(int i = ; i < ; i++){
if(poly[n].count(p)) return;
Rotate(p);
}
flip(p);
for(int i = ; i < ; i++){
if(poly[n].count(p)) return;
Rotate(p);
}
poly[p.size()].insert(p);
} int ans[maxn][maxn][maxn]; struct whc
{
int w,h,c;
whc(){}
whc(int w,int h,int c):w(w),h(h),c(c){}
}; int SIZE[maxn] = {};
whc V[maxn][]; void generatePoly(){
const int dx[] = {,,,-};
const int dy[] = {,-,,};
Polyomino s;
s.insert(Cell(,));
poly[].insert(s); for(int i = ; i < maxn-; i++){
for(set<Polyomino>::iterator it = poly[i].begin(); it != poly[i].end(); it++ ){
FOR_CELL(c,*it){
for(int dir = ; dir < ; dir++){
Cell newc(c->x+dx[dir],c->y+dy[dir]);
if(it->count(newc) == ) check(*it,newc);
}
}
}
} int mp[maxn][maxn][maxn] = {};
for(int n = ; n < maxn; n++){
SIZE[n] = ;
for(set<Polyomino>::iterator it = poly[n].begin(); it != poly[n].end(); it++ ){
int maxx,maxy; maxx = maxy = ;
FOR_CELL(c,*it){
maxx = max(maxx,c->x);
maxy = max(maxy,c->y);
}
if(maxy<maxx) swap(maxx,maxy);
mp[n][maxx][maxy]++;
}
} for(int n = ; n < maxn; n++){
for(int w = ; w < n; w++)
for(int h = w; h < n; h++){
if(mp[n][w][h]){
V[n][SIZE[n]++] = whc(w,h,mp[n][w][h]);
}
}
} } inline int ANS(int n,int w,int h){
if(~ans[n][w][h]) return ans[n][w][h];
else {
int cnt = ;
whc *a = V[n];
for(int i = , sz =SIZE[n] ; i < sz; i++ ){
whc & u = a[i];
if(u.w < w && u.h < h) cnt += u.c;
}
return ans[n][w][h] = cnt;
}
} int main()
{
#ifdef local
freopen("in.txt","r",stdin);
//freopen("out.txt","w",stdout);
#endif // local
generatePoly();
memset(ans,-,sizeof(ans));
int n,w,h;
while(~scanf("%d%d%d",&n,&w,&h)){
if(h<w) swap(w,h);
printf("%d\n",ANS(n,w,h));
}
return ;
}