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Standard Code LibraryHao YuanDepartment of Computer Science and Engineering Shanghai Jiaotong UniversityOctober23,2003Contents1Algorithms and Datastructures31.1High Precision in C (3)1.2High Precision in C Plus Plus (4)1.3High Precision Floating-point Number (6)1.4Fraction Class (8)1.5Binary Heap (8)1.6Winner Tree (9)1.7Digital Tree (10)1.8Segment Tree (10)1.9Segment Tree in IOI’2001 (11)1.10Union-Find Set (11)1.11Quick Sort (11)1.12Merge Sort (12)1.13Radix Sort (12)1.14Select K th Smallest Element (12)1.15KMP (12)1.16Suffix Sort (13)2Graph Theory and Network Algorithms142.1SSSP—Dijkstra+Binary Heap (14)2.2SSSP—Bellman Ford+Queue (15)2.3MST—Kruskal (15)2.4Minimum Directed Spanning Tree (16)2.5Maximum Matching on Bipartite Graph (16)2.6Maximum Cost Perfect Matching on Bipartite Graph (17)2.7Maximum Matching on General Graph (17)2.8Maximum Flow—Ford Fulkson in Matrix (18)2.9Maximum Flow—Ford Fulkson in Link (19)2.10Minimum Cost Maximum Flow in Matrix (20)2.11Minimum Cost Maximum Flow in Link (21)2.12Recognizing Chordal Graph (21)2.13DFS—Bridge (22)2.14DFS—Cutvertex (22)2.15DFS—Block (23)2.16DFS—Topological Sort (24)2.17Strongly Connected Component (24)3Number Theory253.1Greatest Common Divisor (25)3.2Chinese Remainder Theorem (25)3.3Prime Generator (26)3.4φGenerator (26)3.5Discrete Logarithm (27)3.6Square Roots in Z p (28)4Algebraic Algorithms294.1Linear Equations in Z2 (29)4.2Linear Equations in Z (30)4.3Linear Equations in Q (30)4.4Linear Equations in R (31)4.5Roots of Polynomial (31)14.6Roots of Cubic and Quartic (32)4.7Fast Fourier Transform (33)4.8FFT-Polynomial Multiplication (34)4.9FFT-Convolution (34)4.10FFT-Reverse Bits (34)4.11Linear Programming-Primal Simplex (36)5Computational Geometry385.1Basic Operations (38)5.2Extended Operations (39)5.3Convex Hull (41)5.4Point Set Diameter (43)5.5Closest Pair (44)5.6Circles (44)5.7Largest Empty Convex Polygon (46)5.8Triangle Centers (47)5.9Polyhedron Volume (48)5.10Planar Graph Contour (49)5.11Rectangles Area (50)5.12Rectangles Perimeter (52)5.13Smallest Enclosing Circle (54)5.14Smallest Enclosing Ball (55)6Classic Problems576.1Bernoulli Number Generator (57)6.2Baltic OI’99Expressions (58)6.3Bead Coloring—P´o lya Theory (58)6.4Binary Stirling Number (59)6.5Box Surface Distance (59)6.6Calculate Expression (59)6.7Cartesian Tree (60)6.8Catalan Number Generator (61)6.9Coloring Regular Polygon (62)6.10Counting Inverse Pairs (62)6.11Counting Trees (63)6.12Eight Puzzle Problem (63)6.13Extended Honai Tower (66)6.14High Precision Square Root (66)6.15Largest Empty Rectangle (67)6.16Last Non-Zero Digit of N! (69)6.17Least Common Ancestor (69)6.18Longest Common Substring (71)6.19Longest Non Descending Sub Sequence (73)6.20Join and Disjoin (73)6.21Magic Square (74)6.22Optimal Binary Search Tree (75)6.23Pack Rectangles—Cut Rectangles (75)6.24Pack Rectangles—O(N2) (76)6.25Parliament (76)6.26πGenerator (76)6.27Plant Trees—Iteration (77)6.28Plant Trees—Segment Tree (77)6.29Range Maximum Query (78)6.30Travelling Salesman Problem (79)6.31Tree Heights (80)6.32Minimum Cyclic Presentation (81)6.33Maximum Clique (82)6.34Maximal Non-Forbidden Submatrix (83)6.35Maximum Two Chain Problem (83)6.36N Queens Problem (85)6.37de Bruijn Sequence Generator (85)6.38ZOJ1482Partition (86)2while(c.s[i]){ c.s[i+1]=c.s[i]/10; c.s[i]%=10;i++;}while(i>1&&!c.s[i])i−−;c.l e n=i;return c;}HP HP::operator+(const HP&b){int i;HP c; c.s[1]=0;for(i=1;i<=l e n||i<=b.l e n|| c.s[i];i++){i f(i<=l e n) c.s[i]+=s[i];i f(i<=b.l e n) c.s[i]+=b.s[i];c.s[i+1]=c.s[i]/10; c.s[i]%=10;}c.l e n=i−1;i f( c.l e n==0)c.l e n=1;return c;}HP HP::operator−(const HP&b){int i,j;HP c;for(i=1,j=0;i<=l e n;i++){c.s[i]=s[i]−j;i f(i<=b.l e n) c.s[i]−=b.s[i];i f(c.s[i]<0){j=1;c.s[i]+=10;}else j=0;}c.l e n=l e n;while(c.len>1&&!c.s[c.l e n]) c.len−−;return c;}int HP::Compare(const HP&y){i f(len>y.l e n)return1;i f(len<y.l e n)return−1;int i=l e n;while((i>1)&&(s[i]==y.s[i]))i−−;return s[i]−y.s[i];}HP HP::operator/(const HP&b){int i,j;HP d(0),c;for(i=l e n;i>0;i−−){i f(!(d.l e n==1&&d.s[1]==0)){for(j=d.l e n;j>0;j−−)d.s[j+1]=d.s[j];++d.l e n;}d.s[1]=s[i];c.s[i]=0;while((j=pare(b))>=0){d=d−b;c.s[i]++;i f(j==0)break;}}c.l e n=l e n;while((c.len>1)&&(c.s[c.l e n]==0)) c.len−−;return c;}HP HP::operator%(const HP&b){int i,j;HP d(0);for(i=l e n;i>0;i−−){i f(!(d.l e n==1&&d.s[1]==0)){for(j=d.l e n;j>0;j−−)d.s[j+1]=d.s[j];++d.l e n;}d.s[1]=s[i];while((j=pare(b))>=0){d=d−b;i f(j==0)break;} }return d;}5Chapter1Algorithms and Datastructures1.1High Precision in C#define maxlen1000struct HP{int len,s[maxlen];};void PrintHP(HP x){for(int i=x.l e n;i>=1;i−−)cout<<x.s[i];}void Str2HP(const char∗s,HP&x){x.l e n=s t r l e n(s);for(int i=1;i<=x.l e n;i++)x.s[i]=s[x.len−i]−’0’;}void Int2HP(int i n t e,HP&x){i f(i n t e==0){x.l e n=1;x.s[1]=0;return;};for(x.l e n=0;i n t e>0;){x.s[++x.l e n]=i n t e%10;i n t e/=10;};}void Multi(const HP a,const HP b,HP&c){int i,j; c.l e n=a.l e n+b.l e n;for(i=1;i<=c.l e n;i++)c.s[i]=0;for(i=1;i<=a.l e n;i++)for(j=1;j<=b.l e n;j++)c.s[i+j−1]+=a.s[i]∗b.s[j];for(i=1;i<c.l e n;i++){ c.s[i+1]+=c.s[i]/10; c.s[i]%=10;}while(c.s[i]){ c.s[i+1]=c.s[i]/10; c.s[i]%=10;i++;}while(i>1&&!c.s[i])i−−;c.l e n=i;}void Plus(const HP a,const HP b,HP&c){int i; c.s[1]=0;for(i=1;i<=a.l e n||i<=b.l e n|| c.s[i];i++){i f(i<=a.l e n) c.s[i]+=a.s[i];i f(i<=b.l e n) c.s[i]+=b.s[i];c.s[i+1]=c.s[i]/10; c.s[i]%=10;}c.l e n=i−1;i f( c.l e n==0)c.l e n=1;}void Subtract(const HP a,const HP b,HP&c){for(int i=1,j=0;i<=a.l e n;i++){c.s[i]=a.s[i]−j;i f(i<=b.l e n) c.s[i]−=b.s[i];i f(c.s[i]<0){j=1;c.s[i]+=10;}else j=0;}3c.l e n=a.l e n;while(c.len>1&&!c.s[c.l e n]) c.len−−;}int HPCompare(const HP x,const HP y){i f(x.len>y.l e n)return1;i f(x.len<y.l e n)return−1;int i=x.l e n;while((i>1)&&(x.s[i]==y.s[i]))i−−;return x.s[i]−y.s[i];}void Divide(const HP a,const HP b,HP&c,HP&d){int i,j; d.l e n=1; d.s[1]=0;for(i=a.l e n;i>0;i−−){i f(!