CD Making
Time Limit: 1000 ms
Memory Limit: 65535 kB
Description
Tom has N songs and he would like to record them into CDs. A single CD can contain at most K songs. In addition, Tom is very superstitious and he believes the number '13' would bring bad luck, so he will never let a CD contain exactly 13 songs. Tom wants to use as few CDs as possible to record all these songs. Please help him.
Input
There are T test cases. The first line gives T, number of test cases. T lines follow, each contains N and K, number of songs Tom wants to record into CDs, and the maximum number of songs a single CD can contain.
1 ≤ N ≤ 1000, 1 ≤ K ≤ 1000
Output
For each test case, output the minimum number of CDs required, if the above constraints are satisfied.
Sample Input
2
5 2
13 13
Sample Output
3
2
Hint
If Tom has 5 songs to record and a single CD can contain up to 2 songs, Tom has to use 3 CDs at minimum, each contains 2, 2, 1 songs, respectively.
In the second case, Tom wants to record 13 songs, and a single CD can hold 13 songs at most. He would have been able to use only 1 CD if he were not so superstitious. However, since he will not record exactly 13 songs into a single CD, he has to use 2 CDs at least, the first contains 12 songs and the second contains one(Other solutions to achieve 2 CDs are possible, such as (11, 2), (10, 3), etc.).
Source
UESTC
这题目虽然比较简单,但是可借鉴的思想比较丰富,我用的是贪心的思想,得到近似解,然后从近似解去思考得到最终解。
也可以采用用贪心的方法得到近似解(易知近似解比真实解最多大一),那么我们可以检查近似解是否是真实解来得到答案,这里可以给我们启示,可以用贪心来进行启发式搜索,加快搜索的进程。
第三此题也可以用二分搜索的方法求解,二分需要的CD数目,而CD数目的上限很容易得知。
#include <cstdio> int main() { int t, n, k,ans; FILE * fin, * fout; fin = fopen("1.in", "r"); fout = fopen("1.out", "w"); fscanf(fin, "%d", &t); while ( t-- ) { fscanf(fin, "%d %d", &n, &k); if ( 13 == k ) { k--; } ans = n / k; if ( n % k ) { ans++; } if ( 13 == n % k && ( k == 14 || ans == 1 ) ) { ans++; } fprintf(fout, "%d\n", ans); } fclose(fin); fclose(fout); return 0; }