NOIP2018 - 一些板子
好多东西都不熟练……
数论
数论分块「bzoj2956: 模积和」
10.28.2018
#include<bits/stdc++.h>
typedef long long ll;
const int MO = ;
const int inv6 = ; ll n,m,ans,del; inline void Add(ll &x, ll y){x = ((x+y)%MO+MO)%MO;}
ll sum(ll x){return x*(x+)%MO*(*x+)%MO*inv6%MO;}
ll calc(ll x)
{
ll ret = ;
for (ll i=, j=; i<=x; i=j+)
{
j = x/(x/i);
Add(ret, 1ll*(x/i)*(i+j)*(j-i+)/%MO);
}
return ((x%MO*x%MO-ret)+MO)%MO;
}
int main()
{
scanf("%lld%lld",&n,&m);
if (n > m) std::swap(n, m);
ans = calc(n)*calc(m)%MO;
del = n*m%MO*n%MO;
for (ll i=, j=; i<=n; i=j+)
{
j = std::min(n/(n/i), m/(m/i));
ll s1 = (sum(j)-sum(i-))*(n/i)%MO*(m/i)%MO;
ll s2 = (n*(m/i)%MO+m*(n/i)%MO)%MO*((i+j)*(j-i+)/%MO);
Add(del, (s1-s2)%MO);
}
Add(ans, -del);
printf("%lld\n",ans);
return ;
}
图论
点-树链剖分「1036: [ZJOI2008]树的统计Count」
10.24.2018
#include<bits/stdc++.h>
const int maxn = ;
const int maxm = ;
const int INF = 0x3f3f3f3f; struct node
{
int tot,fa,son,top;
}a[maxn];
int n,m;
char opt[];
int f[maxn<<][];
int chTot,chain[maxn],cnVal[maxn],d[maxn],dep[maxn];
int edgeTot,head[maxn],nxt[maxm],edges[maxm]; int read()
{
char ch = getchar();
int num = ;
bool fl = ;
for (; !isdigit(ch); ch=getchar())
if (ch=='-') fl = ;
for (; isdigit(ch); ch=getchar())
num = (num<<)+(num<<)+ch-;
if (fl) num = -num;
return num;
}
void addedge(int u, int v)
{
edges[++edgeTot] = v, nxt[edgeTot] = head[u], head[u] = edgeTot;
edges[++edgeTot] = u, nxt[edgeTot] = head[v], head[v] = edgeTot;
}
void pushup(int rt)
{
f[rt][] = std::max(f[rt<<][], f[rt<<|][]);
f[rt][] = f[rt<<][]+f[rt<<|][];
}
void build(int rt, int l, int r)
{
f[rt][] = -INF;
if (l==r){
f[rt][] = f[rt][] = cnVal[l];
return;
}
int mid = (l+r)>>;
build(rt<<, l, mid), build(rt<<|, mid+, r);
pushup(rt);
}
void dfs1(int x, int fa)
{
a[x].fa = fa, a[x].tot = ;
dep[x] = dep[fa]+, a[x].son = -;
for (int i=head[x]; i!=-; i=nxt[i])
{
int v = edges[i];
if (v!=fa){
dfs1(v, x);
a[x].tot += a[v].tot;
if (a[x].son==-||a[v].tot > a[a[x].son].tot)
a[x].son = v;
}
}
}
void dfs2(int x, int top)
{
chain[x] = ++chTot, cnVal[chTot] = d[x], a[x].top = top;
if (a[x].son==-) return;
dfs2(a[x].son, top);
for (int i=head[x]; i!=-; i=nxt[i])
{
int v = edges[i];
if (v!=a[x].son&&v!=a[x].fa) dfs2(v, v);
}
}
void modify(int rt, int l, int r, int pos, int c)
{
if (l==r){
f[rt][] = f[rt][] = c;
return;
}
int mid = (l+r)>>;
if (pos <= mid) modify(rt<<, l, mid, pos, c);
else modify(rt<<|, mid+, r, pos, c);
pushup(rt);
}
int queryMx(int rt, int L, int R, int l, int r)
{
if (L <= l&&r <= R) return f[rt][];
int mid = (l+r)>>, ret = -INF;