(d.l e n==1&&d.s[1]==0)){for(j=d.l e n;j>0;j−−)d.s[j+1]=d.s[j];++d.l e n;}d.s[1]=a.s[i];c.s[i]=0;while((j=HPCompare(d,b))>=0){Subtract(d,b,d);c.s[i]++;i f(j==0)break;} }c.l e n=a.l e n;while((c.len>1)&&(c.s[c.l e n]==0)) c.len−−;}1.2High Precision in C Plus Plusconst int maxlen=10000;class HP{public:int len,s[maxlen];HP(){(∗this)=0;};HP(int i n t e){(∗this)=i n t e;};HP(const char∗s t r){(∗this)=s t r;};friend ostream&operator<<(ostream&cout,const HP&x);HP operator=(int i n t e);HP operator=(const char∗s t r);HP operator∗(const HP&b);HP operator+(const HP&b);HP operator−(const HP&b);HP operator/(const HP&b);HP operator%(const HP&b);int Compare(const HP&b);};ostream&operator<<(ostream&cout,const HP&x){for(int i=x.l e n;i>=1;i−−)cout<<x.s[i];return cout;}HP HP::operator=(const char∗s t r){l e n=s t r l e n(s t r);for(int i=1;i<=l e n;i++)s[i]=s t r[len−i]−’0’;return∗this;}HP HP::operator=(int i n t e){i f(i n t e==0){l e n=1;s[1]=0;return(∗this);};for(l e n=0;i n t e>0;){s[++l e n]=i n t e%10;i n t e/=10;};return(∗this);}HP HP::operator∗(const HP&b){int i,j;HP c;c.l e n=l e n+b.l e n;for(i=1;i<=c.l e n;i++)c.s[i]=0;for(i=1;i<=l e n;i++)for(j=1;j<=b.l e n;j++)c.s[i+j−1]+=s[i]∗b.s[j];for(i=1;i<c.l e n;i++){ c.s[i+1]+=c.s[i]/10; c.s[i]%=10;}41.3High Precision Floating-point Numberconst int f p r e c=100;//f l o a t i n g−p o i n t p r e c i s i o nHP z e r o=0;class FS{public:FS();void SetZero();FS(int i n t e){(∗this)=i n t e;}FS(char∗s){(∗this)=s;}FS operator=(char∗s);FS operator=(int i n t e);FS operator+(FS b);FS operator−(FS b);FS operator∗(FS b);FS operator/(FS b);friend ostream&operator<<(ostream&cout,FS x);int sign,prec;HP num;};void FS::SetZero(){s i g n=1;num=0;prec=0;}FS::FS(){SetZero();}ostream&operator<<(ostream&cout,FS x){i f(x.sign<0)cout<<”−”;int i,k,low=1;for(i=x.num.l e n;i>x.prec;i−−)cout<<x.num.s[i];i f(x.num.len<=x.prec)cout<<”0”;i f(pare(z e r o)==0){cout<<”.0”;return cout;}k=i;while(k>0&&x.num.s[k]==0)k−−;i f(k==0){cout<<”.0”;return cout;}cout<<”.”;i f(x.num.len<x.prec)for(int j=0;j<x.prec−x.num.l e n;j++)cout<<”0”;while(x.num.s[low]==0)low++;while(i>=low)cout<<x.num.s[i−−];return cout;}FS FS::operator=(int i n t e){prec=0;i f(i n t e>=0){s i g n=1;num=i n t e;}else{s i g n=−1;num=−i n t e;}return(∗this);}FS FS::operator=(char∗s){int p,i,j,l;SetZero();i f(s[0]==’−’){s i g n=−1;s++;};i f(s[0]==’+’){s i g n=1;s++;};l=s t r l e n(s);for(p=0;p<l;p++)i f(s[p]==’.’)break;i f(p==l)prec=0;else prec=l−1−p;for(i=l−1,j=0;i>=0;i−−)i f(s[i]!=’.’)num.s[++j]=s[i]−’0’;while(j>1&&num.s[j]==0)−−j;num.l e n=j;return(∗this);}6void L S h i f t(FS&a,int s l){a.prec+=s l; a.num.l e n+=s l;int i;for(i=a.num.l e n;i>s l;i−−)a.num.s[i]=a.num.s[i−s l];while(i>0) a.num.s[i−−]=0;}void RShift(FS&a,int s l){a.prec−=s l; a.num.len−=s l;int i;for(i=1;i<=a.num.l e n;i++)a.num.s[i]=a.num.s[i+s l];}FS FS::operator+(FS b){FS c;i f(prec>b.prec)L S h i f t(b,prec−b.prec);elsei f(prec<b.prec)L S h i f t((∗this),b.prec−prec);i f(s i