A.二分答案
题目链接：http://www.51nod.com/contest/problem.html#!problemId=1799
题目大意：对于一个乱序数组，问二分查找找到下标为k的情况有多少种。
二分
过程中涉及到$10^9!$，可以预打表每$10^6$保存一个值，故查询时运算次数不超过$10^6$次.
代码如下：
1 #include <cstdio> 2 using namespace std; 3 typedef long long ll; 4 const ll p=1000000007; 5 ll l,r,n,m,k,ans,mid,L,R; 6 ll lt[1005]={1,641102369,578095319,5832229,259081142,974067448,316220877,690120224,251368199,980250487,682498929,134623568,95936601,933097914,167332441,598816162,336060741,248744620,626497524,288843364,491101308,245341950,565768255,246899319,968999,586350670,638587686,881746146,19426633,850500036,76479948,268124147,842267748,886294336,485348706,463847391,544075857,898187927,798967520,82926604,723816384,156530778,721996174,299085602,323604647,172827403,398699886,530389102,294587621,813805606,67347853,497478507,196447201,722054885,228338256,407719831,762479457,746536789,811667359,778773518,27368307,438371670,59469516,5974669,766196482,606322308,86609485,889750731,340941507,371263376,625544428,788878910,808412394,996952918,585237443,1669644,361786913,480748381,595143852,837229828,199888908,526807168,579691190,145404005,459188207,534491822,439729802,840398449,899297830,235861787,888050723,656116726,736550105,440902696,85990869,884343068,56305184,973478770,168891766,804805577,927880474,876297919,934814019,676405347,567277637,112249297,44930135,39417871,47401357,108819476,281863274,60168088,692636218,432775082,14235602,770511792,400295761,697066277,421835306,220108638,661224977,261799937,168203998,802214249,544064410,935080803,583967898,211768084,751231582,972424306,623534362,335160196,243276029,554749550,60050552,797848181,395891998,172428290,159554990,887420150,970055531,250388809,487998999,856259313,82104855,232253360,513365505,244109365,1559745,695345956,261384175,849009131,323214113,747664143,444090941,659224434,80729842,570033864,664989237,827348878,195888993,576798521,457882808,731551699,212938473,509096183,827544702,678320208,677711203,289752035,66404266,555972231,195290384,97136305,349551356,785113347,83489485,66247239,52167191,307390891,547665832,143066173,350016754,917404120,296269301,996122673,23015220,602139210,748566338,187348575,109838563,574053420,105574531,304173654,542432219,34538816,325636655,437843114,630621321,26853683,933245637,616368450,238971581,511371690,557301633,911398531,848952161,958992544,925152039,914456118,724691727,636817583,238087006,946237212,910291942,114985663,492237273,450387329,834860913,763017204,368925948,475812562,740594930,45060610,806047532,464456846,172115341,75307702,116261993,562519302,268838846,173784895,243624360,61570384,481661251,938269070,95182730,91068149,115435332,495022305,136026497,506496856,710729672,113570024,366384665,564758715,270239666,277118392,79874094,702807165,112390913,730341625,103056890,677948390,339464594,167240465,108312174,839079953,479334442,271788964,135498044,277717575,591048681,811637561,353339603,889410460,839849206,192345193,736265527,316439118,217544623,788132977,618898635,183011467,380858207,996097969,898554793,335353644,54062950,611251733,419363534,965429853,160398980,151319402,990918946,607730875,450718279,173539388,648991369,970937898,500780548,780122909,39052406,276894233,460373282,651081062,461415770,358700839,643638805,560006119,668123525,686692315,673464765,957633609,199866123,563432246,841799766,385330357,504962686,954061253,128487469,685707545,299172297,717975101,577786541,318951960,773206631,306832604,204355779,573592106,30977140,450398100,363172638,258379324,472935553,93940075,587220627,776264326,793270300,291733496,522049725,579995261,335416359,142946099,472012302,559947225,332139472,499377092,464599136,164752359,309058615,86117128,580204973,563781682,954840109,624577416,895609896,888287558,836813268,926036911,386027524,184419613,724205533,403351886,715247054,716986954,830567832,383388563,68409439,6734065,189239124,68322490,943653305,405755338,811056092,179518046,825132993,343807435,985084650,868553027,148528617,160684257,882148737,591915968,701445829,529726489,302177126,974886682,241107368,798830099,940567523,11633075,325334066,346091869,115312728,473718967,218129285,878471898,180002392,699739374,917084264,856859395,435327356,808651347,421623838,105419548,59883031,322487421,79716267,715317963,429277690,398078032,316