[原创]HDU 1796 How many integers can you find [容斥定理] 【组合数学】

2017-02-11 12:49:25 Tabris_ 阅读数：360

https://blog.csdn.net/qq_33184171/article/details/54982226

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How many integers can you find

Time Limit: 12000/5000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 7728 Accepted Submission(s): 2281

Problem Description
Now you get a number N, and a M-integers set, you should find out how many integers which are small than N, that they can divided exactly by any integers in the set. For example, N=12, and M-integer set is {2,3}, so there is another set {2,3,4,6,8,9,10}, all the integers of the set can be divided exactly by 2 or 3. As a result, you just output the number 7.

Input
There are a lot of cases. For each case, the first line contains two integers N and M. The follow line contains the M integers, and all of them are different from each other. 0< N<2^31,0< M<=10, and the M integer are non-negative and won’t exceed 20.

Output
For each case, output the number.

Sample Input
12 2
2 3

Sample Output
7

Author
wangye
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$ans = \dfrac{n}{lcm\{一个元素\} }-\dfrac{n}{lcm\{两个元素\} }+\dfrac{n}{lcm\{三个元素\} }-....\dfrac{n}{lcm\{所有元素\} }$

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dfs形式 202ms