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[开发杂谈]The14thUESTCProgrammingContestFinalWarmupD

  2016-04-03 20:47:56

D - Cube


Time Limit: 3000/1000MS (Java/Others)     Memory Limit: 65535/65535KB (Java/Others)

 
As a student of the applied mathematics school of UESTC, WCM likes mathematics. Some day he found an interesting theorem that every 
positive integer's cube can be expressed as the sum of some continuous odd positive integers. For example,

11×11×11=1331=111+113+115+117+119+121+123+125+127+129+131

Facing such a perfect theorem, WCM felt very agitated. But he didn't know how to prove it. He asked his good friend Tom Riddle for help. Tom 
Riddle is a student of the computer science school of UESTC and is skillful at programming. He used the computer to prove the theorem's 
validity easily. Can you also do it?
Given a positive integer N, you should determine how to express this number as the sum of N continuous odd positive integers. You only 
need to output the smallest and the largest number among the N integers.

Input


The input contains an integer on the first line, which indicates the number of test cases. Each test case contains one positive integer N 
on a single line(0<N1000).

Output


For each test case, output two integers on a line, the smallest and the largest number among the NN continuous odd positive integers 
whose sum is N×N×N.

Sample input and output

Sample Input Sample Output
2
11
3
111 131
7 11

Source


The 5th UESTC Programming Contest Final
The 14th UESTC Programming Contest Final Warmup
UESTC 80

My Solution


当时看到11*11*11然后后面的中间有个121 (11*11)然后就把思路给秒了,开心。
11×11×11=1331=111+113+115+117+119+121+123+125+127+129+131
又因为是化成n个连续奇数,所以n为奇数是显然,当为偶数时试了2个,只要头 +1 ,尾 -1 输出就好了,轻松秒了,开心??
#include <iostream>
#include <cstdio>
using namespace std;
//偶数时直接通过奇数时的公式,由规律得出
int main()
{
    int T, N;
    scanf("%d", &T);
    while(T--){
        scanf("%d", &N);
        if(N&1) printf("%d %d\n", N*N - (N/2)*2, N*N + (N/2)*2);
        else printf("%d %d\n", N*N - (N/2)*2 + 1, N*N + (N/2)*2 - 1);
    }
    return 0;
}

Thank you!
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2016-04-03 20:46:48  
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