第八屆省賽 B:Quadrat (打表找規律)
Description
It is well-known that for any n there are exactly four n-digit numbers (including ones with leading zeros) that are self-squares: the last ndigits of the square of such number are equal to the number itself. These four numbers are always suffixes of these four infinite sequences:
...0000000000
...0000000001
...8212890625
...1787109376
For example, 093762 =87909376, which ends with 09376.
You are required to count the numbers that are almost self-squares: such that each of the last n digits of their square is at most d away from the corresponding digit of the number itself. Note that we consider digits 0 and 9 to be adjacent, so for example digits that are at most 3 away from digit 8 are 5, 6, 7, 8, 9, 0 and 1.
Input
The first line contains the number of test cases t,1≤t≤72. Each of the next t lines contains one test case: two numbers n(1≤n≤ 18) and d(0≤ d≤3).
Output
For each test case, output the number of almost self-squares with length n and the (circular) distance in each digit from the square at most d
Sample Input
2 5 0 2 1
Sample Output
4 12
Hint
In the second case, number 12‘s almost self-squares are: 00, 01, 10, 11, 15, 25, 35, 66, 76, 86, 90, 91
題意:
求滿足以下條件
①.這個數為n位(可以有前導零)
②.取它的平方的後n位,與它本身每一位對應之差≤d(這裏的差指的是數字之間的距離,而這個距離是將數字按圈排列,0與9相鄰所求得的)
的數字的個數。
題解:
打表吧
規律就是 res[i][j] = res[i-1][j]*(2*j+1)
代碼:
#include <algorithm> #include <bitset> #include <cmath> #include <cstdio> #include <cstdlib> #include <cstring> #include <deque> #include <iomanip> #include <iostream> #include <map> #include <queue> #include <set> #include <stack> #include <vector> using namespace std; #define is_lower(c) (c >= ‘a‘ && c <= ‘z‘) #define is_upper(c) (c >= ‘A‘ && c <= ‘Z‘) #define is_alpha(c) (is_lower(c) || is_upper(c)) #define is_digit(c) (c >= ‘0‘ && c <= ‘9‘) #define min(a, b) ((a) < (b) ? (a) : (b)) #define max(a, b) ((a) > (b) ? (a) : (b)) #define IO \ ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); #define For(i, a, b) for (int i = a; i <= b; i++) typedef long long ll; typedef unsigned long long ull; const ll inf = 0x3f3f3f3f; const double EPS = 1e-10; const ll inf_ll = (ll)1e18; const ll mod = 1000000007LL; const int maxn = 1000000; ll res[20][5]; void init() { res[1][0] = res[1][1] = 4; res[1][2] = res[1][3] = 8; for(int i = 2; i < 20; i++) { for(int j = 0;j <= 3; j++) res[i][j] = res[i-1][j] * (2 * j + 1); } } int main() { init(); int T; cin >> T; while(T--){ int n,d; cin>>n>>d; cout << res[n][d] << endl; } return 0; }
第八屆省賽 B:Quadrat (打表找規律)