模板合集
Posted lja001100
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SPFA
#include<bits/stdc++.h>
using namespace std;
struct EE
int x,y,dis,next;
edge[550000];
int len = 0,last[11000] = 0;
int n,m;
void ins(int xx,int yy,int dd)
len++;
edge[len].x = xx,edge[len].y = yy,edge[len].dis = dd;
edge[len].next = last[xx];
last[xx] = len;
int d[11000];
queue<int> q;
bool used[11000] = 0;
const int inf = 2147483647;
int s;
int main()
scanf("%d%d%d",&n,&m,&s);
for(int i = 1;i<=m;i++)
int ai,bi,ci;
scanf("%d%d%d",&ai,&bi,&ci);
ins(ai,bi,ci);
for(int i = 1;i<=n;i++)d[i] = inf;
d[s] = 0;
q.push(s);
while(!q.empty())
int nw = q.front();
int res = last[nw];
while(res!=0)
int rd = d[nw]+edge[res].dis;
int i = edge[res].y;
if(d[i]>rd)
d[i] = rd;
if(!used[i])
q.push(i);
used[i] = 1;
res = edge[res].next;
q.pop();
used[nw] = 0;
for(int i = 1;i<=n;i++) printf("%d ",d[i]);
return 0;
dijkstra + heap
#include<bits/stdc++.h>
using namespace std;
const long long inf = 9223372036854775807;
long long dis[2001000];
long long eh[200000] = 0;
bool used[200000] = 0;
struct EE
long long st,val,ne;
edge[2001000];
long long n,m,s;
inline void Read()
scanf("%lld%lld%lld",&n,&m,&s);
for(long long i = 1;i<=m;i++)
long long x;
scanf("%lld%lld%lld",&x,&edge[i].st,&edge[i].val);
edge[i].ne = eh[x];
eh[x] = i;
struct node
long long pos;
long long dis;
bool operator <( const node &x )const
return x.dis<dis;
;
std::priority_queue<node> q;
node nw;
inline void Print()
for(long long i= 1;i<=n;i++)printf("%lld ",dis[i]);
int main()
Read();
for(long long i = 1;i<=n;i++)dis[i] = inf;
dis[s] = 0;
q.push((node)s,0);
while(!q.empty())
nw = q.top();
q.pop();
long long d = nw.dis;
long long p = nw.pos;
if(used[p])continue;
used[p] = 1;
for(long long i = eh[p];i;i = edge[i].ne)
if(dis[edge[i].st]>dis[p]+edge[i].val)
dis[edge[i].st] = dis[p]+edge[i].val;
if(!used[edge[i].st]) q.push((node)edge[i].st,dis[edge[i].st]);
Print();
return 0;
线段树
#include<bits/stdc++.h>
using namespace std;
struct node
long long l,r;
long long c,add;
tr[510000] = 0;
long long a[200007];
int n,m;
inline void bt(int cnt,int l,int r)
tr[cnt].l = l;
tr[cnt].r = r;
tr[cnt].add = 0;
if(l==r)
tr[cnt].c = a[l];
return;
int mid = (l+r)/2;
bt(cnt*2,l,mid);
bt(cnt*2+1,mid+1,r);
tr[cnt].c = tr[cnt*2].c+tr[cnt*2+1].c;
inline void spread(int p)
if(tr[p].add)
tr[p*2].c += tr[p].add*(tr[p*2].r-tr[p*2].l+1);
tr[p*2+1].c += tr[p].add*(tr[p*2+1].r-tr[p*2+1].l+1);
tr[p*2].add += tr[p].add;
tr[p*2+1].add += tr[p].add;
tr[p].add = 0;
inline void change(int nw,int l,int r,int k)
if(l<=tr[nw].l&&r>=tr[nw].r)
tr[nw].c += (long long)k*(tr[nw].r-tr[nw].l+1);
