51nod 1284:2 3 5 7 multiple-repulsion principle

1284 2 3 5 7 multiplier base time limit: 1 seconds space limit: 131072 KB Score: 5 Difficulty: 1-level algorithm topic collection focus on giving a number n, 1 to N, how many of the number is not a multiple of 2 3 5 7. For example, n = 10, only 1 is not a multiple of 2 3 5 7. Input

Enter 1 number n (1 <= n <= 10^18).

Output

The output is not the number of multiples of 2 3 5 7.

Input example

10

Output example

1

the principle of tolerance is described as follows:

To calculate the size of several sets of merge sets, we first calculate the size of a single collection, subtract the part that intersects the two sets, add the portion that intersects the three sets, subtract the portion of four that intersect, and so on, all the parts that intersect the collection.

So the question is not a multiple of 2 3 5 7, which can be expected after a multiple of 2 3 5 7, then minus.

This will use the principle of repulsion, first of all, just divide the number of 2 3 5 7, minus the total number of the product of 22 between them, plus the number of products that divide them by three, plus the number divisible by four.

This number is also interesting, the number of 1 to num divisible by C is the value of num/c.

So, the code:

#include <iostream> #include <algorithm> #include <cmath> #include <vector> #include <string > #include <cstring> #pragma warning (disable:4996) using namespace Std;long long n,num,a,b,c,d,ab,ac,ad,bc,bd, Cd,abc,abd,bcd,acd,abcd;int Main () {CIN>>N;NUM=0;A=N/2;B=N/3;C=N/5;D=N/7;AB=N/6;AC=N/10;AD=N/14;BC=N/15;BD =n/21;cd=n/35;abc=n/30;abd=n/42;acd=n/70;bcd=n/105;abcd=n/210;num=a+b+c+d-ab-ac-ad-bc-bd-cd+abc+abd+acd+ Bcd-abcd;cout<<n-num<<endl;return 0;}

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51nod 1284:2 3 5 7 multiple-repulsion principle