if (L <= mid) ret = queryMx(rt<<, L, R, l, mid);
if (R > mid) ret = std::max(ret, queryMx(rt<<|, L, R, mid+, r));
return ret;
}
int querySm(int rt, int L, int R, int l, int r)
{
if (L <= l&&r <= R) return f[rt][];
int mid = (l+r)>>, ret = ;
if (L <= mid) ret = querySm(rt<<, L, R, l, mid);
if (R > mid) ret += querySm(rt<<|, L, R, mid+, r);
return ret;
}
int queryChainMx(int x, int y)
{
int ret = -INF;
while (a[x].top!=a[y].top)
{
if (dep[a[x].top] > dep[a[y].top]) std::swap(x, y);
ret = std::max(ret, queryMx(, chain[a[y].top], chain[y], , n));
y = a[a[y].top].fa;
}
if (dep[x] > dep[y]) std::swap(x, y);
ret = std::max(ret, queryMx(, chain[x], chain[y], , n));
return ret;
}
int queryChainSm(int x, int y)
{
int ret = ;
while (a[x].top!=a[y].top)
{
if (dep[a[x].top] > dep[a[y].top]) std::swap(x, y);
ret += querySm(, chain[a[y].top], chain[y], , n);
y = a[a[y].top].fa;
}
if (dep[x] > dep[y]) std::swap(x, y);
ret += querySm(, chain[x], chain[y], , n);
return ret;
}
int main()
{
memset(head, -, sizeof head);
n = read();
for (int i=; i<n; i++) addedge(read(), read());
for (int i=; i<=n; i++) d[i] = read();
dfs1(, );
dfs2(, );
build(, , n);
m = read();
while (m--)
{
scanf("%s",opt);
int x = read(), y = read();
if (opt[]=='C') modify(, , n, chain[x], y);
else if (opt[]=='M')
printf("%d\n",queryChainMx(x, y));
else printf("%d\n",queryChainSm(x, y));
}
return ;
}
打挂地方已标注。
边-树链剖分「bzoj2238: Mst」
10.28
#include<bits/stdc++.h>
const int maxn = ;
const int maxm = ;
const int INF = 0x3f3f3f3f; struct Edge
{
int u,v,w,id;
bool vis;
Edge(int a=, int b=, int c=):u(a),v(b),w(c) {}
}ev[maxm],edges[maxm];
struct node
{
int tot,son,top,fa;
}a[maxn];
int n,m,q,cnt,ans;
int dep[maxn],fa[maxn],chain[maxn],chTot,f[maxn<<];
int edgeTot,head[maxn],nxt[maxm];
bool evis[maxm]; int read()
{
char ch = getchar();
int num = ;
bool fl = ;
for (; !isdigit(ch); ch=getchar())
if (ch=='-') fl = ;
for (; isdigit(ch); ch=getchar())
num = (num<<)+(num<<)+ch-;
if (fl) num = -num;
return num;
}
bool cmp1(Edge a, Edge b)
{
return a.w < b.w;
}
bool cmp2(Edge a, Edge b)
{
return a.id < b.id;
}
int get(int x){return x==fa[x]?x:fa[x]=get(fa[x]);}
void addedge(int u, int v, int c)
{
ans += c, fa[fa[u]] = fa[v];
edges[++edgeTot] = Edge(u, v, c), nxt[edgeTot] = head[u], head[u] = edgeTot;
edges[++edgeTot] = Edge(v, u, c), nxt[edgeTot] = head[v], head[v] = edgeTot;
}
void dfs1(int x, int fa)
{
a[x].tot = , a[x].son = a[x].top = -;
a[x].fa = fa, dep[x] = dep[fa]+;
for (int i=head[x]; i!=-; i=nxt[i])
{
int v = edges[i].v;
if (v!=fa){
dfs1(v, x), a[x].tot += a[v].tot;