g n==b.s i g n){c.s i g n=s i g n; c.prec=prec; c.num=num+b.num;i f( pare(z e r o)==0) c.SetZero();}else{c.prec=prec;i f(pare(b.num)==0) c.SetZero();elsei f(pare(b.num)>0){ c.s i g n=s i g n; c.num=num−b.num;}elsei f(pare(b.num)<0){ c.s i g n=b.s i g n; c.num=b.num−num;}i f( pare(z e r o)==0) c.SetZero();}i f(c.prec>f p r e c)RShift(c,c.prec−f p r e c);return c;}FS FS::operator−(FS b){b.s i g n=−b.s i g n;FS c=(∗this)+b;b.s i g n=−b.s i g n;return c;}FS FS::operator∗(FS b){FS c;c.s i g n=s i g n∗ b.s i g n;c.prec=prec+ b.prec;c.num=num∗ b.num;i f(pare(z e r o)==0) c.SetZero();i f(c.prec>f p r e c)RShift(c,c.prec−f p r e c);return c;}FS FS::operator/(FS b)//355/133= 3.1415929203539823008849557522124{FS c,d;//c=d/bd=(∗this);L S h i f t(d,f p r e c);c.s i g n=d.s i g n∗ b.s i g n;c.prec=d.prec;L S h i f t(d, b.prec);c.num=d.num/ b.num;i f(c.prec>f p r e c)RShift(c,c.prec−f p r e c);return c;}71.4Fraction Classint gcd(int a,int b){i f(b==0)return a;return gcd(b,a%b);}int lcm(int a,int b){return a/gcd(a,b)∗b;}class F ra c t io n{public:int a,b;//(a/b=numerator/denominator)int s i g n(int x){return(x>0?1:−1);}F ra c t io n():a(0),b(1){}F ra c t io n(int x):a(x),b(1){}F ra c t io n(int x,int y){int m=gcd(abs(x),abs(y));a=x/m∗s i g n(y);i f(a==0)b=1;else b=abs(y/m);}int get denominator(){return b;}int get numerator(){return a;}F ra c t io n operator+(const F r a c t i o n&f){int m=gcd(b,f.b);return F ra c t io n(f.b/m∗a+b/m∗f.a,b/m∗f.b);}F r a c t i o n operator−(const F ra c t i o n&f){int m=gcd(b,f.b);return F ra c t io n(f.b/m∗a−b/m∗f.a,b/m∗f.b);}F r a c t i o n operator∗(const F r a c t i o n&f){int m1=gcd(abs(a),f.b);int m2=gcd(b,abs(f.a));return F r a c t i o n((a/m1)∗(f.a/m2),(b/m2)∗(f.b/m1));}F r a c t io n operator/(const F r a c t i o n&f){return(∗this)∗F ra c t i o n(f.b,f.a);}friend ostream&operator<<(ostream&out,const F r a c t io n&f){i f(f.a==0)cout<<0;elsei f(f.b==1)cout<<f.a;else cout<<f.a<<’/’<<f.b;return out;}};1.5Binary Heap#define M A X N1048576int n,HeapSize,Heap[M A X N+1];void HeapUp(int p){int q=p>>1,a=Heap[p];while(q){i f(a<Heap[q])Heap[p]=Heap[q];else break;p=q;q=p>>1;}Heap[p]=a;}void AddToHeap(int a){Heap[++HeapSize]=a;HeapUp(HeapSize);}8void HeapDown(int p){int q=p<<1,a=Heap[p];while(q<=HeapSize){i f(q<HeapSize&&Heap[q+1]<Heap[q])q++;i f(Heap[q]<a)Heap[p]=Heap[q];else break;p=q;q=p<<1;}Heap[p]=a;}int GetTopFromHeap(){int TopElement=Heap[1];Heap[1]=Heap[HeapSize−−];HeapDown(1);return TopElement;}void BuildHeap()//Remember t o Let HeapSize=N{for(int i=HeapSize;i>0;i−−)HeapDown(i);}1.6Winner Treeconst int i n f=10000000;const int maxsize=1048576;//2ˆf l o o r(l o g(n))int heap[maxsize∗2],pos[maxsize∗2],n,base;void Update(int i){int j=i<<1;i f(heap[j+1]<heap[j])j++;heap[i]=heap[j];pos[i]=pos[j];}int GetTopFromHeap(int&ps){int r e t=heap[1],p=pos[1];ps=p;heap[p]=i n f;while(p>1){p>>=1;Update(p);}return r e t;}int main(){int i,j;c i n>>n;for(base=1;base<n;base<<=1);base−−;for(i=base+1;i<=(base<<1)+1;i++){pos[i]=i;i f(i<=base+n)cin>>heap[i];else heap[i]=i n f;}for(i=base;i>0;i−−)Update(i);for(i=1;i<=n;i++)cout<<GetTopFromHeap(j)<<endl;return0;}91.7Digital Tree#define maxlen100#define maxsize1000000#define DataType intchar t r e e[maxsize],s[maxlen];int son[maxsize],bro[maxsize],num,k,n;DataType data[maxsize];DataType f i n d(const char∗s){int i,j=0;for(i=0;s[i];i++){j=son[j];while(j&&t r e e[j]!