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/**//*
棰樻剰錛?br> 緇欏畾n( n <= 1000 )涓ぇ灝忎負Vi鐨勭墿鍝侊紝姣忎釜鐗╁搧閮藉彲浠ユ媶鍒嗘垚k嬈★紝鎷嗗垎濂界殑鐗╁搧鍙互緇х畫鎷嗗垎錛孷i鏄暣鏁幫紝浣嗘槸鎷嗗垎濂界殑鐗╁搧鐨勫ぇ灝忓彲浠ユ槸浠繪剰瀹炴暟錛屼緥濡傛湰鏉?br>Vi涓?鐨勭墿鍝佹媶鍒嗘垚5浠斤紝閭ｄ箞姣忎喚澶у皬灝辨槸1.4錛岄棶鏈鍚庤兘涓嶈兘閫氳繃鎷嗗垎鍜岀粍鍚堢粍鍑?br>澶у皬涓簒鐨勭墿鍝侊紙姣忎釜鐗╁搧鐨勪緵搴旈噺鏄棤絀峰鐨勶級銆?br>棰樿В錛?br> 鏁板鎺ㄥ鎬濊礬錛?br> 闂姹傚緱灝辨槸浠ヤ笅鏂圭▼鏈夋病鏈夋暣鏁拌В錛?br> x1*V1/(k^y1) + x2*V2/(k^y2) + 
+ xn*Vn/(k^yn) = x鍏朵腑x1錛寉1鏄湭鐭ラ噺銆傞鍏堣鏄庣‘鐨勪竴鐐規槸錛屼竴涓墿鍝佸彲浠ユ媶鍒嗙殑鏃犻檺灝忥紝涔熷氨鏄?br>k^yi鍙互寰堝ぇ寰堝ぇ錛屽洜涓哄綋k^yi鍙栧緱瓚婂ぇ鏃訛紝鎴戜滑鎬誨彲浠ユ壘鍒発^yi涓繖綾葷墿鍝佹妸瀹?br>榪樺師鎴愬師鏉ョ殑澶у皬錛屾墍浠ヤ笉褰卞搷瑙ｉ錛涚浉鍙嶏紝濡傛灉鍙栧緱姣旇緝灝忕殑璇濆彲鑳芥壘涓嶅埌鍙瑙ｏ紝鍥犱負榪樻病鏈夎揪鍒拌鎷嗗垎鐨勬鏁幫紝鐒跺悗鎴戜滑榪欐牱鑰冭檻錛屼護G = gcd(V1, V2 )錛屽茍涓擳i = Vi / G銆傞偅涔堝師鏂圭▼灝卞彲浠ヨ〃紺烘垚濡備笅褰㈠紡錛?br> G * ( x1*T1/(k^y1) + x2*T2/(k^y2) + + xn*Tn/(k^yn) ) = x 鐒跺悗浠 = k^j錛屼綘鍙互鍋囪榪欎釜M瓚沖澶с傚啀灝嗕笂闈㈢殑鏂圭▼鍙樺艦錛?br> S = x1*T1*(k^(j-y1)) + x2*T2*(k^(j-y2)) + + xn*Tn/(k^(j-yn)); G / M * S = x 鎺ヤ笅鍟︼紝濡傛灉鍦℅涓殑绱犲洜瀛愬悓鏃跺瓨鍦ㄤ簬k涓紝閭ｄ箞鎴戜滑鎶婅繖浜涚礌鍥犲瓙鍏ㄩ儴鍓旈櫎錛岃繖涓姝ュ叾瀹炲氨鏄眰G鍜孧鐨勬渶澶у叕綰︽暟錛岃繖灝辨槸涓轟粈涔圡瑕佸彇瓚沖澶х殑鍘熷洜銆傛柟紼?br>杞彉鎴愶細 G' = G / gcd(G, M); M' = M / gcd(G, M); G' / M' * S = x; 鐒跺悗鎴戜滑灝嗙瓑寮忎袱杈歸兘涔樹笂M'錛屽彲浠ュ緱鍒幫細 G'* S = x * M'; 榪欏洓涓暟閮芥槸鏁存暟錛孏'鍜孧'浜掕川錛屾墍浠'蹇呯劧瑕佹暣闄錛屽惁鍒欐柟紼嬫棤瑙ｃ傞偅涔?br>鎺ヤ笅鏉ュ氨鏄鐪嬶紝濡傛灉鏁撮櫎鐨勮瘽鏄惁涓瀹氭湁瑙ｃ?br> 浠' = x / G'; 閭ｄ箞鏈塖 = x' * M'; 棣栧厛鑰冭檻n = 1鐨勬儏鍐碉紝濡傛灉n = 1錛岄偅涔坸1*(k^(j-y1)) = x' * M';鎴戜滑鍙鍙杧1 = x' * M'錛寉1 = j 灝卞彲浠ヤ簡銆?br> 鐒跺悗鏄痭 > 1鐨勬儏鍐碉紝鎴戜滑鍙栦換鎰忎袱縐嶇墿鍝侊紝鍏朵粬鐗╁搧鍋囪閮戒笉鍙栵紝濡傛灉榪欐牱閮?br>鑳界粍鍚堝嚭鏉ワ紝閭ｄ箞緇撹灝辨樉鐒朵簡銆傛潵鐪嬩笅闈㈢殑鏂圭▼錛?br> A = x1*T1*(k^(j-y1)); B = x2*T2*(k^(j-y2)); A + B = x' * M'; 浜庢槸闂灝辮漿鍙樻垚浜嗙嚎鎬у悓浣欐柟紼嬫槸鍚︽湁鏁存暟瑙ｇ殑闂浜嗐?br> 涓嶅Θ鍋囪y1 < y2錛岄偅涔圙G = gcd(A, B) = k^(j-y2);鍥犱負y1鍜寉2鐨勫悇鑷彇鍊間笉褰卞搷鏈鍚庣粨鏋滐紙鍥犱負鍙敤寰堝涓獂2鏉ヨˉ鍏咃級錛屾垜浠彲浠ュぇ鑳嗙殑灝唝2鍙栧間負j銆備簬鏄疓G灝辯瓑浜?浜嗐傝繖鏍鋒柟紼嬪氨蹇呯劧鏈夎В浜嗐?br> 緇撹寰楄瘉銆?br>