tr[nw].add += k;
return;
spread(nw);
int mid = (tr[nw].l+tr[nw].r)/2;
if(l<=mid) change(nw*2,l,r,k);
if(r>mid) change(nw*2+1,l,r,k);
tr[nw].c = tr[nw*2].c+tr[nw*2+1].c;
inline long long find(int nw,int l,int r)
if(l==tr[nw].l&&r==tr[nw].r) return tr[nw].c;
spread(nw);
int mid = (tr[nw].l+tr[nw].r)/2;
if(r<=mid) return find(nw*2,l,r);
if(l>mid) return find(nw*2+1,l,r);
return find(nw*2,l,mid)+find(nw*2+1,mid+1,r);
int main()
scanf("%d%d",&n,&m);
for(int i = 1;i<=n;i++) scanf("%lld",&a[i]);
bt(1,1,n);
int tp;
for(int i = 1;i<=m;i++)
scanf("%d",&tp);
if(tp==1)
int x,y,k;
scanf("%d%d%d",&x,&y,&k);
change(1,x,y,k);
else
int x,y;
scanf("%d%d",&x,&y);
printf("%lld\n",find(1,x,y));
return 0;
主席树（可持久化线段树）
#include<bits/stdc++.h>
using namespace std;
int n,m;
int a[200010],root[200010] = 0,b[200010],c[200010];
struct node
int l,r,sum;
tr[8000100];
int mc = 0,cnt = 0;
int find(int x)
return lower_bound(c+1,c+mc+1,x)-c;
void update(int l,int r,int &x,int y,int pos)
tr[++cnt] = tr[y],tr[cnt].sum++,x = cnt;
if(l==r) return;
int mid = (l+r)/2;
if(mid>=pos) update(l,mid,tr[x].l,tr[y].l,pos);
else update(mid+1,r,tr[x].r,tr[y].r,pos);
int query(int l,int r,int x,int y,int k)
if(l==r) return l;
int mid = (l+r)/2;
int sum = tr[tr[y].l].sum-tr[tr[x].l].sum;
if(sum>=k) return query(l,mid,tr[x].l,tr[y].l,k);
else return query(mid+1,r,tr[x].r,tr[y].r,k-sum);
int main()
scanf("%d%d",&n,&m);
for(int i = 1;i<=n;i++) scanf("%d",&a[i]),b[i] = a[i];
sort(b+1,b+n+1);
for(int i = 1;i<=n;i++)
if(i==1||b[i]!=b[i-1]) c[++mc] = b[i];
for(int i = 1;i<=n;i++)update(1,n,root[i],root[i-1],find(a[i]));
for(int i = 1;i<=m;i++)
int x,y,k;
scanf("%d%d%d",&x,&y,&k);
printf("%d\n",c[query(1,n,root[x-1],root[y],k)]);
return 0;
树状数组
#include<bits/stdc++.h>
using namespace std;
int n,m;
int a[660001];
int c[660001] = 0;
int lowbit(int x)
return x&(-x);
void bt()
for(int i = 1;i<=n;i++)
int lb = lowbit(i);
for(int j = i;j>=(i-lb+1);j--)
c[i]+=a[j];
int query(int x)
int res = 0;
while(x!=0)
res+= c[x];
x-=lowbit(x);
return res;
void update(int x,int y)
for(int i = x;i<=n;i+=lowbit(i))
c[i]+=y;
int main()
scanf("%d%d",&n,&m);
for(int i = 1;i<=n;i++)
scanf("%d",&a[i]);
bt();
for(int i = 1;i<=m;i++)
int tp,x,y;
scanf("%d%d%d",&tp,&x,&y);
if(tp==1)
update(x,y);
else printf("%d\n",query(y)-query(x-1));
return 0;
树链剖分
#include<bits/stdc++.h>
using namespace std;
#define int long long
struct EE
int to,nxt;
edge[320000] = 0;
int cnt = 0;
int h[160000] = 0;
void ins(int x,int y)
edge[++cnt].to = y;
edge[cnt].nxt = h[x];
h[x] = cnt;
int n,m,r,mod;
int val[160000] = 0;
int dep[160000] = 0;
int fa[160000] = 0;
