算法分析与设计教程（习题答案）

算法分析与设计教程解答指计算机执行程序中的某一条语句的执行次数。指某算法的计算时间只能使用指数函数限界的算法。3.解：事前分析是指求出某个算法的一个时间限界函数(它是一些有关参数的函数)；事间和占用空间的统计资料。能分{fnreturn1;}tc{fn{bmoveaba}}②f(n)=O(n*logn)(Cn0|T(n)=〈typedefstruct{klagoidNRpostOrderBiTreebStacktypeStack[MAX_TREE_SIZE];BiTreep;topsignifbNULLreturn;top=-1;/*栈顶位置初始化*/p=b;pifp=NULL){/*结点第一次进栈*/toplinkpopflagp=p->lchild;/*找该结点的左孩子*/}p=Stack[top].link;tacktopflagifsign){/*结点第二次进栈*/toplinkpStack[top].flag=2;/*标记第二次出栈*/p=p->lchild;}p=NULL;}}}}nn。idmaxminintAintemaxintlowinthigh{h}h}}midlow+high)/2;maxminA,x1,y1,low,mid);maxminA,x2,y2,mid+1,high);maxxxminxx}}{loatrrrrnewfloatn-1];rnewfloatn-1];rnewfloatn-1];foriini+)riri]=r2[i]=r3[i]=0;roductpqcpolyproductpqrk);polyproductpkqkr1+2*k,k);plusppkrk,k);plusqqkr,k);polyproductrkr,r2+k,k);mins(r2+k,r0,2*k-1);mins(r2+k,r1+2*k,2*k-1);plus(r0+k,r2+k,r0+k,2*k-1);plusrk,r1+2*k,r0+2*k,2*k-1);}}voidproductfloatpfloatq[],floatc[]){pqpqcpp)*(q[0]+q[1])-c[0]-c[2];}voidplusfloatpfloatq[],floatc[],intn){iiniqi}voidminsfloatp,floatq[],intn){iinipipiq[i];}FOI10+2/3*5+15+6+18+3=166/3；Pi,0,1,0)；FGI=10+15+4/7*7+18=47；(2)按wi的非降次序列输入时的序列为(1,1,4/5,0,1,1,1)；I背包容量为13，有7件物品，它们的容量组成的向量为(1,2,4,5,3,3,7)，它们的效益值组成的向量为(6,10,18,14,8,7,7)。ncludeiostreamgnamespacestdconstintN2;oidOutputResultintSelectN{rintiiNi}{intBeginN,8,15,15};intEndN4,15,18,19,20};intSelectN0,0,0};while(i<N){art{ctiimeStartEndi}}utResultSelectresult;}小长度。deiendvoidGreedyJobNodeintintoidmainvoidiceratorintconstreturntimeateineNodeiendvoidGreedyJobNodeintintbliceratorintconstreturnavailatesTypevoidGreedyTypeaintn,intm)rn}nMinHeapMachineNodeH(m);MachineNodex;forintiimiailiHInsertx;}forintiniiHDeleteMinx);coutxID<<“从”<<x.avail<<“到”xavailaitime;HInsertx;}}cludeiostreamincludecstringngnamespacestdvoiddeleteSchar*p){while(*p){p(p+1);p}}{cout:"<<endl;Scout多少个数:N"<<endl;do{coutN数字串的长度"<<endl;whilemmint)strlen(S));while(m>0){while(i<(int)strlen(S)&&(S[i]<=S[i+1]))eSSi}whileS[0]=='0')deleteS(&S[0]);rlenSSendlreturn;}ncludeiostreamncludecmathusingnamespacestd;definemaxn05{blelrublexmaxnymaxnPOINTpointsmaxn];maxnintcompconstvoidaconstvoidb序比较函数*/{POINTaabb;aaPOINTabb=(POINT*)b;/*强制类型转换*/return;return-1;return1;}oidinit初始化*/{orcaniini{安装区域*/{pointsilxi]-sqrt(double(d)*d-y[i]*y[i]);pointsirxi]+sqrt(double(d)*d-y[i]*y[i]);}}}idsolve{eofPOINTcomp*/foriinimki=0;oransiini{mki]=1;/*进行贪心策略选择*/orjijnjifmkjpointsjlpointsire)mkj1;}}{{endl}{endl}}return;x01234f1(x)7d1(x)01234x01234f2(x)d2(x)00or11or21x01234f3(x)d3(x)01222includeiostream>usingnamespacestdconstintMAXN=100;nrMAXNMAXNmMAXNMAXNsMAXNMAXNneyintiintj{n{returnmij;}umij];orkikjk{oneyikmoneykj{mp}}turnu}{while(cin>>n){{mcout<<"Case"<<num<<":"<<endl;iiniorjijnj{ijarij5535;mi[j]=r[i][j];money0,n);coutmoneynendl}}turn}Bjb初始条件为：d(i,0)=i,i=0~m;d(0,j)=j,j=0~n。