if (a[x].son==-||a[a[x].son].tot < a[v].tot) a[x].son = v;
}
}
}
void dfs2(int x, int top)
{
a[x].top = top, chain[x] = ++chTot;
if (a[x].son==-) return;
dfs2(a[x].son, top);
for (int i=head[x]; i!=-; i=nxt[i])
{
int v = edges[i].v;
if (v!=a[x].son&&v!=a[x].fa) dfs2(v, v);
}
}
void build(int rt, int l, int r)
{
f[rt] = INF;
if (l==r) return;
int mid = (l+r)>>;
build(rt<<, l, mid), build(rt<<|, mid+, r);
}
void Min(int &x, int y){x = x>y?y:x;}
void pushdown(int rt)
{
Min(f[rt<<], f[rt]), Min(f[rt<<|], f[rt]);
}
void modify(int rt, int L, int R, int l, int r, int c)
{
if (L > R) return;
if (L <= l&&r <= R){
f[rt] = std::min(f[rt], c);
return;
}
int mid = (l+r)>>;
pushdown(rt);
if (L <= mid) modify(rt<<, L, R, l, mid, c);
if (R > mid) modify(rt<<|, L, R, mid+, r, c);
}
int query(int rt, int L, int R, int l, int r)
{
if (L > R) return INF;
if (L <= l&&r <= R) return f[rt];
int mid = (l+r)>>, ret = INF;
pushdown(rt);
if (L <= mid) Min(ret, query(rt<<, L, R, l, mid));
if (R > mid) Min(ret, query(rt<<|, L, R, mid+, r));
return ret;
}
void modifyChain(int x, int y, int c)
{
while (a[x].top!=a[y].top)
{
if (dep[a[x].top] > dep[a[y].top]) std::swap(x, y);
modify(, chain[a[y].top], chain[y], , n, c);
y = a[a[y].top].fa;
}
if (dep[x] > dep[y]) std::swap(x, y);
modify(, chain[x]+, chain[y], , n, c);
}
int queryChain(int x, int y)
{
int ret = INF;
while (a[x].top!=a[y].top)
{
if (dep[a[x].top] > dep[a[y].top]) std::swap(x, y);
Min(ret, query(, chain[a[y].top], chain[y], , n));
y = a[a[y].top].fa;
}
if (dep[x] > dep[y]) std::swap(x, y);
Min(ret, query(, chain[x]+, chain[y], , n));
return ret;
}
int main()
{
memset(head, -, sizeof head);
n = read(), m = read();
for (int i=; i<=n; i++) fa[i] = i;
for (int i=; i<=m; i++)
ev[i].u = read(), ev[i].v = read(), ev[i].w = read(), ev[i].id = i;
std::sort(ev+, ev+m+, cmp1);
for (int i=; i<=m; i++)
if (get(ev[i].u)!=get(ev[i].v)){
int u = ev[i].u, v = ev[i].v;
ev[i].vis = evis[ev[i].id] = , cnt++, addedge(u, v, ev[i].w);
if (cnt==n-) break;
}
if (cnt!=n-){
q = read();
while (q--) puts("Not connected");
return ;
}
dfs1(, );
dfs2(, );
build(, , n);
for (int i=m; i; i--)
if (!ev[i].vis) modifyChain(ev[i].u, ev[i].v, ev[i].w);
std::sort(ev+, ev+m+, cmp2);
for (q=read(); q; q--)
{
int cse = read();
if (!evis[cse]) printf("%d\n",ans);
else{
int cnt = queryChain(ev[cse].u, ev[cse].v);
if (cnt!=INF) printf("%d\n",ans-ev[cse].w+cnt);
else puts("Not connected");
}
}
return ;
}
evis开成maxn一发RE
SPFA负权环「bzoj1715: [Usaco2006 Dec]Wormholes 虫洞」
10.24.2018
#include<bits/stdc++.h>
const int maxn = ;
