ZOJ 3435 Ideal Puzzle Bobble

Posted 2020-09-13 神犇(shenben)

ZOJ Problem Set - 3435

Ideal Puzzle Bobble

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Time Limit: 2 Seconds      Memory Limit: 65536 KB

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Have you ever played Puzzle Bobble, a very famous PC game? In this game, as a very cute bobble dragon, you must keep shooting powerful bubbles to crush all the colorful bubbles upwards. Victory comes when all the bubbles upwards are crushed.

Little Tom is crazy about this game. One day, he finds that all kinds of Puzzle Bobble are 2D Games. To be more excited when playing this game, he comes up with a new idea to design a 3D Puzzle Bobble game! In this game, the bobble dragon is standing in a cubic room with L in length, W in width and H in height. Around him are so many colorful bubbles. We can use 3D Cartesian coordinates (x, y, z) to represent the locations of the bobble dragon and those bubbles. All these coordinates (x, y, z) are triple positive integers ranged from (1, 1, 1) to (L, W, H).

To simplify the problem, let\'s assume the bobble dragon is standing at (1, 1, 1) in the room. And there is one colorful bubble at every (x, y, z) in the room except (1, 1, 1). The dragon is so strong that he can shoot out a magical bubble to crush all the colorful bubbles in the straight line which the magical bubble flies every single time. Note that bubbles are significantly small with respect to the distances between each two bubbles. Our question remains, how many magical bubbles will the cute dragon shoot before crushing all the colorful bubbles around him?

Input

There are multiple cases, no more than 200. Each case contains one single line. In this line, there are three positive integers L, W and H (2 ≤ L, W, H ≤ 1000000) which describes the size of the room. Proceed to the end of the file.

Output

For each case, print the number of the magical bubbles needed to crush all the colorful bubbles in one line.

Sample Input

2 2 2
3 3 3

Sample Output

7
19

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Author: ZHU, Yuke
Contest: ZOJ Monthly, November 2010

　　求(1,1,1)至(x,y,z)的互质个数。

　　即求(0,0,0)到(x-1,y-1,z-1)互质个数。

　　剩下的同SPOJ1007 VLATTICE - Visible Lattice Points

#include<cstdio>
#include<iostream>
#ifdef WIN32
#define LL "%I64d"
#else
#define LL "%lld"
#endif
using namespace std;
typedef long long ll;
const int M=1e6+5;
int L,W,H,T;ll sum[M];
int tot,prime[M/3],mu[M];bool check[M];
void sieve(){
    int n=1e6;mu[1]=1;
    for(int i=2;i<=n;i++){
        if(!check[i]) prime[++tot]=i,mu[i]=-1;
        for(int j=1;j<=tot&&i*prime[j]<=n;j++){
            check[i*prime[j]]=1;
            if(!(i%prime[j])){mu[i*prime[j]]=0;break;}
            else mu[i*prime[j]]=-mu[i];
        }
    }
    for(int i=1;i<=n;i++) sum[i]=sum[i-1]+mu[i];
}
inline ll solve(int x,int y,int z){
    int t=min(x,min(y,z));
    ll ans=3;
    for(int i=1,pos;i<=t;i=pos+1){
        pos=min(x/(x/i),min(y/(y/i),z/(z/i)));
        ans+=1LL*(x/i)*(y/i)*(z/i)*(sum[pos]-sum[i-1]);
    }
    t=min(x,y);
    for(int i=1,pos;i<=t;i=pos+1){
        pos=min(x/(x/i),y/(y/i));
        ans+=1LL*(x/i)*(y/i)*(sum[pos]-sum[i-1]);
    }
    t=min(y,z);
    for(int i=1,pos;i<=t;i=pos+1){
        pos=min(y/(y/i),z/(z/i));
        ans+=1LL*(y/i)*(z/i)*(sum[pos]-sum[i-1]);
    }
    t=min(x,z);
    for(int i=1,pos;i<=t;i=pos+1){
        pos=min(x/(x/i),z/(z/i));
        ans+=1LL*(x/i)*(z/i)*(sum[pos]-sum[i-1]);
    }
    return ans;
}
int main(){
    sieve();
    while(~scanf("%d%d%d",&L,&W,&H)){
        L--,W--,H--;
        printf(LL"\\n",solve(L,W,H));
    }
    return 0;
}