*/
#include <iostream>#include <vector>#include <vector>using namespace std;#define maxn 65537bool f[maxn];int prime[maxn], size;int gcd(int a, int b) { return b==0 ? a : gcd(b, a%b);}void Divide(vector<int>& ans, int v) { ans.clear(); if(v == 1) return ; int i;
for(i = 0; i < size; i++) { if(v % prime[i] == 0) { while(v % prime[i] == 0) v /= prime[i]; ans.push_back(prime[i]); if(v == 1) return ;
} } ans.push_back(v);}int n, x, k;int main() { int i, j; for(i = 2; i < maxn; i++) { if(!f[i]) { prime[size++] = i; for(j = i+i; j < maxn; j += i) { f[j] = 1; } } } while(scanf("%d %d %d", &n, &x, &k) != EOF) { int G = 0; for(i = 0; i < n; i++) { int val; scanf("%d", &val); if(i) G = gcd(G, val); else G = val; } vector<int> vecG; vector<int> vecK; Divide(vecG, G); Divide(vecK, k); bool flag = false; for(i = 0; i < vecG.size(); i++) { for(j = 0; j < vecK.size(); j++) { if(vecG[i] == vecK[j]) break; } if(j == vecK.size()) { while(G % vecG[i] == 0) { G /= vecG[i]; if(x % vecG[i] == 0) x /= vecG[i]; else { flag = true; break; } } if(flag) break; } } printf("%s\n", flag ? "No" : "Yes"); } return 0;}]]>
