看着百度文库学习了一个。
总的来说，左偏树这个可并堆满足 堆的性质 和 左偏 性质。
bzoj2809: [Apio2012]dispatching
把每个忍者先放到节点上，然后从下往上合并，假设到了这个点 总值 大于 预算，那么我们把这个 大根堆 的堆顶弹掉就好了，剩下的就是可合并堆。
感谢prey :)
#include <bits/stdc++.h>
#define rep(i, a, b) for (int i = a; i <= b; i++)
#define drep(i, a, b) for (int i = a; i >= b; i--)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define mp make_pair
#define pb push_back
#define clr(x) memset(x, 0, sizeof(x))
#define xx first
#define yy second
using namespace std;
typedef pair<int, int> pii;
typedef long long ll;
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f3fll;
//************************************************ const int maxn = ; struct Ed {
int u, v, nx; Ed() {}
Ed(int _u, int _v, int _nx) :
u(_u), v(_v), nx(_nx) {}
} E[maxn];
int G[maxn], edtot;
void addedge(int u, int v) {
E[++edtot] = Ed(u, v, G[u]);
G[u] = edtot;
} int pre[maxn], C[maxn], L[maxn], son[maxn];
struct node {
int key, dis, l, r, sz;
} heap[maxn];
int ndtot; int root[maxn];
ll M;
template <typename T> inline void MaxT (T &a, const T b) { if (a < b) a = b; }
ll ans = -;
int merge(int x, int y) {
if (!x) return y;
if (!y) return x;
if (heap[x].key < heap[y].key) swap(x, y);
heap[x].r = merge(heap[x].r, y);
heap[x].sz = heap[heap[x].l].sz + heap[heap[x].r].sz + ;
if (heap[heap[x].l].dis < heap[heap[x].r].dis) swap(heap[x].l, heap[x].r);
heap[x].dis = heap[heap[x].r].dis + ;
return x;
}
ll solve(int x) {
ll sum = C[x];
heap[root[x] = ++ndtot] = (node) {C[x], , , , };
for (int i = G[x], y; i; i = E[i].nx) {
sum += solve(y = E[i].v);
root[x] = merge(root[x], root[y]);
}
while (sum > M) sum -= heap[root[x]].key, root[x] = merge(heap[root[x]].l, heap[root[x]].r);
MaxT(ans, 1ll * heap[root[x]].sz * L[x]);
return sum;
} int main() {
int n; scanf("%d%lld", &n, &M);
int rt;
rep(i, , n) {
scanf("%d%d%d", pre + i, C + i, L + i);
son[pre[i]]++;
if (pre[i] == ) rt = i;
addedge(pre[i], i);
}
solve(rt);
printf("%lld\n", ans);
return ;
}
bzoj4003: [JLOI2015]城池攻占
堆上打个lazytag即可，可以表示成 tag_a * x + tag_b 的形式，标记的合并也很简单，tag_a2 * (tag_a1 * x + tag_b1) + tag_b2，乘开就好。
#include <bits/stdc++.h>
#define rep(i, a, b) for (int i = a; i <= b; i++)
#define drep(i, a, b) for (int i = a; i >= b; i--)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define mp make_pair
#define pb push_back
#define clr(x) memset(x, 0, sizeof(x))
#define xx first
#define yy second
using namespace std;
typedef pair<int, int> pii;
typedef long long ll;
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f3fll;
//************************************************ const int maxn = ; struct Ed {
int u, v, nx; Ed() {}
Ed(int _u, int _v, int _nx) :
u(_u), v(_v), nx(_nx) {}
} E[maxn];
int G[maxn], edtot;
void addedge(int u, int v) {
E[++edtot] = Ed(u, v, G[u]);
G[u] = edtot;
} struct node {
int dis, l, r, sz;
ll key, tag_a, tag_b;
int id;
} heap[maxn];
int ndtot; ll hp[maxn], A[maxn], V[maxn];
int pre[maxn], root[maxn];
ll S[maxn], C[maxn]; void Push_down(int x) {
if (heap[x].tag_a == && heap[x].tag_b == ) return;
int l = heap[x].l, r = heap[x].r;
heap[l].tag_a *= heap[x].tag_a, heap[l].tag_b = heap[l].tag_b * heap[x].tag_a + heap[x].tag_b;
heap[r].tag_a *= heap[x].tag_a, heap[r].tag_b = heap[r].tag_b * heap[x].tag_a + heap[x].tag_b;
heap[l].key = heap[l].key * heap[x].tag_a + heap[x].tag_b;
heap[r].key = heap[r].key * heap[x].tag_a + heap[x].tag_b;
heap[x].tag_a = , heap[x].tag_b = ;
return;
} int merge(int x, int y) {
if (!x) return y;
if (!y) return x;
Push_down(x), Push_down(y);
if (heap[x].key > heap[y].key) swap(x, y);
heap[x].r = merge(heap[x].r, y);
heap[x].sz = heap[heap[x].l].sz + heap[heap[x].r].sz + ;
if (heap[heap[x].l].dis < heap[heap[x].r].dis) swap(heap[x].l, heap[x].r);
heap[x].dis = heap[heap[x].r].dis + ;
return x;
} int Stop[maxn], Peo[maxn];
int dep[maxn];
void solve(int x) {
for (int i = G[x], y; i; i = E[i].nx) {
dep[y = E[i].v] = dep[x] + ;
solve(y);
root[x] = merge(root[x], root[y]);
}
Push_down(root[x]);
while (root[x] && heap[root[x]].key < hp[x]) {
Push_down(root[x]);
Stop[heap[root[x]].id] = x;
Peo[x]++;
root[x] = merge(heap[root[x]].l, heap[root[x]].r);
}
if (root[x]) {
Push_down(root[x]);
if (A[x] == ) heap[root[x]].tag_b = V[x], heap[root[x]].key += V[x];
else heap[root[x]].tag_a = V[x], heap[root[x]].key *= V[x];
}
} int main() {
int n, m; scanf("%d%d", &n, &m);
rep(i, , n) scanf("%lld", hp + i);
rep(i, , n) {
scanf("%d%lld%lld", pre + i, A + i, V + i);
addedge(pre[i], i);
}
rep(i, , m) {
scanf("%lld%lld", S + i, C + i);
heap[++ndtot] = (node) {, , , , S[i], , , i};
root[C[i]] = merge(root[C[i]], ndtot);
}
solve();
rep(i, , n) printf("%d\n", Peo[i]);
rep(i, , m) printf("%d\n", Stop[i] ? dep[C[i]] - dep[Stop[i]] : dep[C[i]] + );
}