考场上写了lct,可惜当时对标记永久化的理解并不是十分深刻,导致调一个错误的程序调了4h+,最后这道题爆0了QwQ
现在写了树链剖分,用标记永久化的线段树维护轻重链,对于$s\rightarrow lca$,$lca\rightarrow t$分开讨论,把$a×dist+b$这个式子打开,提出常数项,发现是一个一次函数(也不是严格的一次函数,只不过有单调性就可以做了)。标记永久化线段树做一下,每个节点维护一个当前区间的最小值就可以统计答案了233
这次又手残把“+”打成“*”调了一上午TwT,肉眼对拍大法好!
#include<cstdio> #include<cstring> #include<algorithm> using namespace std; typedef long long LL; const int N = 100005; const LL inf = 123456789123456789LL; void read(int &k) { k = 0; int fh = 1; char c = getchar(); for(; c < ‘0‘ || c > ‘9‘; c = getchar()) if (c == ‘-‘) fh = -1; for(; c >= ‘0‘ && c <= ‘9‘; c = getchar()) k = (k << 1) + (k << 3) + c - ‘0‘; k = k * fh; } struct node { int nxt, to, w; } E[N << 1]; int n, m, cnt = 0, point[N], fa[N], top[N], son[N], sz[N], pos[N], wt[N], K[N << 2]; LL B[N << 2], val[N << 2], di[N], ans; bool p[N << 2]; void ins(int x, int y, int z) {E[++cnt].nxt = point[x]; E[cnt].to = y; E[cnt].w = z; point[x] = cnt;} void _(int x) { sz[x] = 1; for(int tmp = point[x]; tmp; tmp = E[tmp].nxt) if (E[tmp].to != fa[x]) { fa[E[tmp].to] = x; di[E[tmp].to] = di[x] + E[tmp].w; _(E[tmp].to); sz[x] += sz[E[tmp].to]; if (sz[E[tmp].to] > sz[son[x]]) son[x] = E[tmp].to; } } void __(int x) { pos[x] = ++cnt; wt[cnt] = x; if (son[x]) {top[son[x]] = top[x]; __(son[x]);} for(int tmp = point[x]; tmp; tmp = E[tmp].nxt) if (E[tmp].to != fa[x] && E[tmp].to != son[x]) {top[E[tmp].to] = E[tmp].to; __(E[tmp].to);} } int LCA(int x, int y) { for(; top[x] != top[y]; x = fa[top[x]]) if (di[top[x]] < di[top[y]]) swap(x, y); return di[x] < di[y] ? x : y; } void pushup(int rt, int l, int r) { if (l < r) val[rt] = min(val[rt << 1], val[rt << 1 | 1]); else val[rt] = inf; if (p[rt]) val[rt] = min(val[rt], min(di[wt[l]] * K[rt], di[wt[r]] * K[rt]) + B[rt]); } void Build(int rt, int l, int r) { val[rt] = inf; if (l == r) return; int mid = (l + r) >> 1; Build(rt << 1, l, mid); Build(rt << 1 | 1, mid + 1, r); } void update(int rt, int l, int r, int a, LL b) { if (!p[rt]) { p[rt] = 1; K[rt] = a; B[rt] = b; } else { LL newl = a * di[wt[l]] + b, newr = a * di[wt[r]] + b, befl = K[rt] * di[wt[l]] + B[rt], befr = K[rt] * di[wt[r]] + B[rt]; int mid = (l + r) >> 1; if (newl <= befl && newr <= befr) { K[rt] = a; B[rt] = b; } else if (newl >= befl && newr >= befr) return; else if (a < K[rt]) { double tmp = (b - B[rt]) / (K[rt] - a); if (tmp <= di[wt[mid]]) { update(rt << 1, l, mid, K[rt], B[rt]); K[rt] = a; B[rt] = b; } else update(rt << 1 | 1, mid + 1, r, a, b); } else { double tmp = (B[rt] - b) / (a - K[rt]); if (tmp > di[wt[mid]]) { update(rt << 1 | 1, mid + 1, r, K[rt], B[rt]); K[rt] = a; B[rt] = b; } else update(rt << 1, l, mid, a, b); } } pushup(rt, l, r); } void inc(int rt, int l, int r, int L, int R, int a, LL b) { if (L <= l && r <= R) {update(rt, l, r, a, b); return;} int mid = (l + r) >> 1; if (L <= mid) inc(rt << 1, l, mid, L, R, a, b); if (R > mid) inc(rt << 1 | 1, mid + 1, r, L, R, a, b); pushup(rt, l, r); } void Q(int rt, int l, int r, int L, int R) { if (L == l && r == R) {ans = min(ans, val[rt]); return;} if (p[rt]) ans = min(ans, min(K[rt] * di[wt[L]], K[rt] * di[wt[R]]) + B[rt]); int mid = (l + r) >> 1; if (R <= mid) Q(rt << 1, l, mid, L, R); else if (L > mid) Q(rt << 1 | 1, mid + 1, r, L, R); else {Q(rt << 1, l, mid, L, mid); Q(rt << 1 | 1, mid + 1, r, mid + 1, R);} } int main() { read(n); read(m); int u, v, e, a, b, lca; for(int i = 1; i < n; ++i) { read(u); read(v); read(e); ins(u, v, e); ins(v, u, e); } _(1); cnt = 0; top[1] = 1; __(1); Build(1, 1, n); LL tmp; for(; m; --m) { read(e); if (e == 1) { read(u); read(v); read(a); read(b); lca = LCA(u, v); tmp = 1LL * a * di[u] + b; for(; top[u] != top[lca]; u = fa[top[u]]) inc(1, 1, n, pos[top[u]], pos[u], - a, tmp); inc(1, 1, n, pos[lca], pos[u], - a, tmp); tmp -= (di[lca] << 1) * a; for(; top[v] != top[lca]; v = fa[top[v]]) inc(1, 1, n, pos[top[v]], pos[v], a, tmp); inc(1, 1, n, pos[lca], pos[v], a, tmp); } else { ans = inf; read(u); read(v); for(; top[u] != top[v]; u = fa[top[u]]) { if (di[top[u]] < di[top[v]]) swap(u, v); Q(1, 1, n, pos[top[u]], pos[u]); } if (di[u] > di[v]) swap(u, v); Q(1, 1, n, pos[u], pos[v]); printf("%lld\n", ans); } } return 0; }
Round2加油!
时间: 2024-11-05 22:48:02