const int maxm = ; struct Edge
{
int y,val;
Edge(int a=, int b=):y(a),val(b) {}
}edges[maxm];
int T,n,m,w;
bool vis[maxn];
int dis[maxn],edgeTot,head[maxn],nxt[maxm]; int read()
{
char ch = getchar();
int num = ;
bool fl = ;
for (; !isdigit(ch); ch=getchar())
if (ch=='-') fl = ;
for (; isdigit(ch); ch=getchar())
num = (num<<)+(num<<)+ch-;
if (fl) num = -num;
return num;
}
void addedge(int u, int v, int c)
{
edges[++edgeTot] = Edge(v, c), nxt[edgeTot] = head[u], head[u] = edgeTot;
}
bool dfs(int x)
{
vis[x] = ;
for (int i=head[x]; i!=-; i=nxt[i])
{
int v = edges[i].y;
if (dis[v] > dis[x]+edges[i].val){
dis[v] = dis[x]+edges[i].val;
if (vis[v]||dfs(v)){
vis[x] = ;
return ;
}
}
}
vis[x] = ;
return ;
}
int main()
{
T = read();
while (T--)
{
memset(head, -, sizeof head);
memset(dis, , sizeof dis);
edgeTot = , n = read(), m = read(), w = read();
for (int i=; i<=m; i++)
{
int u = read(), v = read(), c = read();
addedge(u, v, c), addedge(v, u, c);
}
for (int i=; i<=w; i++)
{
int u = read(), v = read(), c = read();
addedge(u, v, -c);
}
bool fl = ;
for (int i=; i<=n; i++)
if (dfs(i)){
puts("YES"), fl = ;
break;
}
if (!fl) puts("NO");
}
return ;
}
差分约束「poj1201Intervals」
10.26.2018
这个和线性规划相比，要把式子全都化成三角形不等式的形式。
所以小于等于或者大于等于的两种情况自己注意。
#include<bits/stdc++.h>
const int maxn = ;
const int maxm = ; struct Edge
{
int y,val;
Edge(int a=, int b=):y(a),val(b) {}
}edges[maxm];
int n,mx;
bool stk[maxn];
std::queue<int> q;
int dis[maxn],vis[maxn];
int edgeTot,head[maxn],nxt[maxm]; int read()
{
char ch = getchar();
int num = ;
bool fl = ;
for (; !isdigit(ch); ch=getchar())
if (ch=='-') fl = ;
for (; isdigit(ch); ch=getchar())
num = (num<<)+(num<<)+ch-;
if (fl) num = -num;
return num;
}
void addedge(int u, int v, int c)
{
edges[++edgeTot] = Edge(v, c), nxt[edgeTot] = head[u], head[u] = edgeTot;
}
void spfa()
{
memset(dis, -0x3f3f3f3f, sizeof dis);
dis[] = , q.push();
while (q.size())
{
int tt = q.front();
q.pop(), stk[tt] = ;
for (int i=head[tt]; i!=-; i=nxt[i])
{
int v = edges[i].y, w = edges[i].val;
if (dis[v] < dis[tt]+w){
dis[v] = dis[tt]+w;
if (!stk[v]) stk[v] = , q.push(v);
}
}
}
}
int main()
{
memset(head, -, sizeof head);
n = read();
for (int i=; i<=n; i++)
{
int a = read()+, b = read()+, c = read();
mx = std::max(mx, b);
addedge(a-, b, c);
}
for (int i=; i<mx; i++) addedge(i, i+, ), addedge(i+, i, -);
spfa();
printf("%d\n",dis[mx]);
return ;
}
≥
#include<bits/stdc++.h>
const int maxn = ;
const int maxm = ; struct Edge
{
int y,val;
Edge(int a=, int b=):y(a),val(b) {}
}edges[maxm];
int n,mx;
bool stk[maxn];