486674,384843585,940338439,937409008,940524812,947549662,833550543,593524514,996164327,987314628,697611981,636177449,274192146,418537348,925347821,952831975,893732627,1277567,358655417,141866945,581830879,987597705,347046911,775305697,125354499,951540811,247662371,343043237,568392357,997474832,209244402,380480118,149586983,392838702,309134554,990779998,263053337,325362513,780072518,551028176,990826116,989944961,155569943,596737944,711553356,268844715,451373308,379404150,462639908,961812918,654611901,382776490,41815820,843321396,675258797,845583555,934281721,741114145,275105629,666247477,325912072,526131620,252551589,432030917,554917439,818036959,754363835,795190182,909210595,278704903,719566487,628514947,424989675,321685608,50590510,832069712,198768464,702004730,99199382,707469729,747407118,302020341,497196934,5003231,726997875,382617671,296229203,183888367,703397904,552133875,732868367,350095207,26031303,863250534,216665960,561745549,352946234,784139777,733333339,503105966,459878625,803187381,16634739,180898306,68718097,985594252,404206040,749724532,97830135,611751357,31131935,662741752,864326453,864869025,167831173,559214642,718498895,91352335,608823837,473379392,385388084,152267158,681756977,46819124,313132653,56547945,442795120,796616594,256141983,152028387,636578562,385377759,553033642,491415383,919273670,996049638,326686486,160150665,141827977,540818053,693305776,593938674,186576440,688809790,565456578,749296077,519397500,551096742,696628828,775025061,370732451,164246193,915265013,457469634,923043932,912368644,777901604,464118005,637939935,956856710,490676632,453019482,462528877,502297454,798895521,100498586,699767918,849974789,811575797,438952959,606870929,907720182,179111720,48053248,508038818,811944661,752550134,401382061,848924691,764368449,34629406,529840945,435904287,26011548,208184231,446477394,206330671,366033520,131772368,185646898,648711554,472759660,523696723,271198437,25058942,859369491,817928963,330711333,724464507,437605233,701453022,626663115,281230685,510650790,596949867,295726547,303076380,465070856,272814771,538771609,48824684,951279549,939889684,564188856,48527183,201307702,484458461,861754542,326159309,181594759,668422905,286273596,965656187,44135644,359960756,936229527,407934361,267193060,456152084,459116722,124804049,262322489,920251227,816929577,483924582,151834896,167087470,490222511,903466878,361583925,368114731,339383292,388728584,218107212,249153339,909458706,322908524,202649964,92255682,573074791,15570863,94331513,744158074,196345098,334326205,9416035,98349682,882121662,769795511,231988936,888146074,137603545,582627184,407518072,919419361,909433461,986708498,310317874,373745190,263645931,256853930,876379959,702823274,147050765,308186532,175504139,180350107,797736554,606241871,384547635,273712630,586444655,682189174,666493603,946867127,819114541,502371023,261970285,825871994,126925175,701506133,314738056,341779962,561011609,815463367,46765164,49187570,188054995,957939114,64814326,933376898,329837066,338121343,765215899,869630152,978119194,632627667,975266085,435887178,282092463,129621197,758245605,827722926,201339230,918513230,322096036,547838438,985546115,852304035,593090119,689189630,555842733,567033437,469928208,212842957,117842065,404149413,155133422,663307737,208761293,206282795,717946122,488906585,414236650,280700600,962670136,534279149,214569244,375297772,811053196,922377372,289594327,219932130,211487466,701050258,398782410,863002719,27236531,217598709,375472836,810551911,178598958,247844667,676526196,812283640,863066876,857241854,113917835,624148346,726089763,564827277,826300950,478982047,439411911,454039189,633292726,48562889,802100365,671734977,945204804,508831870,398781902,897162044,644050694,892168027,828883117,277714559,713448377,624500515,590098114,808691930,514359662,895205045,715264908,628829100,484492064,919717789,513196123,748510389,403652653,574455974,77123823,172096141,819801784,581418893,15655126,15391652,875641535,203191898,264582598,880691101,907800444,986598821,340030191,264688936,369832433,785804644,842065079,423951674,663560047,696623384,496709826,161960209,331910086,541120825,951524114,841656666,162683802,629786193,190395535,269571439,832671304,76770272,341080135,421943723,494210290,751040886,317076664,672850561,72482