HDU 1796 How many integers can you find

How many integers can you findTime limit:12000/5000 MS (java/others) Memory limit:65536/32768 K (java/others)
Total submission (s): 5517 Accepted Submission (s): 1580


Problem Description Now I get a number N, and a m-integers set, you should find out how many integers which is small t Han N, that they can divided exactly by any integers in the set. For example, n=12, and M-integer set are {2,3}, so there are another set {2,3,4,6,8,9,10}, all the integers of the set can B e divided exactly by 2 or 3. As a result, you just output the number 7.
Input There is a lot of cases. For each case, the first line contains integers N and M. The follow line contains the M integers, and all of the them is different from each other. 0<n<2^31,0<m<=10, and the M integer is non-negative and won ' t exceed 20.
Output for each case, output the number.
Sample Input

12 22 3

Sample Output

7

Authorwangye
Source2008 "Insigma International Cup" Zhejiang Collegiate Programming Contest-warm up (4)
RecommendwangyeThe title means giving an array of N and a set containing the number of M, which requires less than n and is the number of multiples of any element in the set. (a bit around, read it two times to understand). The principle to be used in this topic is the principle of tolerance, what is the principle of repulsion? Probably learned about the set or probability theory! The principle of tolerance: first, regardless of overlap, the number of all objects contained in a certain content is calculated first, and then the number of repeated calculation is excluded, so that the results of the calculation are neither omitted nor duplicated.


the crux of the matter is how to implement the principle of tolerance, the simplest is the direct violence, data comparison of water over, there is a way to use DFS optimization. Two methods are available, just the size of the complexity of the time problem. there is a little bit of a hole in the problem, the less careful people may fall into (such as me ...). T_t ... ), the elements in the collection may contain 0, to filter over before they can be manipulated ... Not much to say, directly on the code:

/*author:zxpxxmemory:1616 kbtime:202 mslanguage:c++result:accepted*/#include <algorithm> #include < iostream> #include <cstring> #include <cstdlib> #include <cstdio> #include <string> #include <vector> #include <cmath> #include <ctime> #include <queue> #include <stack> #include < Set> #include <map>using namespace std;typedef long long ll;const int MAXN = 5e5 + 5;const int inf = 0x3f3f3f3f;in T a[130],n,m,ans,p,cur;int gcd (int a,int b) {return!b? A:GCD (b,a%b);} int LCM (int a,int b) {return a/gcd (b) *b;}    void Dfs (int i,int flag,int k) {K=LCM (a[i],k);    ans+=n/(K*flag); for (int j=i+1;j<cur;j++) DFS (J,-FLAG,K);}        int main () {while (~SCANF ("%d%d", &n,&m)) {cur=0;            for (int i=0; i<m; i++) {scanf ("%d", &p);        if (p) a[cur++]=p;        } ans=0;n--;        for (int i=0; i < cur; i++) {DFS (i,1,a[i]); } prinTF ("%d\n", ans); } return 0;}

the code of the search is also coming ...

/*author:zxpxxmemory:1648 kbtime:998 mslanguage:c++result:accepted*/#include <algorithm> #include < iostream> #include <cstring> #include <cstdlib> #include <cstdio> #include <string> #include <vector> #include <cmath> #include <ctime> #include <queue> #include <stack> #include < Set> #include <map>using namespace std;typedef long long ll;const int MAXN = 5e5 + 5;const int inf = 0x3f3f3f3f;in T a[130],m,n,p,cur,ans;int gcd (int a,int b) {return!b? A:GCD (b,a%b);} int LCM (int a,int b) {return a/gcd (b) *b;}    int main () {while (~SCANF ("%d%d", &n,&m)) {n--;     cur=0;        ans=0;            for (int i=0; i<m; i++) {scanf ("%d", &p);        if (p) a[cur++]=p;            } for (int i= 1;i < pow (2,cur); i++) {int cnt=0,flag=0,k=1;                    for (int j = 0; j < cur; j + +) {if (I>>j & 1) {K=LCM (k,a[j]); if (k&Gt;n) {flag=1;                    Break                } cnt++;            }} if (flag) continue;            if (cnt%2) ans+=n/k;        else ans-=n/k;    } printf ("%d\n", ans); } return 0;}

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HDU 1796 How many integers can you find