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好恶心的题。。。。。
证明可以证出来。。。。
欧拉函数：φ(n) = n(1 - 1/p1)(1 - 1/p2)(1 - 1/p3)....
n/φ(n) = (p1/(p1 - 1)) (p2/(p2 - 1)) ....
要使n/φ(n)最大，因为p/(p - 1)随p的增大而减小，所以p应该尽可能的小，p/(p - 1) > 1所以p尽可能的多。。。
也就是说从最小的素数开始往后连乘枚举，找到比n小且离n最近的数。。。。
不得不吐嘈的是，=, =！这个java不能交！比赛的时候能用，现在不能用了。.。。杭电你在卖萌吗？！
吐嘈完毕。。。
我很流氓的用java打了个前n的素数相乘的表。。。。
然后在c里边开数组存起来。。。然后跟输入的字符串n比较。。
打表:
import java.io.*;import java.math.*;import java.util.*;public class Main { public static void main(String[] args) { int t, i, j; int N = 1000; BigInteger n, m, tmp, one; Scanner cin = new Scanner (System.in); one = BigInteger.ONE; boolean[] b= new boolean[N]; int[] pri = new int[N]; int num = 0; for(i = 0; i < N; ++i) b[i] = true; for(i = 2; i < N; ++i) { for(j = i*i; j < N; j += i) b[j] = false; } for(i = 2; i < N; ++i) { if(b[i]) {pri[num++] = i; } } n = cin.nextBigInteger(); m = one; for(i = 0; i < num; ++i) { tmp = m.multiply(BigInteger.valueOf(pri[i])); m = tmp; System.out.println("\"" + m + "\"" + ","); if(tmp.compareTo(n) > 0) break; } }}
比较：
#include #include #include #include #include #include #include #include #include #include #include #include #define CL(arr, val) memset(arr, val, sizeof(arr))#define REP(i, n) for((i) = 0; (i) < (n); ++(i))#define FOR(i, l, h) for((i) = (l); (i) <= (h); ++(i))#define FORD(i, h, l) for((i) = (h); (i) >= (l); --(i))#define L(x) (x) << 1#define R(x) (x) << 1 | 1#define MID(l, r) (l + r) >> 1#define Min(x, y) x < y ? x : y#define Max(x, y) x < y ? y : x#define E(x) (1 << (x))const int eps = 1e-6;const int inf = ~0u>>2;typedef long long LL;using namespace std;char st[55][300] = { "2", "6", "30", "210", "2310", "30030", "510510", "9699690", "223092870", "6469693230", "200560490130", "7420738134810", "304250263527210", "13082761331670030", "614889782588491410", "32589158477190044730", "1922760350154212639070", "117288381359406970983270", "7858321551080267055879090", "557940830126698960967415390", "40729680599249024150621323470", "3217644767340672907899084554130", "267064515689275851355624017992790", "23768741896345550770650537601358310", "2305567963945518424753102147331756070", "232862364358497360900063316880507363070", "23984823528925228172706521638692258396210", "2566376117594999414479597815340071648394470", "279734996817854936178276161872067809674997230", "31610054640417607788145206291543662493274686990", "4014476939333036189094441199026045136645885247730", "525896479052627740771371797072411912900610967452630", "72047817630210000485677936198920432067383702541010310", "10014646650599190067509233131649940057366334653200433090", "1492182350939279320058875736615841068547583863326864530410", "225319534991831177328890236228992001350685163362356544091910", "35375166993717494840635767087951744212057570647889977422429870", "5766152219975951659023630035336134306565384015606066319856068810", "962947420735983927056946215901134429196419130606213075415963491270", "166589903787325219380851695350896256250980509594874862046961683989710", "29819592777931214269172453467810429868925511217482600306406141434158090", "5397346292805549782720214077673687806275517530364350655459511599582614290", "1030893141925860008499560888835674370998623848299590975192766715520279329390", "198962376391690981640415251545285153602734402721821058212203976095413910572270", "39195588149163123383161804554421175259738677336198748467804183290796540382737190", "7799922041683461553249199106329813876687996789903550945093032474868511536164700810", "1645783550795210387735581011435590727981167322669649249414629852197255934130751870910", "367009731827331916465034565550136732339800312955331782619462457039988073311157667212930", "83311209124804345037562846379881038241134671040860314654617977748077292641632790457335110", "19078266889580195013601891820992757757219839668357012055907516904309700014933909014729740190", "4445236185272185438169240794291312557432222642727183809026451438704160103479600800432029464270", "1062411448280052319722448549835623701226301211611796930357321893850294264731624591303255041960530", "256041159035492609053110100510385311995538591998443060216114576417920917800321526504084465112487730", "64266330917908644872330635228106713310880186591609208114244758680898150367880703152525200743234420230",};int main() { //freopen("data.in", "r", stdin); int t, i; char s[200]; scanf("%d", &t); while(t--) { scanf("%s", s); int ls = strlen(s); for(i = 0; i < 54; ++i) { int lt = strlen(st[i]); if(lt > ls) break; else if(lt < ls) continue; if(strcmp(st[i], s) > 0) break; } printf("%s\n", st[i-1]); } return 0;}
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