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divide-an-array-into-subarrays-with-minimum-cost-ii.cpp
209 lines (196 loc) · 6.63 KB
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divide-an-array-into-subarrays-with-minimum-cost-ii.cpp
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// Time: O(nlogd)
// Space: O(d)
// fastest and less verbose
// sliding window, heap
class Solution {
public:
long long minimumCost(vector<int>& nums, int k, int dist) {
static const int64_t INF = numeric_limits<int64_t>::max();
const auto& get_top = [](auto& heap, auto& total, const int d) {
while (-heap.top().second < d) {
heap.pop();
--total;
}
return heap.top();
};
priority_queue<pair<int, int>> max_heap;
priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> min_heap;
int total1 = 0, total2 = 0;
int64_t mn = INF, curr = 0;
for (int i = 1; i < size(nums); ++i) {
max_heap.emplace(nums[i], -i);
curr += nums[i];
if (i > k - 1) {
const auto [x, idx] = get_top(max_heap, total1, i - (1 + dist)); max_heap.pop();
curr -= x;
min_heap.emplace(x, idx);
}
if (i > 1 + dist) {
if (get_top(min_heap, total2, i - (1 + dist)) <= pair(nums[i - (1 + dist)], -(i - (1 + dist)))) {
lazy_delete(min_heap, total2, i - (1 + dist));
} else {
lazy_delete(max_heap, total1, i - (1 + dist));
curr -= nums[i - (1 + dist)] - min_heap.top().first;
max_heap.emplace(min_heap.top()); min_heap.pop();
}
}
if (i >= k - 1) {
mn = min(mn, curr);
}
}
return nums[0] + mn;
}
private:
template<typename T>
void lazy_delete(T& heap, int& total, const int d) {
++total;
if (total <= size(heap) - total) {
return;
}
T new_heap;
while (!empty(heap)) {
const auto x = heap.top(); heap.pop();
if (-x.second <= d) {
--total;
continue;
}
new_heap.emplace(x);
}
heap = move(new_heap);
}
};
// Time: O(nlogd)
// Space: O(d)
// faster but more verbose
// sliding window, heap, freq table
class Solution2 {
public:
long long minimumCost(vector<int>& nums, int k, int dist) {
static const int64_t INF = numeric_limits<int64_t>::max();
const auto& get_top = [](auto& heap, auto& cnt, auto& total) {
while (cnt.count(heap.top())) {
const int x = heap.top(); heap.pop();
if (--cnt[x] == 0) {
cnt.erase(x);
}
--total;
}
return heap.top();
};
priority_queue<int> max_heap;
priority_queue<int, vector<int>, greater<int>> min_heap;
unordered_map<int, int> cnt1, cnt2;
int total1 = 0, total2 = 0;
int64_t mn = INF, curr = 0;
for (int i = 1; i < size(nums); ++i) {
max_heap.emplace(nums[i]);
curr += nums[i];
if (size(max_heap) - total1 > k - 1) {
const int x = get_top(max_heap, cnt1, total1); max_heap.pop();
curr -= x;
min_heap.emplace(x);
}
if ((size(max_heap) - total1) + (size(min_heap) - total2) > 1 + dist) {
if (get_top(min_heap, cnt2, total2) <= nums[i - (1 + dist)]) {
lazy_delete(min_heap, cnt2, total2, nums[i - (1 + dist)]);
} else {
lazy_delete(max_heap, cnt1, total1, nums[i - (1 + dist)]);
curr -= nums[i - (1 + dist)] - min_heap.top();
max_heap.emplace(min_heap.top()); min_heap.pop();
}
}
if (size(max_heap) - total1 == k - 1) {
mn = min(mn, curr);
}
}
return nums[0] + mn;
}
private:
template<typename T>
void lazy_delete(T& heap, auto& cnt, int& total, int x) {
++cnt[x];
++total;
if (total <= size(heap) - total) {
return;
}
T new_heap;
while (!empty(heap)) {
const auto x = heap.top(); heap.pop();
if (cnt.count(x)) {
if (--cnt[x] == 0) {
cnt.erase(x);
}
continue;
}
new_heap.emplace(x);
}
total = 0;
heap = move(new_heap);
}
};
// Time: O(nlogd)
// Space: O(d)
// fast but verbose
// sliding window, bst
class Solution3 {
public:
long long minimumCost(vector<int>& nums, int k, int dist) {
static const int64_t INF = numeric_limits<int64_t>::max();
multiset<int> bst1, bst2;
int64_t mn = INF, curr = 0;
for (int i = 1; i < size(nums); ++i) {
bst1.emplace(nums[i]);
curr += nums[i];
if (size(bst1) > k - 1) {
curr -= *rbegin(bst1);
bst2.emplace(*rbegin(bst1));
bst1.erase(prev(end(bst1)));
}
if (size(bst1) + size(bst2) > 1 + dist) {
if (*cbegin(bst2) <= nums[i - (1 + dist)]) {
bst2.erase(bst2.find(nums[i - (1 + dist)]));
} else {
bst1.erase(bst1.find(nums[i - (1 + dist)]));
curr -= nums[i - (1 + dist)] - *cbegin(bst2);
bst1.emplace(*cbegin(bst2));
bst2.erase(begin(bst2));
}
}
if (size(bst1) == k - 1) {
mn = min(mn, curr);
}
}
return nums[0] + mn;
}
};
// Time: O(nlogd)
// Space: O(d)
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
// concise but slow
// sliding window, ordered set
class Solution4 {
public:
long long minimumCost(vector<int>& nums, int k, int dist) {
using ordered_set = tree<pair<int, int>, null_type, less<pair<int, int>>, rb_tree_tag, tree_order_statistics_node_update>;
ordered_set os;
for (int i = 1; i < 1 + (1 + dist); ++i) {
os.insert({nums[i], i});
}
int64_t curr = 0;
auto it = cbegin(os);
for (int i = 0; i < k - 1; ++i, ++it) {
curr += it->first;
}
int64_t mn = curr;
for (int i = 1 + (1 + dist); i < size(nums); ++i) {
os.insert({nums[i], i});
curr += min(nums[i] - os.find_by_order(k - 1)->first, 0);
curr -= min(nums[i - (1 + dist)] - os.find_by_order(k - 1)->first, 0);
os.erase({nums[i - (1 + dist)], i - (1 + dist)});
mn = min(mn, curr);
}
return nums[0] + mn;
}
};