int son[160000] = 0;
int mxson[160000] = 0;
void dfs1(int u,int ff)
dep[u] = dep[ff] + 1;
fa[u] = ff;
son[u] = 1;
int res = 0;
for(int i = h[u];i;i = edge[i].nxt)
int v = edge[i].to;
if(v==ff) continue;
dfs1(v,u);
son[u] += son[v];
if(son[v]>res) res = son[v],mxson[u] = v;
int cntd = 0;
int num[160000] = 0;
int seg[160000] = 0;
int top[160000] = 0;
void dfs2(int u,int st)
num[u] = ++cntd;
seg[cntd] = val[u];
top[u] = st;
if(son[u]==1)return;
dfs2(mxson[u],st);
for(int i = h[u];i;i = edge[i].nxt)
int v = edge[i].to;
if(v!=fa[u]&&v!=mxson[u]) dfs2(v,v);
//---------Segment Tree
struct tt
int lazy,c,l,r;
tr[640000] = 0;
void bt(int nw,int l,int r)
tr[nw].l = l;
tr[nw].r = r;
if(l==r)
tr[nw].c = seg[l];
return;
int mid = (l+r)/2;
bt(nw*2,l,mid);
bt(nw*2+1,mid+1,r);
tr[nw].c = (tr[nw*2].c+tr[nw*2+1].c) % mod;
void pushdown(int nw)
if(tr[nw].lazy==0) return;
tr[nw*2].lazy += tr[nw].lazy;
tr[nw*2+1].lazy += tr[nw].lazy;
tr[nw*2].c += (tr[nw*2].r-tr[nw*2].l+1) % mod * tr[nw].lazy % mod;
tr[nw*2+1].c += (tr[nw*2+1].r-tr[nw*2+1].l+1) %mod * tr[nw].lazy % mod;
tr[nw*2].lazy%=mod;
tr[nw*2+1].lazy%=mod;
tr[nw*2].c%=mod;
tr[nw*2+1].c%=mod;
tr[nw].lazy = 0;
void update(int nw,int x,int y,int d)
if(tr[nw].l==x&&tr[nw].r==y)
tr[nw].lazy += d;
tr[nw].lazy%=mod;
tr[nw].c += d*(tr[nw].r-tr[nw].l+1)%mod;
tr[nw].c%=mod;
return;
pushdown(nw);
int mid = (tr[nw].l+tr[nw].r)/2;
if(y<=mid) update(nw*2,x,y,d);
else if(x>mid) update(nw*2+1,x,y,d);
else update(nw*2,x,mid,d),update(nw*2+1,mid+1,y,d);
tr[nw].c = (tr[nw*2].c+tr[nw*2+1].c)%mod;
int query(int nw,int x,int y)
if(tr[nw].l==x&&tr[nw].r==y)
return tr[nw].c;
pushdown(nw);
int mid = (tr[nw].l+tr[nw].r)/2;
if(y<=mid) return query(nw*2,x,y);
else if(x>mid) return query(nw*2+1,x,y);
else return (query(nw*2,x,mid)+query(nw*2+1,mid+1,y))%mod;
//----------------------
int opt1(int x,int y)
int res = 0;
while(top[x]!=top[y])
if(dep[top[x]]<dep[top[y]]) swap(x,y);
int sc = num[x];
int se = num[top[x]];
res += query(1,se,sc);
res %= mod;
x = fa[top[x]];
int sp = num[x],sd = num[y];
if(sp>sd) swap(sp,sd);
res += query(1,sp,sd);
res %= mod;
return res;
void opt2(int x,int y,int d)
while(top[x]!=top[y])
if(dep[top[x]]<dep[top[y]]) swap(x,y);
int sc = num[x];
int se = num[top[x]];
update(1,se,sc,d);
x = fa[top[x]];
int sp = num[x],sd = num[y];
if(sp>sd) swap(sp,sd);
update(1,sp,sd,d);
signed main()
scanf("%lld%lld%lld%lld",&n,&m,&r,&mod);
for(int i = 1;i<=n;i++)
scanf("%lld",&val[i]);
val[i] %= mod;
for(int i = 1;i<n;i++)
int x,y;
scanf("%lld%lld",&x,&y);
ins(x,y);
ins(y,x);
dfs1(r,0);
dfs2(r,r);
bt(1,1,n);
for(int i = 1;i<=m;i++)