816,493689107,135625240,100228913,684748812,639655136,906233141,929893103,277813439,814362881,562608724,406024012,885537778,10065330,60625018,983737173,60517502,551060742,804930491,823845496,727416538,946421040,678171399,842203531,175638827,894247956,538609927,885362182,946464959,116667533,749816133,241427979,871117927,281804989,163928347,563796647,640266394,774625892,59342705,256473217,674115061,918860977,322633051,753513874,393556719,304644842,767372800,161362528,754787150,627655552,677395736,799289297,846650652,816701166,687265514,787113234,358757251,701220427,607715125,245795606,600624983,10475577,728620948,759404319,36292292,491466901,22556579,114495791,647630109,586445753,482254337,718623833,763514207,66547751,953634340,351472920,308474522,494166907,634359666,172114298,865440961,364380585,921648059,965683742,260466949,117483873,962540888,237120480,620531822,193781724,213092254,107141741,602742426,793307102,756154604,236455213,362928234,14162538,753042874,778983779,25977209,49389215,698308420,859637374,49031023,713258160,737331920,923333660,804861409,83868974,682873215,217298111,883278906,176966527,954913,105359006,390019735,10430738,706334445,315103615,567473423,708233401,48160594,946149627,346966053,281329488,462880311,31503476,185438078,965785236,992656683,916291845,881482632,899946391,321900901,512634493,303338827,121000338,967284733,492741665,152233223,165393390,680128316,917041303,532702135,741626808,496442755,536841269,131384366,377329025,301196854,859917803,676511002,373451745,847645126,823495900,576368335,73146164,954958912,847549272,241289571,646654592,216046746,205951465,3258987,780882948,822439091,598245292,869544707,698611116}; 7 ll mul(ll a,ll b){return a*b%p;} 8 ll fac(ll n){ 9 ll ans=1; 10 if(n<1000000){ 11 for(ll i=1;i<=n;++i) 12 ans=mul(ans,i); 13 }else{ 14 ans=lt[n/1000000]; 15 for(ll i=n/1000000*1000000+1;i<=n;++i) 16 ans=mul(ans,i); 17 } 18 return ans; 19 } 20 int main(void){ 21 scanf("%lld%lld%lld",&n,&m,&k); 22 l=1,r=n,ans=1,L=m,R=n-m; 23 mid=(l+r)>>1; 24 ll pm=-1; 25 while(l<=r){ 26 if(mid<=k){ 27 l=mid+1; 28 if(pm!=mid){ 29 ans=mul(ans,L); 30 L--; 31 } 32 }else if(mid>k){ 33 r=mid-1; 34 if(pm!=mid){ 35 ans=mul(ans,R); 36 R--; 37 } 38 } 39 pm=mid; 40 mid=(l+r)>>1; 41 } 42 ans=mul(fac(L+R),ans); 43 printf("%lld ",ans); 44 }
B.完美序列
题目链接：http://www.51nod.com/contest/problem.html#!problemId=1780
待做...
C.区间计数
题目链接：http://www.51nod.com/contest/problem.html#!problemId=1962
题目大意：问两个数组有多少个公共区间的最大值相同。
单调栈
代码如下：
1 #include <cstdio> 2 #include <cmath> 3 #include <iostream> 4 #include <cstring> 5 #include <algorithm> 6 using namespace std; 7 int n,a[350005],b[350005],pa[350005],pb[350005]; 8 long long ans; 9 bool cmp(int a,int b){ 10 return a>b; 11 } 12 struct Stack{ 13 int a[350005]; 14 int p; 15 void init(){p=-1;} 16 bool empty(){return p==-1;} 17 int top(){return a[p];} 18 void push(int x){a[++p]=x;} 19 void pop(){p--;} 20 int pre(int x){ 21 int ptr=lower_bound(a,a+p+1,x,cmp)-a-1; 22 if(ptr==-1)return -1; 23 return a[ptr]; 24 } 25 }sa,sb; 26 int main(void){ 27 scanf("%d",&n); 28 for(int i=0;i<n;++i)scanf("%d",&a[i]); 29 for(int i=0;i<n;++i)scanf("%d",&b[i]); 30 memset(pa,-1,sizeof(pa)); 31 memset(pb,-1,sizeof(pb)); 32 sa.init();sb.init(); 33 for(int i=0;i<n;++i){ 34 while(!sa.empty()){ 35 int t=sa.top(); 36 if(t<=a[i]){ 37 if(pb[t]!=-1){ 38 int pre=-1; 39 if(sa.pre(t)!=-1)pre=max(pre,pa[sa.pre(t)]); 40 if(sb.pre(t)!=-1)pre=max(pre,pb[sb.pre(t)]); 41 int l=pa[t],r=pb[t]; 42 if(l>r)swap(l,r); 43 if(l>pre)ans+=1LL*(l-pre)*(i-r); 44 } 45 pa[t]=-1; 46 sa.pop(); 47 }else break; 48 } 49 while(!sb.empty()){ 50 int t=sb.top(); 51 if(t<=b[i]){ 52 if(pa[t]!=-1){ 53 int pre=-1; 54 if(sa.pre(t)!=-1)pre=max(pre,pa[sa.pre(t)]); 55 if(sb.pre(t)!=-1)pre=max(pre,pb[sb.pre(t)]); 56 int l=pa[t],r=pb[t]; 57 if(l>r)swap(l,r); 58 if(l>pre)ans+=1LL*(l-pre)*(i-r); 59 } 60 pb[t]=-1; 61 sb.pop(); 62 }else break; 63 } 64 pa[a[i]]=pb[b[i]]=i; 65 sa.push(a[i]),sb.push(b[i]); 66 } 67 while(!sa.empty()){ 68 int t=sa.top(); 69 if(pb[t]!=-1){ 70 int pre=-1; 71 if(sa.pre(t)!=-1)pre=max(pre,pa[sa.pre(t)]); 72 if(sb.pre(t)!=-1)pre=max(pre,pb[sb.pre(t)]); 73 int l=pa[t],r=pb[t]; 74 if(l>r)swap(l,r); 75 if(l>pre)ans+=1LL*(l-pre)*(n-r); 76 } 77 pa[t]=-1; 78 sa.pop(); 79 } 80 printf("%lld ",ans); 81 }