集训前复习
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Kruskal
#include<iostream> #include<algorithm> #include<cstring> #include<cstdio> using namespace std; #define re register int n,m,ans,fa[5001]; struct bian{ int from,to,v; }len[200010]; inline int fd(){ int s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } bool cmp(bian a,bian b){ return a.v < b.v; } int find(int x){ if(x == fa[x]) return x; else return fa[x] = find(fa[x]); } int main() { freopen("kru.in","r",stdin); freopen("kru.out","w",stdout); n = fd(),m = fd(); for(re int i=1;i<=n;++i) fa[i] = i; for(re int i=1;i<=m;++i) len[i].from = fd(),len[i].to = fd(),len[i].v = fd(); sort(len+1,len+1+m,cmp); for(re int i=1;i<=m;++i){ int fa1 = find(len[i].from),fa2 = find(len[i].to); if(fa1 != fa2){ fa[fa1] = fa2; ans += len[i].v; } } printf("%d",ans); return 0; }
Prim
#include<iostream> #include<cstring> #include<cstdio> using namespace std; #define re register #define inf 19260817 const int maxn = 2*1e5+5; int n,m,now,cnt,ans,head[maxn<<1],dis[maxn],vis[maxn]; struct bian{ int to,next,v; }len[maxn<<1]; inline int fd(){ int s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } void add(int from,int to,int v){ len[++cnt].v = v; len[cnt].to = to; len[cnt].next = head[from]; head[from] = cnt; } int main() { n = fd(),m = fd(); for(re int i=1;i<=m;++i){ int from = fd(),to = fd(),v = fd(); add(from,to,v),add(to,from,v); } for(re int i=1;i<=n;++i) dis[i] = inf,vis[i] = 0; dis[1] = 0; for(re int k=head[1];k;k=len[k].next){ int to = len[k].to,v = len[k].v; dis[to] = min(dis[to],dis[1]+v); } now = 1; for(re int i=1;i<=n-1;++i){ int minn = inf; vis[now] = 1; for(re int j=1;j<=n;++j) if(!vis[j]&&minn>dis[j]) minn = dis[j],now = j; //遍历n个点,保证每次选不同的点,一共选n-1次. ans += minn; for(re int j=head[now];j;j=len[j].next){ int to = len[j].to,v = len[j].v; if(vis[to]) continue; dis[to] = min(dis[to],v);//dis可理解为加入生成树的最小代价. } } printf("%d",ans); //用kru理解,手动模拟贪心选小边再选大边的‘hack‘,感性证明. return 0; }
DJ:
#include<iostream> #include<cstring> #include<cstdio> #include<queue> using namespace std; #define e exit(0); #define re register #define inf 2147483647 const int maxn = 2*1e5+5; int n,m,s,cnt,head[maxn],dis[maxn],vis[maxn]; struct bian{ int to,next,v; }len[maxn]; inline int fd(){ int s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } void add(int from,int to,int v){ len[++cnt].v = v; len[cnt].to = to; len[cnt].next = head[from]; head[from] = cnt; } void dj(int s){ for(re int i=1;i<=n;++i) dis[i] = inf,vis[i] = 0; dis[s] = 0; priority_queue<pair<int,int> > q; q.push(make_pair(0,s)); while(q.size()){ int now = q.top().second; q.pop(); if(vis[now]) continue; vis[now] = 1; for(re int k=head[now];k;k=len[k].next){ int to = len[k].to,v = len[k].v; if(dis[to] > dis[now]+v){ dis[to] = dis[now]+v; q.push(make_pair(-dis[to],to)); } } } } int main() { freopen("dj.in","r",stdin); freopen("dj.out","w",stdout); n = fd(),m = fd(),s = fd(); for(re int i=1;i<=m;++i){ int from = fd(),to = fd(),v = fd(); add(from,to,v); } dj(s); for(re int i=1;i<=n;++i){ if(i == s) dis[i] = 0; printf("%d ",dis[i]); } return 0; }
Spfa