int opt,x,y,z;
scanf("%lld",&opt);
if(opt==1)
scanf("%lld%lld%lld",&x,&y,&z);
opt2(x,y,z);
else if(opt==2)
scanf("%lld%lld",&x,&y);
printf("%lld\n",opt1(x,y));
else if(opt==3)
scanf("%lld%lld",&x,&y);
update(1,num[x],num[x]+son[x]-1,y);
else
scanf("%lld",&x);
printf("%lld\n",query(1,num[x],num[x]+son[x]-1));
return 0;
treap
#include<bits/stdc++.h>
using namespace std;
const int inf = 1e7+1;
int root = 1;
struct treap
int fa,son[2],c,cnt,cnts,lv;
tr[220000] = 0;
int cnte = 1;
int used[220000] = 0;
void pushup(int nw)
tr[nw].cnt = tr[nw].cnts + tr[tr[nw].son[0]].cnt + tr[tr[nw].son[1]].cnt;
void rotate(int &nw,int tp)
int k = tr[nw].son[tp^1];
tr[nw].son[tp^1] = tr[k].son[tp];
tr[k].son[tp] = nw;
pushup(nw);
pushup(k);
nw = k;
void ins(int &p,int c)
if(!used[p])
used[p] = 1;
tr[p].c = c;
tr[p].cnt = 1;
tr[p].cnts = 1;
tr[p].lv = rand();
if(!tr[p].son[0])tr[p].son[0] = ++cnte;
if(!tr[p].son[1])tr[p].son[1] = ++cnte;
return;
if(tr[p].c == c)
tr[p].cnts++;
tr[p].cnt++;
return;
int tp = c>tr[p].c;
ins(tr[p].son[tp],c);
if(tr[p].lv < tr[tr[p].son[tp]].lv) rotate(p,tp^1);
pushup(p);
void del(int &p,int c)
if(!used[p]) return;
if(c!=tr[p].c) del(tr[p].son[c>tr[p].c],c);
else
if(!used[tr[p].son[0]]&&!used[tr[p].son[1]])
tr[p].cnt--;
tr[p].cnts--;
if(tr[p].cnt==0) used[p] = 0;
else if(used[tr[p].son[0]]&&!used[tr[p].son[1]])
rotate(p,1);
del(tr[p].son[1],c);
else if(!used[tr[p].son[0]]&&used[tr[p].son[1]])
rotate(p,0);
del(tr[p].son[0],c);
else if(used[tr[p].son[0]]&&used[tr[p].son[1]])
int tp = (tr[tr[p].son[0]].lv>tr[tr[p].son[1]].lv);
rotate(p,tp);
del(tr[p].son[tp],c);
pushup(p);
int opt3(int p,int c)
if(!used[p]) return 0;
if(tr[p].c==c) return tr[tr[p].son[0]].cnt+1;
if(tr[p].c<c) return tr[tr[p].son[0]].cnt + tr[p].cnts + opt3(tr[p].son[1],c);
if(tr[p].c>c) return opt3(tr[p].son[0],c);
int opt4(int p,int rk)
if(!used[p]) return 0;
if(tr[tr[p].son[0]].cnt>=rk) return opt4(tr[p].son[0],rk);
if(tr[tr[p].son[0]].cnt+tr[p].cnts>=rk) return tr[p].c;
return opt4(tr[p].son[1],rk-tr[tr[p].son[0]].cnt-tr[p].cnts);
int opt5(int p,int c)
if(!used[p]) return -inf;
if(tr[p].c>=c) return opt5(tr[p].son[0],c);
else return max(tr[p].c,opt5(tr[p].son[1],c));
int opt6(int p,int c)
if(!used[p]) return inf;
if(tr[p].c<=c) return opt6(tr[p].son[1],c);
else return min(tr[p].c,opt6(tr[p].son[0],c));
int n;
int main()
srand(time(0));
scanf("%d",&n);
for(int i = 1;i<=n;i++)
int opt,x;
scanf("%d%d",&opt,&x);
if(opt==1)
ins(root,x);
else if(opt==2)
del(root,x);
else if(opt==3)
printf("%d\n",opt3(root,x));
else if(opt==4)
printf("%d\n",opt4(root,x));
else if(opt==5)
printf("%d\n",opt5(root,x));
