题目大意:给定一个序列, 给出m种操作,在每种操作中, l, r, d表示将区间[l, r]的所有值加d.之后的k个操作中,x, y表示该次将第x种操作到第y种操作都执行一次, 问经所有操作之后序列中每个元素的值。
这道题显然就是区间更新, 单点查询, 用线段树可以完成。
问题是有的操作需反复执行,如果直接一个一个更新,肯定超时。
事实上,k个操作相当于将之前m个操作中指定区间的操作的d值更新,可以将操作也用线段树维护,看每个操作的d值一共加了几次(一共需要执行多少次),然后即可求出最终的序列。
参考代码:
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;
const int N = 1e5+10;
ll a[N], b[N];
ll kk[N];
struct node {
int left, right;
ll max;
ll lazy;
} e[N * 4];
struct op {
int left, right;
ll val;
} op[N];
void push_up(int p) {
e[p].max = max(e[p*2].max, e[p*2+1].max);
}
void push_down(int p) {
if (e[p].lazy != 0) {
e[p*2].lazy += e[p].lazy;
e[p*2].max += e[p].lazy;
e[p*2+1].lazy += e[p].lazy;
e[p*2+1].max += e[p].lazy;
e[p].lazy = 0;
}
}
void build(int p, int l, int r, ll a[]) {
e[p].left = l;
e[p].right = r;
e[p].lazy = 0;
if (l == r) {
e[p].max = a[l];
}
else {
int mid = (l + r) / 2;
build(p*2, l, mid, a);
build(p*2+1, mid+1, r, a);
push_up(p);
}
}
void update(int p, int l, int r, ll val) {
if (l <= e[p].left && e[p].right <= r) {
e[p].lazy += val;
e[p].max += val;
}
else {
push_down(p);
int mid = (e[p].left + e[p].right) / 2;
if (l <= mid) update(p*2, l, r, val);
if (r > mid) update(p*2+1, l, r, val);
push_up(p);
}
}
ll query_max(int p, int l, int r) {
if (l <= e[p].left && e[p].right <= r) {
return e[p].max;
}
int mid = (e[p].left + e[p].right) / 2;
push_down(p);
ll ans = 0;
if (l <= mid) ans = max(ans, query_max(p*2, l, r));
if (r > mid) ans = max(ans, query_max(p*2+1, l, r));
return ans;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(NULL);
int n, m, k;
cin >> n >> m >> k;
for (int i = 1;i <= n;++i) cin >> a[i];
int l, r, d;
for (int i = 1;i <= m;++i) {
cin >> op[i].left >> op[i].right >> op[i].val;
}
for (int i = 1;i <= m;++i) {
kk[i] = 0;
}
int x, y;
build(1, 1, m, kk);
for (int i = 1;i <= k;++i) {
cin >> x >> y;
update(1, x, y, 1);
}
for (int i = 1;i <= m;++i) {
kk[i] = query_max(1, i, i);
op[i].val = op[i].val * kk[i];
}
build(1, 1, n, a);
for (int i = 1;i <= m;++i) {
update(1, op[i].left, op[i].right, op[i].val);
}
for (int i = 1;i <= n;++i) {
b[i] = query_max(1, i, i);
}
for (int i = 1;i <= n;++i) {
if (i > 1) cout << " ";
cout << b[i];
}
cout << endl;
return 0;
}