=s[i])j=bro[j];i f(!j)return−1;}return data[j];}void add(const char∗s,DataType x){int i,j=0,p;for(i=0;s[i];i++){p=j;j=son[j];while(j&&t r e e[j]!=s[i])j=bro[j];i f(!j){t r e e[++num]=s[i];son[num]=0;bro[num]=son[p];son[p]=num;data[num]=−1;j=num;}}data[j]=x;}void i n i t(){num=0;bro[num]=0;son[num]=0;data[0]=−1;}1.8Segment Treeint cc[1<<22],m,n;//memset cc f i r s tvoid update(int i i,int s,int t,int ss,int tt,bool i n s e r t){i f(ss>t t)return;int mid((s+t)/2);i f(s==s s&&t==t t){i f(i n s e r t)cc[i i]=t−s+1;else cc[i i]=0;return;}i f(cc[i i]==0)i f(!i n s e r t)return;else cc[i i∗2]=cc[i i∗2+1]=0;else i f(cc[i i]==t−s+1)i f(i n s e r t)return;else{cc[i i∗2]=mid−s+1;cc[i i∗2+1]=t−mid;}update(i i∗2,s,mid,ss,min(mid,t t),i n s e r t);update(i i∗2+1,mid+1,t,max(mid+1,s s),tt,i n s e r t);cc[i i]=cc[i i∗2]+cc[i i∗2+1];}int query(int i i,int s,int t,int ss,int t t){i f(ss>t t)return0;int mid((s+t)/2);i f(s==s s&&t==t t)return cc[i i];i f(cc[i i]==0)cc[i i∗2]=cc[i i∗2+1]=0;i f(cc[i i]==t−s+1){cc[i i∗2]=mid−s+1;cc[i i∗2+1]=t−mid;}return query(i i∗2,s,mid,ss,min(mid,t t))+query(i i∗2+1,mid+1,t,max(mid+1,s s),t t);1.9Segment Tree in IOI’2001//upper:maximum p o s s i b l e r i g h t p o i n t o f i n t e r v a l sint upper,t r e e[maxinterval+1];void i n i t(){upper=0;memset(t r e e,0,s i z e o f(t r e e));}void update(int r,int x)//sum[1..r]+=x{while(r<=upper){t r e e[r]+=x;r+=(r&(rˆ(r−1)));}}int sum(int r)//r e t u r n sum[1..r]{int r e s=0;while(r>0){r e s+=t r e e[r];r−=(r&(rˆ(r−1)));}return r e s;}1.10Union-Find Setint rank[maxn],pnt[maxn];void makeset(int x){rank[pnt[x]=x]=0;}int f i n d(int x){int px=x,i;while(px!=pnt[px])px=pnt[px];while(x!=px){i=pnt[x];pnt[x]=px;x=i;};return px;}void merge(int x,int y)//or j u s t pnt[f i n d(x)]=f i n d(y) {i f(rank[x=f i n d(x)]>rank[y=f i n d(y)])pnt[y]=x;else{pnt[x]=y;rank[y]+=(rank[x]==rank[y]);}; }1.11Quick Sortvoid q u i c k s o r t(int b,int e,int a[]){int i=b,j=e,x=a[(b+e)/2];do{while(a[i]<x)i++;while(a[j]>x)j−−;i f(i<=j)std::swap(a[i++],a[j−−]);}while(i<j);i f(i<e)q u i c k s o r t(i,e,a);i f(j>b)q u i c k s o r t(b,j,a);}1.12Merge Sortvoid s o r t(int b,int e){i f(e−b<=0)return;int mid=(b+e)/2,p1=b,p2=mid+1,i=b;s o r t(b,mid);s o r t(mid+1,e);while(p1<=mid||p2<=e)i f(p2>e||(p1<=mid&&a[p1]<=a[p2]))t[i++]=a[p1++];else t[i++]=a[p2++];for(i=b;i<=e;i++)a[i]=t[i];}1.13Radix Sort#define base(1<<16)int n,a[maxn],t[maxn],bucket[base+2];void RadixSort(int n,int a[],int t[],int bucket[]){int