else if(opt==6)
printf("%d\n",opt6(root,x));
return 0;
LCA
#include<bits/stdc++.h>
using namespace std;
struct EE
int to,nxt;
edge[1010000];
int h[660000] = 0;
int cnt = 0;
void ins(int x,int y)
edge[++cnt].to = y;
edge[cnt].nxt = h[x];
h[x] = cnt;
int n,m,s;
int f[660000][77] = 0;
int dep[660000] = 0;
int lg[660000] = 0;
void dfs(int u,int fa)
f[u][0] = fa;
for(int i = 1;(1<<i)<=dep[u];i++)
f[u][i] = f[f[u][i-1]][i-1];
for(int i = h[u];i;i = edge[i].nxt)
int v = edge[i].to;
if(v==fa) continue;
dep[v] = dep[u]+1;
dfs(edge[i].to,u);
void calclg()
for(int i = 1;i<=n;i++)
lg[i] = lg[i-1]+((1<<lg[i-1])==i);
int main()
scanf("%d%d%d",&n,&m,&s);
for(int i = 1;i<n;i++)
int x,y;
scanf("%d%d",&x,&y);
ins(x,y);
ins(y,x);
dfs(s,-1);
calclg();
for(int i = 1;i<=m;i++)
int x,y;
scanf("%d%d",&x,&y);
if(dep[x]<dep[y]) swap(x,y);
while(dep[x]>dep[y])
x = f[x][lg[dep[x]-dep[y]]-1];
if(x==y)
printf("%d\n",x);
continue;
for(int k = lg[dep[x]]-1;k>=0;k--)
if(f[x][k]!=f[y][k])
x = f[x][k],y = f[y][k];
printf("%d\n",f[x][0]);
return 0;
Dinic
#include<bits/stdc++.h>
using namespace std;
struct node
int x,y,c,next,other;
a[2110000];
int len,last[11000],st,ed;
int n,f,d;
void ins(int x,int y,int c)
len++;int k1 = len;
a[len].x = x,a[len].y = y,a[len].c = c;
a[len].next = last[x];
last[x] = len;
len++; int k2 = len;
a[len].x = y,a[len].y = x,a[len].c = 0;
a[len].next = last[y];
last[y] = len;
a[k1].other = k2;
a[k2].other = k1;
queue<int> q;
int h[11000],m;
bool build_h() // BFS
memset(h,0,sizeof(h));
h[st] = 1;
q.push(st);
while(!q.empty())
int x = q.front();
for(int k = last[x];k;k=a[k].next)
int y = a[k].y;
if(a[k].c>0&&h[y]==0)
h[y] = h[x]+1;
q.push(y);
q.pop();
if(h[ed]>0)return 1;
else return 0;
int findflow(int x,int f) //DFS
if(x==ed) return f;
int s = 0,t;
for(int i = last[x];i;i=a[i].next)
int y = a[i].y;
if(a[i].c>0&&h[y]==(h[x]+1)&&s<f)
s+=(t = findflow(y,min(a[i].c,f-s)));
a[i].c -= t;a[a[i].other].c+=t;
if(s==0)h[x] = 0;
return s;
int main()
scanf("%d%d%d%d",&n,&m,&st,&ed);
len = 0;
memset(last,0,sizeof(last));
int s = 0,t;
int ai,bi,ci;//(qwq)
for(int i = 1;i<=m;i++)
scanf("%d%d%d",&ai,&bi,&ci);
ins(ai,bi,ci);
while(build_h())
s+=findflow(st,99999999);
printf("%d\n",s);
return 0;
exgcd
#include<bits/stdc++.h>
using namespace std;
#define int long long
int a,b;
int a1,b1;
int exgcd(int a,int b,int &x,int &y)
if(b==0)
x = 1,y = 0;
return a;
int res = exgcd(b,a%b,x,y);
int tmp = x;
x = y,y = tmp-y*(a/b);
return res;
signed main()
scanf("%lld%lld",&a,&b);
exgcd(a,b,a1,b1);
printf("%lld",(a1%b+b)%b);
return 0;
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