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/**//*棰樻剰錛?br> 鍦ㄤ竴涓笁緇寸┖闂翠腑錛岀粰瀹氫竴浜涚偣錛岃繖浜涚偣鐨剒鍧愭爣閮芥槸澶т簬0鐨勩傝姹傛眰鍑轟竴涓渾閿ワ紙搴曢潰鏄渾褰級錛屼嬌寰楄繖涓渾閿ョ殑搴曢潰鍦▃ = 0鐨勫鉤闈笂錛屽畠鑳藉鍖呭惈鎵鏈夌粰瀹氱殑鐐瑰茍涓斿渾閿ョ殑浣撶Н瑕佹眰鏈灝忋?br>棰樿В錛?br> 鏁板鎺ㄥ + 涓夊垎鎬濊礬錛?br> 榪欐槸涓涓緢鏈夋剰鎬濈殑棰橈紝铏界劧鏄笁緇寸殑錛屼絾鏄彲浠ュ緢瀹規槗鐨勮漿鍖栧埌浜岀淮鍘?br>銆傛潵鐪媂-Z榪欎釜騫抽潰錛屾垜浠皢鎵鏈夌殑鐐硅繘琛屽渾鍛ㄦ槧灝勶紝鐒跺悗灝嗘墍鏈夌殑鐐歸兘鎶曞獎鍒?br>X-Z騫抽潰鐨勭殑絎竴璞￠檺鍘伙紝鐒跺悗闂灝辮漿鍖栨垚浜嗗湪X-Z騫抽潰涓婃壘鍒頒竴鏉℃枩鐜囦負璐?br>鐨勭洿綰縇錛孡鍜孹姝ｆ柟鍚戙乑姝ｆ柟鍚戝洿鎴愮殑涓夎褰㈠寘鍚墍鏈夌偣錛屽鏋滃亣璁綥鍜孹杞寸殑浜ょ偣涓篟錛屽拰Z杞寸劍鐐逛負H錛岃姹俻i*H*R^2鐨勫兼渶灝忋?br> 鐒跺悗鎴戜滑鏉ョ湅鐪婬鍜孯涔嬮棿鏈変粈涔堝崈涓濅竾緙曠殑鍏崇郴銆傞鍏圠榪欐潯綰垮繀瀹氬拰鏌愪竴涓粰瀹氱殑鐐規摝杈癸紝涔熷氨鏄粡榪囬偅涓偣錛屾垜浠亣璁懼畠緇忚繃P(a, b)錛?nbsp;騫朵笖L鐨勬枩鐜?br>涓篕(K < 0)錛岄偅涔圠鐨勬柟紼嬪氨鍙互琛ㄧず涓?nbsp;L: y = K * (x - a) + b錛屽垯H鍜孯灝?br>鍙互鍒╃敤榪欎釜鏂圭▼琛ㄧず鍑烘潵錛?br>H = -a * K + b;R = -b / K + a;閭ｄ箞鎵姹傜殑鍦嗛敟鐨勪綋縐氨鏄細V = pi*H*R^2 = pi * (-a * K + b) * (-b / K + a) ^ 2瀹規槗寰楀埌V(K)榪欎釜鍑芥暟鐨勫鏁幫細V'(K) = - pi * (aK^2 + 2bK) * (aK - b)^2 / K^2褰卞搷榪欎釜瀵兼暟鐨勬璐熸х殑鍞竴鏉′歡鏄?nbsp;-(aK^2 + 2bK)褰?2b/a < K < 0鏃禫'(K)澶т簬闆訛紝涔熷氨鏄疺鐨勫兼槸闅忕潃K閫掑鐨勩?br>褰揔 < -2b/a鏃禫'(K)灝忎簬闆訛紝涔熷氨鏄疺鐨勫兼槸闅忕潃K閫掑噺鐨勩?br>浜庢槸鍙互寰楀嚭涓涓粨璁猴紝褰揔 = -2b/a 鏃禫鍙栧緱鏈灝忓箋?br>浜庢槸鎴戜滑鐭ラ亾浜哣鐨勫崟宄版э紝鐒跺悗灝卞彲浠ラ氳繃鏋氫婦鍗婂緞R錛屽洜涓篟瀵逛簬V鍏鋒湁鍗曡胺鎬э紝鎵浠ユ灇涓綬鐨勬椂鍊欏彲浠ラ噰鐢ㄤ笁鍒嗐傛瘡嬈￠氳繃涓夊垎R鎵懼埌鏈灝忕殑H錛岃繖涓繃紼嬪彲浠ラ氳繃鏋氫婦姣忎釜鐐癸紝鎵懼埌鏈澶х殑鏋佽alpha錛孯*tan(alpha)灝辨槸H浜嗐?br> 榪欓噷闇瑕佹敞鎰忕殑灝辨槸綺懼害闂浜嗐?br>*/#include <iostream>#include <cmath>#include <algorithm>using namespace std;#define eps 1e-6const double pi = acos(-1.0);struct Point { double x, y, z; double v, h; void SCANF() { scanf("%lf %lf %lf", &x, &y, &z); v = z; h = sqrt(x*x + y*y); }}pt[ 10001 ];int n;double MaxH, MaxV;double Calc(double R) { int i; double Max = 0; int idx = 0; for(i = 0; i < n; i++) { double