std::queue<int> q;
int dis[maxn],vis[maxn];
int edgeTot,head[maxn],nxt[maxm]; int read()
{
char ch = getchar();
int num = ;
bool fl = ;
for (; !isdigit(ch); ch=getchar())
if (ch=='-') fl = ;
for (; isdigit(ch); ch=getchar())
num = (num<<)+(num<<)+ch-;
if (fl) num = -num;
return num;
}
void addedge(int u, int v, int c)
{
edges[++edgeTot] = Edge(v, c), nxt[edgeTot] = head[u], head[u] = edgeTot;
}
void spfa()
{
memset(dis, 0x3f3f3f3f, sizeof dis);
dis[mx] = , q.push(mx);
while (q.size())
{
int tt = q.front();
q.pop(), stk[tt] = ;
for (int i=head[tt]; i!=-; i=nxt[i])
{
int v = edges[i].y, w = edges[i].val;
if (dis[v] > dis[tt]+w){
dis[v] = dis[tt]+w;
if (!stk[v]) stk[v] = , q.push(v);
}
}
}
}
int main()
{
memset(head, -, sizeof head);
n = read();
for (int i=; i<=n; i++)
{
int a = read()+, b = read()+, c = read();
mx = std::max(mx, b);
addedge(b, a-, -c);
}
for (int i=; i<mx; i++) addedge(i, i+, ), addedge(i+, i, );
spfa();
printf("%d\n",-dis[]);
return ;
}
≤
点树上差分「bzoj4390: [Usaco2015 dec]Max Flow」
11.5.2018
#include<bits/stdc++.h>
const int maxn = ;
const int maxm = ;
const int maxLog = ; int n,m;
int f[maxn][maxLog],sum[maxn],ans;
int edgeTot,head[maxn],edges[maxm],nxt[maxm],dep[maxn]; int read()
{
char ch = getchar();
int num = ;
bool fl = ;
for (; !isdigit(ch); ch=getchar())
if (ch=='-') fl = ;
for (; isdigit(ch); ch=getchar())
num = (num<<)+(num<<)+ch-;
if (fl) num = -num;
return num;
}
void addedge(int u, int v)
{
edges[++edgeTot] = v, nxt[edgeTot] = head[u], head[u] = edgeTot;
edges[++edgeTot] = u, nxt[edgeTot] = head[v], head[v] = edgeTot;
}
void dfs(int x, int fa)
{
f[x][] = fa, dep[x] = dep[fa]+;
for (int i=head[x]; i!=-; i=nxt[i])
if (edges[i]!=fa) dfs(edges[i], x);
}
int lca(int u, int v)
{
if (dep[u] > dep[v]) std::swap(u, v);
for (int i=; i>=; i--)
if (dep[u] <= dep[v]-(<<i))
v = f[v][i];
if (u==v) return u;
for (int i=; i>=; i--)
if (f[u][i]!=f[v][i])
u = f[u][i], v = f[v][i];
return f[u][];
}
void fnd(int x)
{
for (int i=head[x]; i!=-; i=nxt[i])
if (edges[i]!=f[x][])
fnd(edges[i]), sum[x] += sum[edges[i]];
if (ans < sum[x]) ans = sum[x];
}
int main()
{
memset(head, -, sizeof head);
n = read(), m = read();
for (register int i=; i<n; i++) addedge(read(), read());
dfs(, );
for (register int j=; j<=; j++)
for (register int i=; i<=n; i++)
f[i][j] = f[f[i][j-]][j-];
for (register int i=; i<=m; i++)
{
register int u = read(), v = read(), ger = lca(u, v);
sum[u]++, sum[v]++, sum[ger]--, sum[f[ger][]]--;
}
fnd();
printf("%d\n",ans);
return ;
}
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