includecstdioincludeiostreamincludestringusingnamespacestd;tb{returnabb:a;}rppcharccharc{returnc2;return0;}charchangecharc{creturn";return";return0;}charscatconstcharschars2){charscharcallocstrlens)+strlen(s2)+1,sizeof(char));returns;}charctoscharc){charscharcallocsizeof(char));returns;}{arstrregsprintf("请输入括号个数:");nm=(int**)calloc(n+1,sizeof(int*));regschar**)calloc(n+1,sizeof(char**));foriini){m[i]=(int*)calloc(n+1,sizeof(int));regsi(char**)calloc(n+1,sizeof(char*));forjjnj){regsij=(char*)calloc(2*n,sizeof(char));}}hstdincharcallocnsizeofcharprintf("请输入以()和[]组合的括号串:");foriinicstriprintf:%s\n",str);forllnl){foriinl++i){jil1;ntminlwforkikj++k){ifppstristrkminmi1][k-1]+m[k+1][j])){minm[i+1][k-1]+m[k+1][j];w=k;}}w{m[i][j]=min;strcpyregsijscatscatscatctosstriregsi+1][w-1]),ctos(pp(str[istrwregsw[j]));}{strcpyregsijscatchangestriregsi[j]));}}}nreturn0;}–L表示有多少“段”不同的颜色方块jijk，设这“若干段”中最后面的那一段是p(i<=p<j)，得分olorjowshopfriendFlowintintint)vatevoidBacktrack(inti);xtf所需的处理时间*/业调度*/优作业调度*/和*/值*//voidFlowshop::Backtrack(inti){forintjjnjbestxjxj;estff}forintjijnj{Mxjfifif1)?f2[i-1]:f1)+M[x[j]][2];fwapxixjBacktracki1);wapxixj}Mxj}}tMintnintbestx{lowshopXXxnewintn]；Xfnewintn+1]；MMnnestxbestxstfubXf;XfforintiiniXfi,X.x[i]=i;XBacktrack;teXfturnXbestf}orfriendintmColoringintintint);ivateboolOkintk);m//a;boolColor::Ok(intk){orintjjnj/用性*/akjxjxkturnfalseturntrue}voidColor::Backtrack(intt){forintiinii}orintiimiBacktrackt;}}ingintnintminta{orXnmasumrintiinipi;pXBacktrackurnXsum}mpriendintMaxStampintintintvatevoidBacktrackintiintrintn/*邮票面值数*/maxvalueaxintaxlvoidStampBacktrackinti,intr){forintjjxi*(m-1);j++)forintkkmyjk+)yjxiky[j]+k;while(y[r]<maxint)maxvaluer1;forintj=1;j<=n;j++)bestxjxj}lorintkkmaxlkforintjxij=r;j++){jBacktrackir)forintkkmaxlk+)zk}}}mpintnintmintbestx{允许贴的邮票数*/值*//界*/所需最少邮票数*/解*/XnnmmaxvaluemaxintmaxintmaxlmaxlestxbestxXxnewintn1];Xynewintmaxl+1];orintiiniXxi0;orintiimaxliXyimaxint;Xx1;Xy0;XBacktrack);xynXmaxvalue}includeiostream>usingnamespacestdconstintNormalize=9;intNumboolC9];boolL17];boolR17];voidTryinti{forintjjj){ifCjtrueLijNormalizetrueRij)==true){falseijNormalizefalsefalse{ryi}{Num++;coutNum:"<<;orkkk}jtrueLijNormalizetrue;Rijtrue;}}}{Num0;oriiitrueforiiiLiRi=true;ryreturn;}includeiostream>usingnamespacestddefineMAX200defineMAXN20intbMAXN];intcompconstvoidaconstvoidb数*/{returnintb-*(int*)a;}oidNonRecursComput{MAXNboolflag;x[0]=-1;while(lev>=0){法主要程序*/xlevxlev{}{ifcmbxlev&&(cn>0))/*如(cm>=b[x[lev]]≥0，则尝试再用b[x[lev]]*/{evbxlev{Possibleendlrn}vtxlevt}/点位置*/{ak}}}iflev/*回溯到根部又无路可走，则无解*/tImpossibleendlturn}{while(cin>>m>>n>>k){ak{coutCasecnt":"<<endl;foriikiqsortbksizeofintcompnmincnint(cm/b[0]);mpossibleendlnRecursComput}}return;}ludeiostream的个数下界*/usingnamespacestddefineMAXN35structnode/*结点结构*/{nodeNODENODEp[MAXN];/*表示结点数组*/oidinitintm{maxb1<<m)-1/*记有向图的顶点最大数-1*/riimaxbi{pileft1;piright-1;pivisited=-1;ikk)&maxb;ileftkkpirightk}右孩子、无访问标记*/点-左支*//点-右支*/}{boolflagtrue;foriiki){{ak}}turnflag}dCompt{boolflagfalsepvisited=0;}while(true){树*/while(i<=maxb&&p[a[i-1]].left!