nv = pt[i].v / (R - pt[i].h); if(nv > Max) { Max = nv; idx = i; } } return Max * R;}int main() { int t; int i; scanf("%d", &t); while(t--) { scanf("%d", &n); MaxH = MaxV = 0; for(i = 0; i < n; i++) { pt[i].SCANF(); if(pt[i].h > MaxH) MaxH = pt[i].h; if(pt[i].v > MaxV) MaxV = pt[i].v; } double l = MaxH + eps, r = 1e6; double ml, mr; while(l + 1e-6 < r) { ml = (2 * l + r) / 3; mr = (l + 2 * r) / 3; double lans = Calc(ml) * ml * ml; double rans = Calc(mr) * mr * mr; if( lans > rans ) { l = ml + 1e-5; }else r = mr - 1e-5; } double ans = (l + r) / 2; printf("%.3lf %.3lf\n", Calc(ans), ans); } return 0;}]]>
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/**//*棰樻剰錛?br> 緇欏嚭n(n <= 500)涓暟ai(ai <= 5000)錛屾眰浠栦滑鐨勬渶澶т笉鑳界粍鍚堟暟銆?br>瑙ｆ硶錛?br>鏁拌 + 鏈鐭礬鎬濊礬錛?br> 緇忓吀鐨勭粍鍚堥棶棰楥hange Making Problem錛岃繖涓鐩湁涓涓檺鍒跺氨鏄粰瀹氱殑鏁板皬浜庣瓑浜?000錛岄鐩殑鎰忔濆緢娓呮錛屽氨鏄眰涓涓暟S錛屼嬌寰楀畠涓嶈兘琚?br>浠諱綍ai鐨勫嶆暟鎵緇勫悎鍑烘潵錛屽茍涓斿畠鐨勫兼渶澶с?br> 閭ｄ箞濡傛灉榪檔涓暟鐨刧cd涓嶄負1錛屽繀鐒舵壘涓嶅埌榪欐牱鐨凷錛屽洜涓哄鏋淪涓嶈兘琚?br>瀹冧滑鐨刧cd鏁撮櫎錛屾案榪滀笉鍙兘緇勫悎鍑烘潵錛岃繖鏍稴灝卞彲浠ュ緢澶э紝鑷劧涔熷氨娌℃湁鏈澶х殑S浜嗐?br> 鐜板湪璁ㄨ鎵鏈塧i鐨刧cd涓?鐨勬儏鍐點傚浜庝換鎰忕殑鏁存暟A錛屽鏋淎鑳借浠ヤ笂鐨?br>ai緇勫悎鍑烘潵錛岄偅涔?nbsp;B = A + k*a0 蹇呯劧鑳借緇勫悎錛堝彧瑕佸姞涓妅涓猘0鍗沖彲錛夈備簬鏄垜浠彲浠ュ惂鎵鏈夋暣鏁板垝鍒嗘垚a0涓瓑浠風被錛岀瓑浠風被涓殑鏁版āa0鐨勫肩浉鍚岋紝涓?br>涓緥瀛愶紝a0=3錛屾垜浠彲浠ュ皢0,1,2,3,4,5,6鍒掑垎鎴?0,3,6)(1,4)(2,5)榪欎笁涓?br>絳変環綾伙紝濡傛灉鐩稿悓絳変環綾諱腑鐨勬煇涓暟鑳借緇勫悎錛岄偅涔堟瘮瀹冨ぇ鐨勬墍鏈夊湪璇ョ瓑浠?br>綾諱腑鐨勬暟蹇呯劧鑳借緇勫悎鍑烘潵銆傛墍浠ョ幇鍦ㄥ彧瑕佹眰鍑烘瘡涓瓑浠風被涓殑鏈灝忕殑鑳借緇勫悎鍑烘潵鐨勬暟錛岀劧鍚庡彇鎵鏈夌瓑浠風被涓渶灝忔暟鐨勬渶澶у糒錛孡-a[0]灝辨槸闂鐨?br>絳旀錛堝師鍥犲緢綆鍗曪紝鍥犱負L鑳借緇勫悎鍑烘潵錛屾瘮L澶х殑騫朵笖鍦ㄥ悓涓絳変環綾諱腑鐨勬暟蹇呯劧鑳介氳繃鍔犱笂鑻ュ共涓猘[0]鏉ユ眰寰楋紝浜庢槸L-a[0]灝辨垚浜嗘渶澶т笉鑳界粍鍚堟暟錛夈?br> 