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HDU 4430 Yukari's Birthday

2024-07-21 10:55:25   221人阅读

Yukari‘s Birthday

Time Limit: 6000ms
Memory Limit: 32768KB
This problem will be judged on HDU. Original ID: 4430
64-bit integer IO format: %I64d      Java class name: Main
 
Today is Yukari‘s n-th birthday. Ran and Chen hold a celebration party for her. Now comes the most important part, birthday cake! But it‘s a big challenge for them to place n candles on the top of the cake. As Yukari has lived for such a long long time, though she herself insists that she is a 17-year-old girl.
To make the birthday cake look more beautiful, Ran and Chen decide to place them like r ≥ 1 concentric circles. They place ki candles equidistantly on the i-th circle, where k ≥ 2, 1 ≤ i ≤ r. And it‘s optional to place at most one candle at the center of the cake. In case that there are a lot of different pairs of r and k satisfying these restrictions, they want to minimize r × k. If there is still a tie, minimize r.
 

Input

There are about 10,000 test cases. Process to the end of file.
Each test consists of only an integer 18 ≤ n ≤ 1012.
 

Output

For each test case, output r and k.
 

Sample Input

181111111

Sample Output

1 172 103 10

Source

2012 Asia ChangChun Regional Contest
 
解题：二分。根据等比数列，可知x(1-xn) = k*(1-x)
 
n的范围比较小，枚举n再二分x即可。
 
 1 #include <iostream> 2 #include <cstdio> 3 #include <cstring> 4 #include <cmath> 5 #include <algorithm> 6 #include <climits> 7 #include <vector> 8 #include <queue> 9 #include <cstdlib>10 #include <string>11 #include <set>12 #include <stack>13 #define LL long long14 #define pii pair<int,int>15 #define INF 0x3f3f3f3f16 using namespace std;17 LL mypow(LL x,LL y){18     LL ans = 1;19     while(y){20         if(y&1) ans *= x;21         y >>= 1;22         x *= x;23     }24     return ans;25 }26 int main() {27     LL n,r,k,lt,rt,mid;28     while(~scanf("%I64d",&n)){29         r = 1;30         k = n-1;31         for(int i = 2; i <= 41; i++){32             lt = 2;33             rt = (LL)pow(n,1.0/i);34             while(lt <= rt){35                 mid = (lt+rt)>>1;36                 LL sum = (mid-mypow(mid,i+1))/(1-mid);37                 if(sum == n||sum == n-1){38                     if(i*mid < r*k){39                         r = i;40                         k = mid;41                     }42                     break;43                 }else if(sum < n) lt = mid+1;44                 else rt = mid-1;45             }46         }47         printf("%I64d %I64d\n",r,k);48     }49     return 0;50 }
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HDU 4430 Yukari's Birthday


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