#include<iostream> #include<cstring> #include<cstdio> #include<queue> using namespace std; #define e exit(0); #define re register #define inf 2147483647 const int maxn = 2*1e5+5; int n,m,s,cnt,head[maxn],dis[maxn],vis[maxn]; struct bian{ int to,next,v; }len[maxn]; inline int fd(){ int s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } void add(int from,int to,int v){ len[++cnt].v = v; len[cnt].to = to; len[cnt].next = head[from]; head[from] = cnt; } void dj(int s){ for(re int i=1;i<=n;++i) dis[i] = inf,vis[i] = 0; dis[s] = 0; queue<int> q; q.push(s); vis[s] = 1; while(q.size()){ int now = q.front(); q.pop(); vis[now] = 0; for(re int k=head[now];k;k=len[k].next){ int to = len[k].to,v = len[k].v; if(dis[to] > dis[now]+v){ dis[to] = dis[now]+v; if(!vis[to]){ q.push(to); vis[to] = 1; } } } } } int main() { n = fd(),m = fd(),s = fd(); for(re int i=1;i<=m;++i){ int from = fd(),to = fd(),v = fd(); add(from,to,v); } dj(s); for(re int i=1;i<=n;++i){ if(i == s) dis[i] = 0; printf("%d ",dis[i]); } return 0; }
Trie:
#include<iostream> #include<cstring> #include<cstdio> using namespace std; #define re register const int maxn = 10000*51*26+5; char a[60]; int n,m,cnt,root,trie[maxn][27],vis[maxn],check[maxn]; inline int fd(){ int s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } void insert(char a[]){ int lenth = strlen(a); root = 0; for(re int i=0;i<lenth;++i){ int x = a[i]-‘a‘; if(!trie[root][x]) trie[root][x] = ++cnt; root = trie[root][x]; } vis[root] = 1; } int find(char a[]){ int lenth = strlen(a); root = 0; for(re int i=0;i<lenth;++i){ int x = a[i]-‘a‘; if(!trie[root][x]) return 1; root = trie[root][x]; } if(!vis[root]) return 1; if(check[root]) return 2; check[root] = 1; return 3; } int main() { freopen("trie.in","r",stdin); freopen("trie.out","w",stdout); n = fd(); for(re int i=1;i<=n;++i){ scanf("%s",a); insert(a); } m = fd(); for(re int i=1;i<=m;++i){ scanf("%s",a); int flag = find(a); if(flag == 1) printf("WRONG "); if(flag == 2) printf("REPEAT "); if(flag == 3) printf("OK "); } return 0; }
LCA( bz )
#include<iostream> #include<cstring> #include<cstdio> using namespace std; #define re register const int maxn = 5*1e5+5; int n,m,s,cnt,head[maxn],h[maxn],fa[maxn],bz[maxn][24]; struct bian{ int to,next,v; }len[maxn<<1]; inline int fd(){ int s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } void add(int from,int to){ len[++cnt].to = to; len[cnt].next = head[from]; head[from] = cnt; } void dfs(int x){ for(re int k=head[x];k;k=len[k].next){ int to = len[k].to; if(!h[to]){ fa[to] = x; h[to] = h[x]+1; dfs(to); } } } void makebz(){ for(re int i=1;i<=n;++i) bz[i][0] = fa[i]; for(re int j=1;j<=19;++j) for(re int i=1;i<=n;++i) bz[i][j] = bz[bz[i][j-1]][j-1]; } int LCA(int x,int y){ if(h[x] < h[y]) swap(x,y); for(re int j=19;j>=0;--j) if(h[bz[x][j]] >= h[y]) x = bz[x][j]; if(x == y) return x; for(re int j=19;j>=0;--j) if(bz[x][j] != bz[y][j]) x = bz[x][j],y = bz[y][j]; return fa[x]; } int main() { freopen("Lca.in","r",stdin); freopen("Lca.out","w",stdout); n = fd(),m = fd(),s = fd(); for(re int i=1;i<=n-1;++i){ int from = fd(),to = fd(); add(from,to),add(to,from); } fa[s] = s,h[s] = 1; dfs(s); makebz(); for(re int i=1;i<=m;++i){ int from = fd(),to =fd(); printf("%d ",LCA(from,to)); } return 0; }
Treearray:
#include<iostream> #include<cstring> #include<cstdio> using namespace std; #define re register const int maxn = 5*1e5+5; int n,m,tree[maxn]; inline int fd(){ int s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } int lowbit(int x){ return x&(-x); } void add(int id,int v){ while(id<=n){ tree[id] += v; id += lowbit(id); } } long long ask(int x){ long long sum = 0; while(x){ sum += tree[x]; x -= lowbit(x); } return sum; } int main() { freopen("Treearray.in","r",stdin); freopen("Treearray.out","w",stdout); n = fd(),m = fd(); for(re int i=1;i<=n;++i){ int num = fd(); add(i,num); } for(re int i=1;i<=m;++i){ int flag = fd(),x = fd(),y = fd(); if(flag == 1) add(x,y); else if(flag == 2) printf("%lld ",ask(y)-ask(x-1)); } return 0; }
Treearraycf:
#include<iostream> #include<cstring> #include<cstdio> using namespace std; #define re register const int maxn = 5*1e5+5; int n,m,tree[maxn],val[maxn]; inline int fd(){ int s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } int lowbit(int x){ return x&(-x); } void add(int x,int v){ while(x<=n){ tree[x] += v; x += lowbit(x); } } long long ask(int x){ long long sum = 0; while(x){ sum += tree[x]; x -= lowbit(x); } return sum; } int main() { freopen("Treearraycf.in","r",stdin); freopen("Treearraycf.out","w",stdout); n = fd(),m = fd(); for(re int i=1;i<=n;++i) val[i] = fd(); for(re int i=1;i<=n;++i) add(i,val[i]-val[i-1]); for(re int i=1;i<=m;++i){ int flag = fd(); if(flag == 1){ int x = fd(),y = fd(),v = fd(); add(x,v),add(y+1,-v);//cf理解. } else if(flag == 2){ int x = fd(); printf("%lld ",ask(x)); } } return 0; }
RMQ:
#include<iostream> #include<cstring> #include<cstdio> using namespace std; #define re register const int maxn = 1e6+10; int n,m,f[maxn][24],logn[maxn]; inline int fd(){ int s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } int main() { freopen("RMQ.in","r",stdin); freopen("RMQ.out","w",stdout); n = fd(),m = fd(); logn[0] = -1; for(re int i=1;i<=n;++i) f[i][0] = fd(),logn[i] = logn[i>>1]+1; for(re int j=1;j<=19;++j) for(re int i=1;i+(1<<j)-1<=n;++i) f[i][j] = max(f[i][j-1],f[i+(1<<j-1)][j-1]); //f[i+(i<<j-1)][j-1]; for(re int i=1;i<=m;++i){ int L = fd(),R = fd(); int id = logn[R-L+1]; printf("%d ",max(f[L][id],f[R-(1<<id)+1][id])); } //f[R-(1<<id)+1]; return 0; }
Invfm:
#include<iostream> #include<cstring> #include<cstdio> using namespace std; #define re register int n,mod; inline int fd(){ int s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } int qsm(int x,int y){ int base = 1; while(y){ if(y&1) base = (base%mod*x%mod)%mod; x = (x%mod*x%mod)%mod; y>>=1; } return base; } int main() { freopen("Ivfm.in","r",stdin); freopen("Ivfm.out","w",stdout); n = fd(),mod = fd(); for(re int i=1;i<=n;++i){ int ans = qsm(i,mod-2); ans = (ans%mod+mod)%mod; printf("%d ",ans); } return 0; }
Invexgcd:
#include<iostream> #include<cstring> #include<cstdio> using namespace std; #define re register int n,x1,y1,x2,y2,mod; inline int fd(){ int s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } void exgcd(int a,int b){ if(!b){ x1 = 1; y1 = 0; return; } exgcd(b,a%b); x2 = x1,y2 = y1; x1 = y2; y1 = x2 - (a/b)*y2; } int main() { freopen("Invexgcd.in","r",stdin); freopen("Invexgcd.out","w",stdout); n = fd(),mod = fd(); for(re int i=1;i<=n;++i){ exgcd(i,mod); printf("%d ",(x1%mod+mod)%mod); } return 0; }
Invdt:
#include<iostream> #include<cstring> #include<cstdio> using namespace std; #define re register const int maxn = 3*1e6+10; int n,mod,inv[maxn]; inline int fd(){ int s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } int main() { freopen("Invdt.in","r",stdin); freopen("Invdt.out","w",stdout); n = fd(),mod = fd(); inv[1] = 1; for(re int i=2;i<=n;++i) inv[i] = ((1ll*(-inv[mod%i])*(mod/i))%mod+mod)%mod; for(re int i=1;i<=n;++i) printf("%d ",inv[i]); return 0; }
Tyfc:
#include<iostream> #include<cstring> #include<cstdio> using namespace std; #define re register int a,b,x1,x2,y1,y2; inline int fd(){ int s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } void exgcd(int a,int b){ if(!b){ x1 = 1; y1 = 0; return; } exgcd(b,a%b); x2 = x1,y2 = y1; x1 = y2; y1 = x2 - a/b*y2; } int main() { freopen("Tyfc.in","r",stdin); freopen("Tyfc.out","w",stdout); a = fd(),b = fd(); exgcd(a,b); x1 = (x1%b+b)%b; printf("%d",x1); return 0; }
bdfc:
#include<iostream> #include<cstring> #include<cstdio> using namespace std; #define e exit(0) #define re register int a,b,c,g,x1,y1,x2,y2,x,y; inline int fd(){ int s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } int gcd(int x,int y){ if(!y) return x; else return gcd(y,x%y); } void exgcd(int a,int b){ if(!b){ x1 = 1; y1 = 0; return; } exgcd(b,a%b); x2 = x1,y2 = y1; x1 = y2; y1 = x2 - a/b*y2; } int main() { freopen("bdfc.in","r",stdin); freopen("bdfc.out","w",stdout); a = fd(),b = fd(),c = fd(); g = gcd(a,b); exgcd(a,b); x1 = x1*(c/g),y1 = y1*(c/g); for(re int k = 0;k<=100;++k){ x = x1 + k*(b/g); y = y1 - k*(a/g); printf("%d %d ",x,y); } return 0; }
CRT:
#include<iostream> #include<cstring> #include<cstdio> using namespace std; #define e exit(0) #define re register #define LL long long const int maxn = 1010; long long n,M=1,k,x1,y1,x2,y2,ans,a[maxn],b[maxn]; inline long long fd(){ long long s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } void exgcd(LL a,LL b){ if(!b){ x1 = 1; y1 = 0; return; } exgcd(b,a%b); x2 = x1,y2 = y1; x1 = y2; y1 = x2-a/b*y2; } int main() { freopen("CRT.in","r",stdin); freopen("CRT.out","w",stdout); n = fd(); for(re LL i=1;i<=n;++i){ a[i] = fd(),b[i] = fd(); M*=a[i]; } for(re LL i=1;i<=n;++i){ LL mi = M/a[i]; exgcd(mi,a[i]); k = x1; ans += k*mi*b[i]; } ans = ((ans%M)+M)%M; printf("%lld",ans); //注意最后模数为M. return 0; }
jzqsm:
#include<iostream> #include<cstring> #include<cstdio> using namespace std; #define e exit(0) #define re register #define LL long long const long long mod = 1e9+7; long long n,k; struct jz{ long long a[101][101]; jz(){memset(a,0,sizeof(a));} inline jz operator*(const jz & b)const{ jz p; for(re LL k=1;k<=n;++k) for(re LL i=1;i<=n;++i) for(re LL j=1;j<=n;++j) p.a[i][j] = (p.a[i][j]%mod+(1ll*a[i][k]%mod*b.a[k][j]%mod)%mod)%mod; return p; } }; inline long long fd(){ long long s=1,t=0; char c=getchar(); while(c<‘0‘||c>‘9‘){ if(c==‘-‘) s=-1; c=getchar(); } while(c>=‘0‘&&c<=‘9‘){ t=t*10+c-‘0‘; c=getchar(); } return s*t; } jz qsm(jz x,LL y){ jz base; for(re LL i=1;i<=n;++i) base.a[i][i] = 1; while(y){ if(y&1) base = base*x; x = x*x; y>>=1; } return base; } int main() { freopen("jzqsm.in","r",stdin); freopen("jzqsm.out","w",stdout); n = fd(),k = fd(); jz ori; for(re LL i=1;i<=n;++i) for(re LL j=1;j<=n;++j) ori.a[i][j] = fd(); jz p = qsm(ori,k); for(re LL i=1;i<=n;++i){ for(re LL j=1;j<=n;++j) printf("%lld ",p.a[i][j]); printf(" "); } return 0; }
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