k,i,j;for(j=0;j<base;j++)bucket[j]=0;for(k=base−1,i=0;i<2;i++,k<<=16){for(j=0;j<n;j++)bucket[a[j]&k]++;for(j=1;j<base;j++)bucket[j]+=bucket[j−1];for(j=n−1;j>=0;j−−)t[−−bucket[a[j]&k]]=a[j];for(j=0;j<n;j++)a[j]=t[j];}}1.14Select K th Smallest Elementint s e l e c t(int∗a,int b,int e,int k){i f(b==e)return a[b];int x=a[b+rand()%(e−b+1)],i=b,j=e;i−−;j++;while(i<j){while(a[++i]<x);while(a[−−j]>x);i f(i<j)std::swap(a[i],a[j]);}i f(j==e)j−−;i=j−b+1;i f(k<=i)return s e l e c t(a,b,j,k);else return s e l e c t(a,j+1,e,k−i);}1.15KMPint f a i l[maxlen];void m a k e f a i l(char∗t,int l t){−−t;for(int i=1,j=0;i<=l t;i++,j++){f a i l[i]=j;while(j>0&&t[i]!=t[j])j=f a i l[j];}}//s t a r t matching p a t t e r n T in S[i..)int kmp(char∗s,int l s,char∗t,int l t,int i,int&l o n g e s t,int&l p) {l o n g e s t=l p=0;−−s;−−t;for(int j=1;i<=l s;i++,j++){while(j>0&&s[i]!=t[j])j=f a i l[j];i f(j>l o n g e s t){l o n g e s t=j;l p=i−j;}i f(j==l t)return i−l t;}return−1;}1.16Suffix SortSuffixSort:input s[0..n),output id[0..n)#define nb next//”new b u c k e t”o v e r l a i d on”next”#define head h e i g h t//head i s never used when computing h e i g h t#define rank b//a f t e r S u f f i x S o r t,”rank”o v e r l a i d on”b u c k e t”char s[maxn];int n,i d[maxn],h e i g h t[maxn],b[maxn],next[maxn];bool cmp(const int&i,const int&j){return s[i]<s[j];}void S u f f i x S o r t(){int i,j,k,h;for(i=0;i<n;i++)i d[i]=i;std::s o r t(id,i d+n,cmp);for(i=0;i<n;i++)i f(i==0||s[i d[i]]!=s[i d[i−1]])b[i d[i]]=i;else b[i d[i]]=b[i d[i−1]];for(h=1;h<n;h<<=1){for(i=0;i<n;i++)head[i]=next[i]=−1;for(i=n−1;i>=0;i−−)i f(i d[i]){j=i d[i]−h;i f(j<0)j+=n;next[j]=head[b[j]];head[b[j]]=j;}j=n−h;next[j]=head[b[j]];head[b[j]]=j;for(i=k=0;i<n;i++)i f(head[i]>=0)for(j=head[i];j>=0;j=next[j])i d[k++]=j;for(i=0;i<n;i++)i f(i>0&&i d[i]+h<n&&i d[i−1]+h<n&&b[i d[i]]==b[i d[i−1]]&&b[i d[i]+h]==b[i d[i−1]+h])nb[i d[i]]=nb[i d[i−1]];else nb[i d[i]]=i;for(i=0;i<n;i++)b[i]=nb[i];}}GetHeight:height[i]=LCP(s[id[i]],s[id[i]−1]void GetHeight(){int i,j,h;h e i g h t[0]=0;for(i=0;i<n;i++)rank[i d[i]]=i;for(h=0,i=0;i<n;i++)i f(rank[i]>0){j=i d[rank[i]−1];while(s[i+h]==s[j+h])++h;h e i g h t[rank[i]]=h;i f(h>0)−−h;}Chapter2Graph Theory and Network Algorithms2.1SSSP—Dijkstra+Binary Heapconst int i n f=1000000000;int n,m,num,len,next[maxm],ev[maxm],ew[maxm];int value[maxn],mk[maxn],nbs[maxn],ps[maxn],heap[maxn];void update(int r){int q=ps[r],p=q>>1;while(p&&value[heap[p]]>value[r]){ps[heap[p]]=q;heap[q]=heap[p];q=p;p=q>>1;}heap[q]=r;ps[r]=q;}int getmin(){int r e t=heap[1],p=1,q=2,r=heap[len−−];while(q<=l e n){i f(q<l e n&&value[heap[q+1]]<value[heap[q]])q++;i f(value[heap[q]]<value[r]){ps[heap[q]]=p;heap[p]=heap[q];p=q;q=p<<1;}else break;}heap[p]=r;ps[r]=p;return r e t;}void d i j k s t r a(int src,int dst){int i,j,u,v;for(i=1;i<=n;i++){value[i]=i n f;mk[i]=ps[i]=0;};value[s r c]=0;heap[l e n=1]=s r c;ps[s r c]=1;while(!mk[dst]){i f(l e n==0)return;u=getmin();mk[u]=1;for(j=nbs[u];j;j=next[j]){v=ev[j];i f(!mk[v]&&value[u]+ew[j]<value[v]){i f(ps[v]==0){heap[++l e n]=v;ps[v]=l e