浜庢槸闂灝辮漿鍖栨垚浜嗗浣曞湪鐩稿悓絳変環綾諱腑鎵懼埌鏈灝忕殑閭ｄ釜鑳借ai緇勫悎鍑?br>鏉ョ殑鏁般傚彲浠ュ埄鐢ㄦ渶鐭礬鏉ユ眰錛屾渶鐭礬鐨刱ey淇℃伅灝辨槸瀹冩湰韜肩殑澶у皬錛屽鏋?br>涓や釜鏁皒,y, (x + ai) % a0 == y % a0錛岄偅涔堟垜浠氨鍦▁鍜寉涔嬪墠榪炰笂涓鏉℃潈鍊間負ai鐨勮竟錛屾瀯鍥懼畬鎴愬悗灝卞彲浠ヤ粠0榪欎釜鐐瑰紑濮嬫悳浜嗭紝鏈鍚庨亶鍘?鍒癮[0]-1鎵?br>鍒版渶澶х殑閭ｄ釜鏁癓鍗沖彲銆?br>*/#include <iostream>#include <algorithm>#include <queue>using namespace std;#define maxn 5010#define inf 200000000int a[500];struct Point { int val; int mod_val; int dis; Point(int _v, int _mv, int _d) { val = _v; mod_val = _mv; dis = _d; } friend bool operator < (Point a, Point b) { return a.dis > b.dis; }};int dis[maxn], nv[maxn];priority_queue < Point > Q;int gcd(int a, int b) { if(b == 0) return a; return gcd(b, a%b);}int main() { int n; int i; while(scanf("%d", &n) != EOF) { int G = 0; for(i = 0; i < n; i++) { scanf("%d", &a[i]); if(!i) G = a[0]; else G = gcd(G, a[i]); } if(G != 1) { printf("INF\n"); continue; } sort(a, a + n); for(i = 0; i < a[0]; i++) { dis[i] = inf; } dis[0] = 0; nv[0] = 0; while(!Q.empty()) { Q.pop(); } Q.push(Point(0, 0, 0)); while(!Q.empty()) { Point id = Q.top(); Q.pop(); for(i = 0; i < n; i++) { int nex = (id.mod_val + a[i]) % a[0]; if(id.dis + a[i] < dis[nex]) { dis[nex] = id.dis + a[i]; nv[nex] = id.val + a[i]; Q.push(Point(nv[nex], nex, dis[nex])); } } } int Max = 0; for(i = 0; i < a[0]; i++) { if(dis[i] != inf && nv[i] > Max) { Max = nv[i]; } } printf("%d\n", Max - a[0]); } return 0;}]]>