Codeforces 417E Square Table(随机算法)

转载自：http://blog.csdn.net/keshuai19940722/article/details/24105103，多谢这位给的思路

今天学了个新姿势，随机算法。
有时简单粗暴的办法往往胜于苦心经营的办法。后者往往还出不来结果呢。

题目大意：给出n和m，要求给出一个矩阵，要求每一列每一行的元素的平方总和是一个平方数。
解题思路：构造，按照
a a a b
a a a b
a a a b
c c c d
的方式取构造，然后a，b，c，d的值用随机生成数去枚举，不过我觉得用暴力也是可以的。

用随机算法做，218ms

#include <cstdio>  #include <cstring>  #include <cmath>  #include <cstdlib>    bool judge (int s) {      int k = sqrt(s);      return k * k == s;  }    int main () {      int n, m;      int a, b, c, d;        scanf("%d%d", &n, &m);        while (true) {          a = rand()%100 + 1;          b = rand()%100 + 1;          c = rand()%100 + 1;          d = rand()%100 + 1;            if (judge(a * a * (m-1) + b * b)           && judge(a * a * (n-1) + c * c)           && judge(b * b * (n-1) + d * d)           && judge(c * c * (m-1) + d * d) )              break;      }        for (int i = 1; i < n; i++) {          for (int j = 1; j < m; j++)              printf("%d ", a);          printf("%d\n", b);      }        for (int i = 1; i < m; i++)              printf("%d ", c);      printf("%d\n", d);      return 0;  }  

不用随机算法做，46ms

//Hello. I'm Peter.#include<cstdio>#include<iostream>#include<sstream>#include<iomanip>#include<cstring>#include<string>#include<cmath>#include<cstdlib>#include<algorithm>#include<functional>#include<cctype>#include<ctime>#include<stack>#include<queue>#include<deque>#include<vector>#include<set>#include<map>#include<limits>using namespace std;#define input freopen("data.txt","r",stdin)#define output freopen("output.txt","r",stdin)#define INT (0x3f3f3f3f)*2#define LL (0x3f3f3f3f3f3f3f3f)*2#define clr(a) memset(a,0,sizeof(a))#define clr_minus1(a) memset(a,-1,sizeof(a))#define clr_NULL(a) memset(a,NULL,sizeof(a))#define clr_INT(a) memset(a,INT,sizeof(a))#define clr_true(a) memset(a,true,sizeof(a))#define clr_false(a) memset(a,false,sizeof(a))#define clr_queue(q) while(!q.empty()) q.pop()#define clr_stack(s) while(!s.empty()) s.pop()#define rep(i, a, b) for (int i = a; i < b; i++)#define dep(i, a, b) for (int i = a; i > b; i--)#define repin(i, a, b) for (int i = a; i <= b; i++)#define depin(i, a, b) for (int i = a; i >= b; i--)#define ll long long#define eps#define MOD#define MAXN 100#define N#define Mbool is_square(int x){    int tt=(int)sqrt((double)x);    if(tt*tt==x) return true;    else return false;}int main(){    int n,m;    cin>>n>>m;    bool ok=false;    int ansa=0,ansb=0,ansc=0,ansd=0;    repin(d,1,MAXN)    {        if(ok) break;        repin(a,1,MAXN)        {            if(ok) break;            repin(b,1,MAXN)            {                if(ok) break;                repin(c,1,MAXN)                {                    if(is_square((m-1)*a*a+b*b) && is_square((m-1)*c*c+d*d)                       && is_square((n-1)*a*a+c*c) && is_square((n-1)*b*b+d*d) )                    {                        ok=true;                        ansa=a;                        ansb=b;                        ansc=c;                        ansd=d;                        break;                    }                }            }        }    }    repin(i,1,n-1)    {        repin(j,1,m-1)        {            printf("%d ",ansa);        }        printf("%d\n",ansb);    }    repin(i,1,m-1)    {        printf("%d ",ansc);    }    printf("%d\n",ansd);}