n;}value[v]=value[u]+ew[j];update(v);}}}void readdata(){int i,u,v,w;cin>>n>>m;num=0;for(i=1;i<=n;i++)nbs[i]=0;while(m−−){cin>>u>>v>>w;next[++num]=nbs[u];nbs[u]=num;ev[num]=v;ew[num]=w;}d i j k s t r a(1,n);//Minimum Distance saved at v a l u e[1..n]}2.2SSSP—Bellman Ford+Queueconst int maxn=maxm=1000005const int i n f=1000000000int nbs[maxn],next[maxm],value[maxn],open[maxn],open1[maxn];int ev[maxm],ew[maxm],mk[maxn],n,m,num,cur,t a i l;void BellmanFord(int s r c){int i,j,k,l,t,u,v,p=0;for(i=1;i<=n;i++){value[i]=i n f;mk[i]=0;}value[s r c]=t a i l=0;open[0]=s r c;while(++p,t a i l>=0){for(i=0;i<=t a i l;i++)open1[i]=open[i];for(cur=0,t=t a i l,t a i l=−1;cur<=t;cur++)for(u=open1[cur],i=nbs[u];i;i=next[i]){v=ev[i];i f(value[u]+ew[i]<value[v]){value[v]=value[u]+ew[i];i f(mk[v]!=p){open[++t a i l]=v;mk[v]=p;}}}}}2.3MST—Kruskal#define maxn1000005#define maxm1000005int i d[maxm],eu[maxm],ev[maxm],ew[maxm],n,m,pnt[maxn];int cmp(const int&i,const int&j){return ew[i]<ew[j];}int f i n d(int x){i f(x!=pnt[x])pnt[x]=f i n d(pnt[x]);return pnt[x];} int Kruskal(){int r e t=0,i,j,p;for(i=1;i<=n;i++)pnt[i]=i;//node[1..n]for(i=0;i<m;i++)i d[i]=i;//ew[0..m−1]std::s o r t(id,i d+m,cmp);for(j=−1,i=1;i<n;i++){while(p=i d[++j],f i n d(eu[p])==f i n d(ev[p]));r e t+=ew[p];pnt[f i n d(ev[p])]=f i n d(eu[p]);}return r e t;}2.4Minimum Directed Spanning Treeint n,g[maxn][maxn],used[maxn],pass[maxn],eg[maxn],more,queue[maxn];void combine(int id,int&sum){int t o t=0,from,i,j,k;for(;i d!=0&&!pass[i d];i d=eg[i d]){queue[t o t++]=i d;pass[i d]=1;}for(from=0;from<t o t&&queue[from]!=i d;from++);i f(from==t o t)return;more=1;for(i=from;i<t o t;i++){sum+=g[eg[queue[i]]][queue[i]];i f(i!=from){used[queue[i]]=1;for(j=1;j<=n;j++)i f(!used[j])i f(g[queue[i]][j]<g[i d][j])g[i d][j]=g[queue[i]][j];}}for(i=1;i<=n;i++)i f(!used[i]&&i!=i d){for(j=from;j<t o t;j++){k=queue[j];i f(g[i][i d]>g[i][k]−g[eg[k]][k])g[i][i d]=g[i][k]−g[eg[k]][k];}}}int msdt(int r o o t){//r e t u r n t h e t o t a l l e n g t h o f MDSTint i,j,k,sum=0;memset(used,0,s i z e o f(used));for(more=1;more;){more=0;memset(eg,0,s i z e o f(eg));for(i=1;i<=n;i++)i f(!used[i]&&i!=r o o t){for(j=1,k=0;j<=n;j++)i f(!used[j]&&i!=j)i f(k==0||g[j][i]<g[k][i])k=j;eg[i]=k;}memset(pass,0,s i z e o f(pass));for(i=1;i<=n;i++)i f(!used[i]&&!pass[i]&&i!=r o o t)combine(i,sum);}for(i=1;i<=n;i++)i f(!used[i]&&i!=r o o t)sum+=g[eg[i]][i];return sum;}2.5Maximum Matching on Bipartite Graphint nx,ny,m,g[M A X N][M A X N],sy[M A X N],cx[M A X N],cy[M A X N];int path(int u){for(int v=1;v<=ny;v++)i f(g[u][v]&&!sy[v]){sy[v]=1;i f(!cy[v]||path(cy[v])){cx[u]=v;cy[v]=u;return1;}}return0;}int MaximumMatch(){int i,r e t=0;memset(cx,0,s i z e o f(cx));memset(cy,0,s i z e o f(cy));for(i=1;i<=nx;i++)i f(!cx[i]){memset(sy,0,s i z e o f(sy));r e t+=path(i);} return r e t;}2.6Maximum Cost Perfect Matching on Bipartite Graphint cx[maxn],cy[maxn],sx[maxn],sy[maxn],l x[maxn],l y[maxn];int nx,ny,match,g[maxn][maxn];int path(int