=-1&&p[a[i-1]].left!=0{aipai-1]].left;pai.visited=0;}值*/子标志*/入右子树的标志*/{rjjmaxbjcoutajm-1)))>>(m-1));/*按字符串输出*/}else/*如个数未满足要求*/{ifpairightpairight0NotEquali-1,p[a[i-1]].right))/*如右子树可行，进入右子树*/{aipai].right;pai].visited=0;}}while(!flag)子的值*/右孩子标志*/进入左子树的标志*/溯*/{while(i>0&&p[a[i-1]].visited==1){a[i]=-1;pai.visited=-1;}树返回*/问标志*/ifpairightpairight!=0right{aipairightpai].visited=0;}}}}{oriini{timpossibleendl{pt}}return0;}值*/子标志*/子树的标志*/ludeiostreamludecstdlibusingnamespacestdt*/使用的情况*/已经找到解*/voidaconstvoidb{returnint*)a-*(int*)b;}idfindintx{ifx/*已经找到目标*/{}foriini+)/*找到第一个未使用过的元素作为下一个集合的第一个元素*/{ak}usedi;Trackxiseti;usedi;/*对于找不到的情况，按原路返回*/}intkintsum{{umrn}多重复判断*/{isumsetiquarter{usediTracknumisunseti);usedi}}}{while(T--){memsetused0,sizeof(used));oriini{seti}{oendl}erqsortsetnsizeofset,cmp);{oendl}sendlcoutnoendl}return;}ludeiostreamudecstringudecstdlibefineH#defineW6#defineJH3#defineJW1usingnamespacestdrtableHWbooliswH[W];ewjJHJWlflag的高度*/的宽度*/宝石的高度*/宝石的宽度*/宝石的状态*/当前格是否为空*/的状态*/downOp{orjjWj{x=H-1;foriHii一遍得到下一个状态(宝石下落后)*/，依次将为空的位置填满*/{tablexjtableij}forixii/*最后为空的赋值为‘W’*/bleijW}}voidsearch/*消去宝石*/{flagtrue/*默认本次操作没有消去宝石*/oriiHijjWj{jjWj{{{ifistepk件，将不符合条件、越界的舍去*/{iftableistepkjstepktablei][j]&&tableistepkjstepk][1]]==table[i][j]){while(i+t*step[k][0]>=0&&tableitstepkjtstepk][1]]==table[i][j])到该方向上的所有能消的宝石*/{sWitstepkjtstepktrue}}}}}}e}{while(T--){iiHi{ei}riiJHi{i}oriHii{{ak}}forihJHihi+)/*将新增的宝石放入容器*/{}while1){ak}iiHi{jjWj{ableij}}}turn}化算法ncludeiostreamcludecstdlibncludectimeusingnamespacestd;{ignedinttimeNULLforkkk+)utfloatrandendlreturn0;}2.解：tn{randomseedxrandomnwhile(i<n){xxx)%n;lidnyxkik}}returnd;}eclassTypeBOOLmajority_monte<TypeA[],Type&x,intn,doublee){BOOLflagFALSE;randomseedforttst{njjnjiak}}turnflag}为O(nlog(1/e))。boolQueen:QueensLV(intstopVegas){omNumberrndwhile((k<=stopVegas)&&(count>0)){forintiini{unti}}returncount;}dnQueenintn{enXnforintiini{pi;}pqlfoundfalsewhile(!X.QueensLV(stop));opforintiinicout<<p[i]<<"";e}rnfound}图论与网络流问题ncludeiostreamusingnamespacestd;defineINF5535nstintMAXN限*/voidinit/*首先输入有向图的信息*/foriini)forjjnj)Fforiiei){labl}}/中无边的元素设为无穷大*/，构造网络矩阵*/ntmaxflowintnintcMAXNintsourceintsinkintflowMAXN流*/{urnINFmemset(flow,0,sizeof(flow));while(1){foriiniprevi与汇点相同，则返回*/可行流*/分量初始化*/previsourcesource;{ifnewccijflowijvivj，flow[i][j]<c[i][j]，则给vj(vi,d(vj))*/prevqueqj]=i+1;inewcdinewcfnewcflowjiprevqueq=j]=i-1;jdinewcdinewc}vj列*/Path入调入过程*/flowpreviidsink;ielseflowiprevid[sink];evi}forjiinjflowsourcei+]);/*统计计算从源点发出的流量*/returnj;}{owwhile(cin>>n>>e){nkn边数*/息*/MaxFlow=max_flow(n,g,source,sink,flow);coutMaxFlowendl/*输出最大流*/}return;}cludecstdioludequeueludealgorithmcludemapusingnamespacestd;defineMAX01defineMAXL01defineMAXR01uctedge{intleftrightEdgeedge0000];boolconMAX[MAX];boolyesintusedMAX];CH最大值*/最大值*/的左右点的数目*/阵*/能否形成二部图*/{vateightLrMatchLMAXRolvisitedMAXRindAugmentintreverseintintdinitlicoolbuildvoidMATCHinit){forintiicountlefti+)tchRiforintiicountrighti+)rMatchL[i]=-1;}voidMATCHreverseintleft,intright){MatchLrightleftwhile(prev[left]!