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  • [51NOD]2 3 5 7的倍数(容斥原理)

    题目链接:http://www.51nod.com/onlineJudge/questionCode.html#!problemId=1284

    似乎最近没怎么做容斥原理啊,来复习一发概念。

    容斥原理公式:

    一般做法都是先搞一个式子出来,再枚举所有子集,用式子来确定符号和子集的关系。小学生容斥。。

      1 /*
      2 ━━━━━┒ギリギリ♂ eye!
      3 ┓┏┓┏┓┃キリキリ♂ mind!
      4 ┛┗┛┗┛┃\○/
      5 ┓┏┓┏┓┃ /
      6 ┛┗┛┗┛┃ノ)
      7 ┓┏┓┏┓┃
      8 ┛┗┛┗┛┃
      9 ┓┏┓┏┓┃
     10 ┛┗┛┗┛┃
     11 ┓┏┓┏┓┃
     12 ┛┗┛┗┛┃
     13 ┓┏┓┏┓┃
     14 ┃┃┃┃┃┃
     15 ┻┻┻┻┻┻
     16 */
     17 #include <algorithm>
     18 #include <iostream>
     19 #include <iomanip>
     20 #include <cstring>
     21 #include <climits>
     22 #include <complex>
     23 #include <fstream>
     24 #include <cassert>
     25 #include <cstdio>
     26 #include <bitset>
     27 #include <vector>
     28 #include <deque>
     29 #include <queue>
     30 #include <stack>
     31 #include <ctime>
     32 #include <set>
     33 #include <map>
     34 #include <cmath>
     35 using namespace std;
     36 #define fr first
     37 #define sc second
     38 #define cl clear
     39 #define BUG puts("here!!!")
     40 #define W(a) while(a--)
     41 #define pb(a) push_back(a)
     42 #define Rint(a) scanf("%d", &a)
     43 #define Rll(a) scanf("%I64d", &a)
     44 #define Rs(a) scanf("%s", a)
     45 #define Cin(a) cin >> a
     46 #define FRead() freopen("in", "r", stdin)
     47 #define FWrite() freopen("out", "w", stdout)
     48 #define Rep(i, len) for(int i = 0; i < (len); i++)
     49 #define For(i, a, len) for(int i = (a); i < (len); i++)
     50 #define Cls(a) memset((a), 0, sizeof(a))
     51 #define Clr(a, x) memset((a), (x), sizeof(a))
     52 #define Full(a) memset((a), 0x7f7f7f, sizeof(a))
     53 #define lrt rt << 1
     54 #define rrt rt << 1 | 1
     55 #define pi 3.14159265359
     56 #define RT return
     57 #define lowbit(x) x & (-x)
     58 #define onecnt(x) __builtin_popcount(x)
     59 typedef long long LL;
     60 typedef long double LD;
     61 typedef unsigned long long ULL;
     62 typedef pair<int, int> pii;
     63 typedef pair<string, int> psi;
     64 typedef pair<LL, LL> pll;
     65 typedef map<string, int> msi;
     66 typedef vector<int> vi;
     67 typedef vector<LL> vl;
     68 typedef vector<vl> vvl;
     69 typedef vector<bool> vb;
     70 
     71 LL ret;
     72 LL n;
     73 
     74 int main() {
     75     // FRead();
     76     while(cin >> n) {
     77         LL a,b,c,d,ab,ac,ad,bc,bd,cd,abc,abd,acd,bcd,abcd;
     78         a = n / 2;
     79         b = n / 3;
     80         c = n / 5;
     81         d = n / 7;
     82 
     83         ab = n / 6;
     84         ac = n / 10;
     85         ad = n / 14;
     86         bc = n / 15;
     87         bd = n / 21;
     88         cd = n / 35;
     89 
     90         abc = n / 30;
     91         abd = n / 42;
     92         acd = n / 70;
     93         bcd = n / 105;
     94 
     95         abcd = n / 210;
     96 
     97         cout << n-(a+b+c+d-ab-ac-ad-bc-bd-cd+abc+abd+acd+bcd-abcd) << endl;
     98     }
     99     RT 0;
    100 }
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  • 原文地址:https://www.cnblogs.com/kirai/p/5837471.html
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