// O((n + q) sqrt(q))
#include "candies.h"
#include <algorithm>
#include <cmath>
#include <vector>
struct Buckets {
int n;
int bucket_size, bucket_cnt;
std::vector<int> vals;
std::vector<long long> mini, maxi, sums;
Buckets(int _n): n(_n) {
bucket_size = sqrt(n);
bucket_cnt = (n + bucket_size - 1) / bucket_size;
vals.assign(n, 0);
mini.assign(bucket_cnt, 0);
maxi.assign(bucket_cnt, 0);
sums.assign(bucket_cnt, 0);
}
void update(int x, int val) {
vals[x] = val;
int bucket = x / bucket_size;
mini[bucket] = maxi[bucket] = sums[bucket] = 0;
for (int i = std::min(n, (bucket + 1) * bucket_size) - 1;
i >= bucket * bucket_size; --i) {
sums[bucket] += vals[i];
maxi[bucket] = std::max(maxi[bucket], sums[bucket]);
mini[bucket] = std::min(mini[bucket], sums[bucket]);
}
}
std::tuple<int, int, int> query(int c) {
int sufsum = 0, sufmin = 0, sufmax = 0;
for (int bucket = bucket_cnt - 1; bucket >= 0; --bucket) {
long long nsufsum = sufsum + sums[bucket],
nsufmin = std::min(1LL * sufmin, sufsum + mini[bucket]),
nsufmax = std::max(1LL * sufmax, sufsum + maxi[bucket]);
if (nsufmax - nsufmin > c) {
for (int i = std::min(n, (bucket + 1) * bucket_size) - 1;
i >= bucket * bucket_size; --i) {
sufsum += vals[i];
sufmin = std::min(sufmin, sufsum);
sufmax = std::max(sufmax, sufsum);
if (sufmax - sufmin > c) return std::make_tuple(sufmin, sufmax, i);
}
}
sufsum = nsufsum; sufmax = nsufmax; sufmin = nsufmin;
}
return std::make_tuple(sufmin, sufmax, 0);
}
inline int at(int x) { return vals[x]; }
};
std::vector<int> distribute_candies(std::vector<int> c, std::vector<int> l,
std::vector<int> r, std::vector<int> v) {
int n = c.size(), q = v.size();
std::vector<std::vector<std::pair<int, int>>> queriesL(n), queriesR(n);
for (int i = 0; i < q; ++i) {
queriesL[l[i]].emplace_back(i, v[i]);
queriesR[r[i]].emplace_back(i, v[i]);
}
std::vector<int> s(n);
Buckets tree(q);
for (int i = 0; i < n; ++i) {
for (auto [idx, val] : queriesL[i]) {
tree.update(idx, -val);
}
auto [mini, maxi, idx] = tree.query(c[i]);
if (maxi - mini <= c[i]) {
s[i] = -mini;
} else {
if (tree.at(idx) < 0) {
s[i] = c[i] - maxi;
} else {
s[i] = -mini;
}
}
for (auto [idx, val] : queriesR[i]) {
tree.update(idx, 0);
}
}
return s;
}