=-1){leftrMatchLnextRprevleft;ghtnextR}t}voidMATCHfindAugmentintstart){forintiicountlefti+)prev[i]=-1;forintiicountrighti+)visitedifalse}intQQpushstart;boolfoundfalse;while(!Q.empty()&&!found){popforinttotocountright!found;to++){{itedtotruefrMatchLto{ersefromto}{pushrMatchLtoprevrMatchLtofrom}}}}}h{forintiicountleftientiforintiicountleftiiflMatchRi)max;rnmax}oolMATCHbuild{eftightforintiicountlefti+)forintjjcountrightjmapij]=false;rintiimi{{wv;}mapatw][at[v]]=true;}urntrue}voidmarkintiintside){forintjjnj{sedj{usedj-side;markj,1-side);}usedjside{rn}}}{MATCHmatch;whilescanf("%d%d",&n,&m)!=EOF){forintiini{forintjjnjalseused[i]=-1;}orintiimi{scanfddedgeiwedgeivconedgeiwedgeivconedgei].v][edge[i].w]=true;}eforintiinyesi++)sedi{sedimarki;}{printfNon);}leftright部分点数*/forintiini{t}{tght}printfdn,match.maxMatch());}}ncludeiostreamncludestdiohincludestdlibhusingnamespacestddefineCourse_MAX101defineStudMAX301boolusedStud_MAX];Num课程和学生最大数目*/数、学生数*/XmapidInput{scanfddCourseNumStudNum输入课程数、学生数*/memsetmap,0,sizeof(map));iiCourseNumi{forjjkj{mapix1]=true;}}}boolDFSintt)/生编号*/{{{{}}}nfalse}{orjjTj{moriiCourseNumi{}rintfYESnintfNOn}return;}上ncludeiostreamncludecmathusingnamespacestd;defineMAXN;defineINF000000XNMAXNBoyMAXNMAXNmn{oriimijjnjoyijoriimiforjjnj{gjigirlBoyji;}}intkuhnmunkresintmintnintmatMAXNintmatchintmatch{AXNtMAXNlMAXNpqijkoriinioriimiforliINFjjnj++)limatijlimatijl[i];memsetmatch2,0xff,sizeof(int)*n);foriimi{memsettxffsizeof(t));forppqmatchi0;p++)forkspjjnmatch1[i]<0;j++)lkljmatkjtj{pjp合*/}{Fkkqkjjnjiftjlskljmatskj]<p)plsk]]+l2[j]-mat[s[k]][j];jjnjkkqk}}riimiretmatimatch1[i]];rnret}最优匹配值*/{matchMAXNiwhile(cin>>m){MM=kuhn_munkres(m,n,g,match1,match2);endl}return;}defineMAXN0{intcf/*容量，流量*/}matrixedge[MAXN][MAXN];/*流及容量(邻接矩阵)*/intm,n;/*读入的排水沟(即弧)数目和汇合结点(即顶点)数目*/ints,t;/*源点(结点1)、汇点(结点N)*/sidualMAXNMAXNqeintpreMAXNintvisMAXNmaxflowminaugmentidfindaugmentpath{队列头和尾*/流流量、每次增广时的可改进量*/memsetvis,0,sizeof(vis));ressssmemsetresidual0,sizeof(residual));memsetpre,0,sizeof(pre));whileqs<qe&&pre[t]==0){foriini{{gecuicedgecuif{residualcu][i]=edge[cu][i].c-edge[cu][i].f;icui}eifedgecuif{residual[cu][i]=edge[cu][i].f;icui}}}}}voidaugmentflow{{minaugment0;}while(i!=s){改进量*/广路上可改进量的最小值*/iijlpreii}minaugment=j;}voidupdateflow{rnwhile(i!=s){dgepreiicedgepreiifepreiifminaugmentelseifedgepreiifepreiifminaugment}dsolve{maxflow0;while(1){mentpathtflowmaxflowminaugment;dateflow}}{while(scanf("%d%d",&m,&n)!=EOF){memsetedge0,sizeof(edge));mi{量*//uvcc}printfdnmaxflow);}return;}includecstdioincludevectorincludecassert>includealgorithmusingnamespaces