hdu 4394 - Digital Square (dfs or bfs)Digital Square

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概述

题目：

Digital Square

题意：

输入N，找到最小的M，使得M²%10^x=N (x=0,1,2,3....)

思路：

%10^x取的是最后几位，只有满足m*m%x == n%x,即先匹配后几位的数才可能向上匹配到n 。明显的一个位数递推，dfs和bfs均可

要注意向上枚举最高位数时，是从0开始而非1开始，因为有可能一个数就可以直接匹配到n。

代码：

dfs：

//#pragma comment(linker, "/STACK:102400000,102400000")
#include "iostream"
#include "cstring"
#include "algorithm"
#include "cmath"
#include "cstdio"
#include "sstream"
#include "queue"
#include "vector"
#include "string"
#include "stack"
#include "cstdlib"
#include "deque"
#include "fstream"
#include "map"
using namespace std;
typedef long long LL;
const long long LINF = (long long)1e30;
const int INF = 522133279;
const int MAXN = 100000+100;
#define eps 1e-14
const int mod = 100000007;

LL n;
LL minc;

LL minll(LL a , LL b)
{
    return a > b ? b : a;
}

void dfs(LL x , LL cur)
{
    if(cur*cur%x == n)
    {
        minc = minll(minc,cur);
        return;
    }

    for(int i = 0 ; i <= 9 ; i++)
    {
        LL tmp = i*x + cur;
        if(tmp*tmp%x == n%x)
            dfs(x*10 , tmp);
    }
}

int main()
{
    //freopen("in","r",stdin);
    //freopen("out","w",stdout);

    int t;
    scanf("%d",&t);

    while(t--)
    {
        cin >> n;
        minc = LINF;
        dfs(1,0);
        if(minc == LINF)
            cout << "None" << endl;
        else
            cout << minc << endl;
    }

    return 0;
}

bfs：

//#pragma comment(linker, "/STACK:102400000,102400000")
#include "iostream"
#include "cstring"
#include "algorithm"
#include "cmath"
#include "cstdio"
#include "sstream"
#include "queue"
#include "vector"
#include "string"
#include "stack"
#include "cstdlib"
#include "deque"
#include "fstream"
#include "map"
using namespace std;
typedef long long LL;
const int INF = 522133279;
const int MAXN = 1000000+100;
#define eps 1e-14
const int mod = 100000007;

LL n;
int ok;

struct node
{
    LL data;
    int x;


    node()
    {}

    node(LL xx , int xxx) : data(xx) , x(xxx) {}

    bool operator < (const node& b)const
    {
        return data > b.data;
    }
};

void bfs()
{
    priority_queue<node> que;
    node tmp,cur;
    que.push(node(0,0));

    while(!que.empty())
    {
        tmp = que.top();
        que.pop();
        LL p = (LL)pow(10.0, tmp.x);

        if((tmp.data*tmp.data)%p == n)
        {
            cout << tmp.data << endl;
            ok=1;
            return;
        }

        for(int i = 0 ; i <= 9 ; i++)
        {
            cur.x = tmp.x+1;
            cur.data = tmp.data + i*p;

            if(cur.data*cur.data%(p*10) == n%(p*10))
                que.push(cur);
        }
    }
}

int main()
{
    //freopen("in","r",stdin);
    //freopen("out","w",stdout);

    int t;
    cin >>t;

    while(t--)
    {
        ok=0;
        cin >> n;
        bfs();
        if(!ok)
            cout << "None" << endl;
    }

    return 0;
}