u){sx[u]=1;for(int v=1;v<=ny;v++)i f(g[u][v]==l x[u]+l y[v]&&!sy[v]){ sy[v]=1;i f(!cy[v]||path(cy[v])){cx[u]=v;cy[v]=u;return1;}}return0;}void KuhnMunkres(){int i,j,u,min;memset(lx,0,s i z e o f(l x));memset(ly,0,s i z e o f(l y));memset(cx,0,s i z e o f(cx));memset(cy,0,s i z e o f(cy));for(i=1;i<=nx;i++)for(j=1;j<=ny;j++)i f(l x[i]<g[i][j])l x[i]=g[i][j];for(match=0,u=1;u<=nx;u++)i f(!cx[u]){memset(sx,0,s i z e o f(sx));memset(sy,0,s i z e o f(sy));while(!path(u)){min=0x3f f f f f f f;for(i=1;i<=nx;i++)i f(sx[i])for(j=1;j<=ny;j++)i f(!sy[j])i f(l x[i]+l y[j]−g[i][j]<min)min=l x[i]+l y[j]−g[i][j];for(i=1;i<=nx;i++)i f(sx[i]){l x[i]−=min;sx[i]=0;}for(j=1;j<=ny;j++)i f(sy[j]){l y[j]+=min;sy[j]=0;} };}}2.7Maximum Matching on General Graph//t o t a l i s t h e maximum c a r d i n a l i t y,p[1..n]means a match:i<−>p[i]int g[maxn][maxn],p[maxn],l[maxn][3],n,t o t a l,s t a t u s[maxn],v i s i t e d[maxn]; void s o l v e(){int i,j,k,pass;memset(p,0,s i z e o f(p));do{i=0;do{i f(p[++i])pass=0;else{memset(l,0,s i z e o f(l));l[i][2]=0x f f;pass=path(i);for(j=1;j<=n;j++)for(k=1;k<=n;k++)i f(g[j][k]<0)g[j][k]=−g[j][k];};}while(i!=n&&!pass);i f(pass)t o t a l+=2;}while(i!=n&&t o t a l!=n);}void upgrade(int r){int j=r,i=l[r][1];for(p[i]=j;l[i][2]<0x f f;){p[j]=i;j=l[i][2];i=l[j][1];p[i]=j;}p[j]=i;}int path(int r){int i,j,k,v,t,q u i t;memset(s t a t u s,0,s i z e o f(s t a t u s));s t a t u s[r]=2;do{q u i t=1;for(i=1;i<=n;i++)i f(s t a t u s[i]>1)for(j=1;j<=n;j++)i f(g[i][j]>0&&p[j]!=i)i f(s t a t u s[j]==0){i f(p[j]==0){l[j][1]=i;upgrade(j);return1;}elsei f(p[j]>0){g[i][j]=g[j][i]=−1;s t a t u s[j]=1;l[j][1]=i;g[j][p[j]]=g[p[j]][j]=−1;l[p[j]][2]=j;s t a t u s[p[j]]=2;q u i t=0;}}elsei f(s t a t u s[j]>1&&(s t a t u s[i]+s t a t u s[j]<6)){q u i t=0;g[i][j]=g[j][i]=−1;memset(v i s i t e d,0,s i z e o f(v i s i t e d));v i s i t e d[i]=1;k=i;v=2;while(l[k][v]!=0x f f){k=l[k][v];v=3−v;v i s i t e d[k]=1;}k=j;v=2;while(!v i s i t e d[k]){k=l[k][v];v=3−v;}i f(s t a t u s[i]!=3)l[i][1]=j;i f(s t a t u s[j]!=3)l[j][1]=i;s t a t u s[i]=s t a t u s[j]=3;t=i;v=2;while(t!=k){i f(s t a t u s[l[t][v]]!=3)l[l[t][v]][v]=t;t=l[t][v];s t a t u s[t]=3;v=3−v;}t=j;v=2;while(t!=k){i f(s t a t u s[l[t][v]]!=3)l[l[t][v]][v]=t;t=l[t][v];s t a t u s[t]=3;v=3−v;}}}while(!q u i t);return0;}2.8Maximum Flow—Ford Fulkson in Matrix//Remember t o memset C[maxn][maxn]f o r a new caseint c[maxn][maxn],f[maxn][maxn],pnt[maxn],open[maxn],d[maxn],mk[maxn];int maxflow(int n,int s,int t){int cur,t a i l,i,j,u,v,flow=0;memset(f,0,s i z e o f(f));do{memset(mk,0,s i z e o f(mk));memset(d,0,s i z e o f(d));open[0]=s;mk[s]=1;d[s]=0x3f f f f f f f;for(pnt[s]=cur=t a i l=0;cur<=t a i l&&!mk[t];cur++)for(u=open[cur],v=1;v<=n;v++)i f(!mk[v]&&f[u][v]<c[u][v]){mk[v]=1;open[++t a i l]=v;pnt[v]=u;i f(d[u]<c[u][v]−f[u][v])d[v]=d[u];else d[v]=c[u][v]−f[u][v];}i f(!mk[t])break;flow+=d[t];for(u=t;u!=s;){v=u;u=pnt[v];f[u][v]+=d[t];f[v][u]=−f[u][v];} }while(d[t]>0);return flow;}。