题目传送门:http://pan.baidu.com/s/1pLvQmx1
离线版题目:http://paste.ubuntu.com/18292275/
数据传送门:http://pan.baidu.com/s/1dFDf8p7
哎呀,第一次看到这个题,一脸懵逼。之前在POJ上倒是做过矩阵的KMP,但这货没有模式串啊!
但是乱搞了一阵之后,如有神助般想到了二分+Hash,时间复杂度O(n^2*log(n))嗯,刚刚好!
于是就开始码Hash,码完之后不放心,还写了一个O(n^4)的SA来对拍,然后满心欢喜,终于可以A题啦!
然后被卡T了 QAQ, 只有暴力分QAQ, 然后今天就爆炸了,这题写了4h+啊!60分滚粗
下面说一点正事,这题正解也是Hash,那么能体现出优劣的就是Hash的方式了
Ⅰ.Sparse_Table版本: http://paste.ubuntu.com/18292055/
在考试的时候YY出来的,提前处理出以每一个点为右上角、边长为2的整次方幂的Hash值
然后任意一个矩阵都可以用4个矩阵拼起来
但是预处理是O(n^2*log(n))的时间复杂度
所以大的点全部跑了1.09-1.27s不等,全部被判T。然而std最大的点都跑了0.6s+啊!被卡常了( ▼-▼ )
Ⅱ.前缀和版本: http://paste.ubuntu.com/18292096/
这个是std的算法。统计二维的前缀和,然后每一维单独乘以一个以幂的级数递增的质数
然后要提取矩阵的时候,前缀和减一减,然后统一次数即可。于是预处理只需要O(n^2)即可
Ⅲ.常规矩阵Hash: http://paste.ubuntu.com/18292122/
之前两个算法都可以做到随机访问。这个Hash方式不行。
它是把x轴和y轴分开Hash,然后滑动窗口,虽然不能做到O(1)的随机访问,但是遍历的话,还是可以做到O(1)的
总结:三种Hash方式应该都是不错的,但从时间复杂度和代码的优美程度来讲,我以后会选择第二种
另外,Hash都会涉及到判重的问题,一般来讲,大家都是使用set
但这一次lcr给我提供了一个很好的解决方案:sort+unique
理论复杂度一样,但实测效果比set快了3-4倍
有图有真相:
贴一份前缀Hash+unique的版本:
#include<iostream> #include<cstdio> #include<algorithm> #define UL unsigned long long using namespace std; const int MAXN = 500+9; const int N = MAXN*MAXN; const UL P = 131313131; const UL Q = 49999; int n,m,lim; char pat[MAXN]; UL mat[MAXN][MAXN],PP[MAXN*2],QQ[MAXN*2],tmp[N]; inline int read(){ char c=getchar(); int buf=0,f=1; while (c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();} while (c<='9'&&c>='0'){buf=buf*10+c-'0';c=getchar();} return buf*f; } inline UL GetHash(int x, int y, int L){ UL ret = 0; ret = mat[x][y] + mat[x+L][y+L]; ret -= mat[x+L][y] + mat[x][y+L]; return ret*PP[1000-y]*QQ[1000-x]; } inline void init(){ m = read(); n = read(); UL p=P,q; lim = min(n,m); for (int j=1;j<=m;j++){ scanf("%s",pat+1); q = Q; for (int i=1;i<=n;i++,q*=Q) mat[i][j] = (UL)pat[i]*q*p; p *= P; } for (int i=n;i;i--) for (int j=m;j;j--) mat[i][j] += mat[i+1][j]+mat[i][j+1]-mat[i+1][j+1]; QQ[1] = Q; PP[1] = P; for (int i=2;i<=1000;i++) QQ[i] = QQ[i-1]*Q, PP[i] = PP[i-1]*P; } inline bool judge(int L){ int cnt = 0; for (int i=1;i<=n-L+1;i++) for (int j=1;j<=m-L+1;j++) tmp[++cnt] = GetHash(i,j,L); sort(tmp+1,tmp+1+cnt); int tot = unique(tmp+1,tmp+1+cnt) - tmp - 1; return tot != cnt; } int main(){ freopen("matrix.in","r",stdin); freopen("matrix.out","w",stdout); init(); int l=1,r=lim,mid,vout=0; while (l <= r){ mid = (l+r)/2; if (judge(mid)) l = mid+1, vout = mid; else r = mid - 1; } printf("%d\n",vout); return 0; }
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Ankara küçük nakliyat hizmeti Ankara gibi büyük şehirler de oldukça önemli bir yere sahiptir. Şehir içi ve şehirler arası küçük çaplı eşya taşımacılığı anlamına gelen ve birçok kişi veya kurum tarafından icra edilmektedir. Burada en önemli olan uygun fiyat ve hızlı çözümdür. Bunun içinde en ideal çözüm bünyemizde yer alan Ankara küçük nakliye ihtiyaçlarınıza doğru çözümler sunan firmalarımızdan alabilirsiniz.
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