UVA - 10624 Super Number(回溯)
2014-09-04 16:06
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Super Number
Input: Standard Input
Output: Standard Output
Time Limit: 3 Seconds
Don't you think 162456723 very special? Look at the picture below if you are unable to find its speciality. (a | b means �b is divisible by a�)
Figure: Super Numbers
Given n, m (0 < n < m < 30), you are to find a m-digit positive integer X such that for every i (n <= i <= m), the first i digits of X is a multiple of i.
If more than one such X exists, you should output the lexicographically smallest one. Note that the first digit of X should not be 0.
Input
The first line of the input contains a single integer t(1 <= t <= 15), the number of test cases followed. For each case, two integers n and m are
separated by a single space.
题目大意:
要求你求出一个超级数字,超级数字的定义如下:
由m位,所有前i位,都能被数字i整除(n <= i <= m),如果超级数字不止一个要求输出字典序最小的超级数字。
注意:超级数字的第一位不能为0
举个例子:
输入
1 10
输出
1020005640
1 % 1 = 0
10 % 2 = 0
102 % 3 = 0
1020 % 4 = 0
10200 % 5 = 0
102000 % 6 = 0
1020005 % 7 = 0
...
1020005640 % 10 = 0
所以当n=1,m=10时,1020005640是超级数字。
解析:数字最多有30位需要用数组进行保存,回溯求解,先1~9,枚举出第一位,再用回溯枚举出剩下的位数,每个位数的值为0~9,注意当cur < n时可以直接枚举下一位,当cur >= n时,需要判断前cur位是否能被cur整除,但是这个数字可能非常大(最多30位),所以要模拟除法的过程,步骤如下:
1.从首位开始对cur求余数
2.(余数*10+下一位) % cur
3.重复2的操作,直到当前的位数 == cur结束。
Input: Standard Input
Output: Standard Output
Time Limit: 3 Seconds
Don't you think 162456723 very special? Look at the picture below if you are unable to find its speciality. (a | b means �b is divisible by a�)
Figure: Super Numbers
Given n, m (0 < n < m < 30), you are to find a m-digit positive integer X such that for every i (n <= i <= m), the first i digits of X is a multiple of i.
If more than one such X exists, you should output the lexicographically smallest one. Note that the first digit of X should not be 0.
Input
The first line of the input contains a single integer t(1 <= t <= 15), the number of test cases followed. For each case, two integers n and m are
separated by a single space.
Output
For each test case, print the case number and X. If no such number, print -1.Sample Input�������������������������� Output for Sample Input
2 1 10 3 29 | Case 1: 1020005640 Case 2: -1 |
要求你求出一个超级数字,超级数字的定义如下:
由m位,所有前i位,都能被数字i整除(n <= i <= m),如果超级数字不止一个要求输出字典序最小的超级数字。
注意:超级数字的第一位不能为0
举个例子:
输入
1 10
输出
1020005640
1 % 1 = 0
10 % 2 = 0
102 % 3 = 0
1020 % 4 = 0
10200 % 5 = 0
102000 % 6 = 0
1020005 % 7 = 0
...
1020005640 % 10 = 0
所以当n=1,m=10时,1020005640是超级数字。
解析:数字最多有30位需要用数组进行保存,回溯求解,先1~9,枚举出第一位,再用回溯枚举出剩下的位数,每个位数的值为0~9,注意当cur < n时可以直接枚举下一位,当cur >= n时,需要判断前cur位是否能被cur整除,但是这个数字可能非常大(最多30位),所以要模拟除法的过程,步骤如下:
1.从首位开始对cur求余数
2.(余数*10+下一位) % cur
3.重复2的操作,直到当前的位数 == cur结束。
#include <cstdio> #include <cstring> using namespace std; bool ok; int m,n; int num[35]; inline int judge(int cur) { int sum = 0; for(int i = 1; i <= cur; i++) { sum = (sum * 10 + num[i]) % cur; } return sum; } inline void dfs(int cur) { if(cur == m+1) { ok = true; return ; } for(int i = 0; i < 10; i++) { num[cur] = i; if(cur < n || (cur >= n && !judge(cur)) ) { dfs(cur+1); } if(ok) { return ; } } } int main() { int t; int cas = 1; scanf("%d",&t); while(t--) { scanf("%d%d",&n,&m); for(int i = 1; i < 10; i++) { num[1] = i; ok = false; dfs(2); if(ok) { break; } } printf("Case %d: ",cas++); if(ok) { for(int i = 1; i <= m; i++) { printf("%d",num[i]); } printf("\n"); }else { printf("-1\n"); } } return 0; }
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