题意：
求【a，b】间的欧拉函数和。这道题卡内存，只能开一个数组。
思路：
ϕ(n) = n * （p-1)/p * ... 可利用线性筛法求出所有ϕ(n) 。
#include <algorithm> #include <iterator> #include <iostream> #include <cstring> #include <iomanip> #include <cstdlib> #include <cstdio> #include <string> #include <vector> #include <bitset> #include <cctype> #include <queue> #include <cmath> #include <list> #include <map> #include <set> using namespace std; //#pragma GCC optimize(3) //#pragma comment(linker, "/STACK:102400000,102400000") //c++ #define lson (l , mid , rt << 1) #define rson (mid + 1 , r , rt << 1 | 1) #define debug(x) cerr << #x << " = " << x << " "; #define pb push_back #define pq priority_queue typedef long long ll; typedef unsigned long long ull; typedef pair<ll ,ll > pll; typedef pair<int ,int > pii; typedef pair<int ,pii> p3; //priority_queue<int> q;//这是一个大根堆q //priority_queue<int,vector<int>,greater<int> >q;//这是一个小根堆q #define fi first #define se second //#define endl ' ' #define OKC ios::sync_with_stdio(false);cin.tie(0) #define FT(A,B,C) for(int A=B;A <= C;++A) //用来压行 #define REP(i , j , k) for(int i = j ; i < k ; ++i) //priority_queue<int ,vector<int>, greater<int> >que; const ll mos = 0x7FFFFFFFLL; //2147483647 const ll nmos = 0x80000000LL; //-2147483648 const int inf = 0x3f3f3f3f; const ll inff = 0x3f3f3f3f3f3f3f3fLL; //18 const double PI=acos(-1.0); template<typename T> inline T read(T&x){ x=0;int f=0;char ch=getchar(); while (ch<'0'||ch>'9') f|=(ch=='-'),ch=getchar(); while (ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar(); return x=f?-x:x; } // #define _DEBUG; //*// #ifdef _DEBUG freopen("input", "r", stdin); // freopen("output.txt", "w", stdout); #endif /*-----------------------show time----------------------*/ const int maxn = 3000009; ll sum[maxn]; /* const int maxn = 3000009; int prime[316819]; int phi[maxn]; ll sum[maxn]; bool flag[maxn]; void getphi(){ phi[1] = 1,sum[1] = 1; int tot = 0; for(int i=2; i<maxn; i++){ if(flag[i] == 0){ prime[++tot] = i; phi[i] = i-1; } for(int j=1; i * prime[j] < maxn && j<=tot; j++){ flag[i*prime[j]] = 1; if(i%prime[j] == 0){ phi[i * prime[j]] = phi[i] * prime[j]; break; } else phi[i * prime[j]] = phi[i]*(prime[j] - 1); } sum[i] = sum[i-1] + phi[i]; } } */ void getphi(){ sum[1] = 1; for(int i=2; i<maxn; i++){ if(!sum[i]){ for(int j=i; j<maxn; j+=i){ if(!sum[j])sum[j] = j; sum[j] = sum[j] / i * (i-1); } } } for(int i=1; i<maxn; i++)sum[i] += sum[i-1]; } int main(){ int a,b; getphi(); while(~scanf("%d%d", &a, &b)){ printf("%lld ", sum[b] - sum[a-1]); } return 0; }
还有POJ的2478也是区间累计欧拉函数的和
#include <algorithm> #include <iterator> #include <iostream> #include <cstring> #include <iomanip> #include <cstdlib> #include <cstdio> #include <string> #include <vector> #include <bitset> #include <cctype> #include <queue> #include <cmath> #include <list> #include <map> #include <set> using namespace std; //#pragma GCC optimize(3) //#pragma comment(linker, "/STACK:102400000,102400000") //c++ #define lson (l , mid , rt << 1) #define rson (mid + 1 , r , rt << 1 | 1) #define debug(x) cerr << #x << " = " << x << " "; #define pb push_back #define pq priority_queue typedef long long ll; typedef unsigned long long ull; typedef pair<ll ,ll > pll; typedef pair<int ,int > pii; typedef pair<int ,pii> p3; //priority_queue<int> q;//这是一个大根堆q //priority_queue<int,vector<int>,greater<int> >q;//这是一个小根堆q #define fi first #define se second //#define endl ' ' #define OKC ios::sync_with_stdio(false);cin.tie(0) #define FT(A,B,C) for(int A=B;A <= C;++A) //用来压行 #define REP(i , j , k) for(int i = j ; i < k ; ++i) //priority_queue<int ,vector<int>, greater<int> >que; const ll mos = 0x7FFFFFFFLL; //2147483647 const ll nmos = 0x80000000LL; //-2147483648 const int inf = 0x3f3f3f3f; const ll inff = 0x3f3f3f3f3f3f3f3fLL; //18 const double PI=acos(-1.0); template<typename T> inline T read(T&x){ x=0;int f=0;char ch=getchar(); while (ch<'0'||ch>'9') f|=(ch=='-'),ch=getchar(); while (ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar(); return x=f?-x:x; } // #define _DEBUG; //*// #ifdef _DEBUG freopen("input", "r", stdin); // freopen("output.txt", "w", stdout); #endif /*-----------------------show time----------------------*/ const int maxn = 1000009; ll sum[maxn]; void getphi(){ sum[1] = 0; for(int i=2; i<maxn; i++){ if(!sum[i]){ for(int j=i; j<maxn; j+=i){ if(!sum[j])sum[j] = j; sum[j] = sum[j] / i * (i-1); } } } for(int i=1; i<maxn; i++)sum[i] += sum[i-1]; } int main(){ int a; getphi(); while(~scanf("%d", &a) && a){ printf("%lld ", sum[a]); } return 0; }