暴力&打表

_LH巨神好像不太会打表，这里来普及一下

还有暴力这么重要的东西网上讲的人竟然不多……

一.打表

打表，就是针对一些输入数据比较小的题目的一种骗分技巧，当然有时候也可以在正解或暴力中起一定优化作用。

例题：

奇怪的道路

小宇从历史书上了解到一个古老的文明。这个文明在各个方面高度发达，交通方面也不例外。考古学家已经知道，这个文明在全盛时期有n座城市，编号为1..n。m条道路连接在这些城市之间，每条道路将两个城市连接起来，使得两地的居民可以方便地来往。一对城市之间可能存在多条道路。 据史料记载，这个文明的交通网络满足两个奇怪的特征。首先，这个文明崇拜数字K，所以对于任何一条道路，设它连接的两个城市分别为u和v，则必定满足1 <=|u - v| <= K。此外，任何一个城市都与恰好偶数条道路相连（0也被认为是偶数）。不过，由于时间过于久远，具体的交通网络我们已经无法得知了。小宇很好奇这n个城市之间究竟有多少种可能的连接方法，于是她向你求助。 方法数可能很大，你只需要输出方法数模1000000007后的结果。输入共一行，为3个整数n，m，K。输出1个整数，表示方案数模1000000007后的结果。100%的数据满足1<= n <= 30, 0 <= m <= 30, 1 <= K <= 8.两种可能的连接方法不同当且仅当存在一对城市，它们间的道路数在两种方法中不同。在交通网络中，有可能存在两个城市无法互相到达。

样例

样例输入

 3 4 1

样例输出

 3

题解

标准打表题，暴力跑出后打成表就AC了

#include<bits/stdc++.h>
using namespace std;
int 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3,47252436,237336,7509215,75849681,444258387,875167573,326100802,71784664,291524911,0,15839068,290554498,369907086,596761540,806277922,17550276,466297428,1344904,88888218,596993040,771929606,800045419,768717185,627291033,225935811,0,208164262,396412526,545042045,55971604,823821553,67943828,942511744,6724520,942719094,652620989,556898297,330537368,478549381,443863967,539735808,0,352206378,477364399,543238700,530043160,446518094,118014733,523115656,30260340,98850933,652277016,687520562,699915333,60255797,521932769,397723703,0,481425779,104175988,460853369,113482160,975753847,142004378,706767058,124403620,757594100,767891803,212361843,123164471,300733034,911339168,813527344,0,117694771,853156476,492087676,812158545,952575900,129480393,391024011,472733756,80084616,248783034,357802079,437569768,793625806,941035414,846414572,0,964889689,233304343,840627368,927016078,709917342,206623582,855548252,676056037,924392372,758556584,429461916,401873011,30174409,818276362,925920867,0,493830902,930173836,63283080,380981345,797070332,275915045,779180592,586853445,164658914,149343171,160865609,635628977,39727486,693325525,787535425,0,76612472,170218958,803874415,232669876,944792822,216807522,397737658,620076241,646515533,499611139,989633245,159076189,517411608,911032206,864759288,0,197952609,342740002,33199783,189777211,411872674,627690142,367901744,860228716,968080215,89505587,869864117,14597641,793299398,363246663,986982171,0,276114524,375756712,736606180,655057692,864313306,985826255,191786946,532655639,36571349,488218396,457088350,244633725,177956313,145979048,201860393};
int main()
{
    int n,m,k;
    scanf("%d%d%d",&n,&m,&k);
    cout<<ans[n-1][m][k-1]<<endl;
    return 0;
}

当然打表的形式多种多样，例题中的表只是最常见的一种。

列举一些常用的表：

1.素数表

2.阶乘表

3.逆元表

当然打表并不一定要直接初始化，也可以通过线性筛/递推打出，所谓预处理其实就是优雅的打表。

打表也不一定要全打出，如果小的点暴力足够拿分就不必费事费力，只打出极限数据就好，这叫做信仰打表。

（一般来说毒瘤出题人都卡着数据极限范围出数据）

打表程序如下：

#include<bits/stdc++.h>
using namespace std;
int work(int x){
    return 1;
}
int main(){
    freopen("1.out","w",stdout);
    int x=1001;
    printf("#include<cstdio>\nusing namespace std;\nint a[%d]={0",x);//想打多少就设它加1,如想打1000个x就为1001
    for(register int i=1;i<x;++i)
        printf(",%d",work(i));//work就是暴力，work(i)就是由题目条件得出的结果
    printf("};\nint main(){\n    \n    return 0;\n}");
    return 0;
}
//把1.out粘贴出来自己加个输入输出就行了
//linux可以多开几个终端打不同部分的表，最后合并

二.暴力

暴力形式就多种多样了，列举常见的几种。

1.暴搜

最常见的暴力形式，灵活多变，绝大部分题目都有暴搜的解法。

一般采用dfs，当然极个别题目用到了bfs。

2.dp

一些题目正解很难想到，但一些复杂度极高的dp（$\Theta(2^N)$，$\Theta(N^4)$）等却能很快想到。

这时我们不妨先打出这样的dp再想正解。

3.状压

个别题的送分形式。一般来说数据范围小于20可考虑。

4.打表

已经详细讲解，不再赘述。

5.贪心

可能是错解，不过不妨一试。

6.Hash

字符串常用暴力手段，简单粗暴。

7.分块&莫队

优雅的暴力形式（莫队奇偶性排序加O2碾爆正解）

8.Simpson积分

虽说是暴力，然而我其实并不会用…………

9.随机化

有的时候可以碾爆正解哦～

还有许多其他手段。

注意考试除非一下就想到正解，否则必打暴力。

就算打出正解，暴力也可以成为对拍利器。

不过暴力虽好，但不能满足于暴力，仍然要积极想正解，只会暴力永远平庸，正解才会让你脱颖而出。

end