hdoj-1976-How many integers can you find
2016-04-18 21:23
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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
Sample Output
给定n和一个大小为m的集合,集合元素为非负整数。为1…n内能被集合里任意一个数整除的数字个数。n<=2^31,m<=10。
数据范围比较大,暴力去找肯定超时,2^31数组也存不了容斥原理地简单应用。先找出1…n内能被集合中任意一个元素整除的个数,再减去能被集合中任意两个整除的个数,即能被它们两只的最小公倍数整除的个数,因为这部分被计算了两次,然后又加上三个时候的个数,然后又减去四个时候的倍数…所以深搜,最后判断下集合元素的个数为奇还是偶,奇加偶减。
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
#include<iostream> #include<cstdio> #include<iostream> #include<algorithm> #define ll long long using namespace std; ll n,m,a[12],ans,p; ll gcd(ll a,ll b) { if (!b) return a; return gcd(b,a%b); } void DFS(ll i,ll w,ll k) { for (;i<=n;i++) if (a[i]) { p=a[i]*w/gcd(a[i],w); ans+=k*(m/p); DFS(i+1,p,-k); } return; } int main() { ll i; while (cin>>m>>n) { for (i=1;i<=n;i++) cin>>a[i]; ans=0; m--; DFS(1,1,1); cout<<ans<<endl; } return 0; }
给定n和一个大小为m的集合,集合元素为非负整数。为1…n内能被集合里任意一个数整除的数字个数。n<=2^31,m<=10。
数据范围比较大,暴力去找肯定超时,2^31数组也存不了容斥原理地简单应用。先找出1…n内能被集合中任意一个元素整除的个数,再减去能被集合中任意两个整除的个数,即能被它们两只的最小公倍数整除的个数,因为这部分被计算了两次,然后又加上三个时候的个数,然后又减去四个时候的倍数…所以深搜,最后判断下集合元素的个数为奇还是偶,奇加偶减。
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