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maximum-total-beauty-of-the-gardens.cpp
151 lines (147 loc) · 6.2 KB
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maximum-total-beauty-of-the-gardens.cpp
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// Time: O(nlogn)
// Space: O(1)
// sort, prefix sum, greedy, two pointers, improved from solution3
class Solution {
public:
long long maximumBeauty(vector<int>& flowers, long long newFlowers, int target, int full, int partial) {
const auto it = partition(begin(flowers), end(flowers), [&target](int x) { return x < target; });
sort(begin(flowers), it);
const long long n = distance(begin(flowers), it);
long long prefix = 0, suffix = accumulate(begin(flowers), it, 0ll);
long long result = 0;
for (long long right = 0, left = 0; right <= n; ++right) {
if (right) {
suffix -= flowers[right - 1];
}
const auto total = newFlowers - (static_cast<long long>(n - right) * target - suffix);
if (total < 0) {
continue;
}
while (!(left == right || (left && (total + prefix) / left <= flowers[left]))) {
prefix += flowers[left++];
}
const auto mn = min(left ? (total + prefix) / left : 0ll, static_cast<long long>(target) - 1);
result = max(result, mn * partial + (static_cast<long long>(size(flowers)) - right) * full);
}
return result;
}
};
// Time: O(nlogn)
// Space: O(1)
// sort, prefix sum, greedy, two pointers, improved from solution4
class Solution2 {
public:
long long maximumBeauty(vector<int>& flowers, long long newFlowers, int target, int full, int partial) {
const auto it = partition(begin(flowers), end(flowers), [&target](int x) { return x < target; });
sort(begin(flowers), it);
const long long n = distance(begin(flowers), it);
vector<long long> prefix(n + 1);
for (int i = 0; i < n; ++i) {
prefix[i + 1] = prefix[i] + flowers[i];
}
long long result = 0, suffix = 0;
for (long long right = n, left = n; right >= 0; --right) {
if (right != n) {
suffix += flowers[right];
}
const auto total = newFlowers - (static_cast<long long>(n - right) * target - suffix);
if (total < 0) {
break;
}
left = min(left, right);
while (!(left == 0 || (prefix[left] - prefix[left - 1]) * left - prefix[left] <= total)) {
--left;
}
const auto mn = min(left ? (total + prefix[left]) / left : 0ll, static_cast<long long>(target) - 1);
result = max(result, mn * partial + (static_cast<long long>(size(flowers)) - right) * full);
}
return result;
}
};
// Time: O(nlogn)
// Space: O(n)
// sort, prefix sum, greedy, binary search
class Solution3 {
public:
long long maximumBeauty(vector<int>& flowers, long long newFlowers, int target, int full, int partial) {
const auto& check = [](const auto& prefix, const auto& total, auto x) {
return x && (total + prefix[x]) / x <= prefix[x + 1] - prefix[x];
};
const auto& binary_search = [&check](const auto& prefix, const auto& total, auto left, auto right) {
while (left <= right) {
const auto mid = left + (right - left) / 2;
if (check(prefix, total, mid)) {
right = mid - 1;
} else {
left = mid + 1;
}
}
return left;
};
const auto it = partition(begin(flowers), end(flowers), [&target](int x) { return x < target; });
sort(begin(flowers), it);
const long long n = distance(begin(flowers), it);
vector<long long> prefix(n + 1);
for (int i = 0; i < n; ++i) {
prefix[i + 1] = prefix[i] + flowers[i];
}
long long suffix = accumulate(begin(flowers), it, 0ll);
long long result = 0;
for (long long right = 0; right <= n; ++right) {
if (right) {
suffix -= flowers[right - 1];
}
const auto total = newFlowers - (static_cast<long long>(n - right) * target - suffix);
if (total < 0) {
continue;
}
const auto left = binary_search(prefix, total, 0, right - 1);
const auto mn = min(left ? (total + prefix[left]) / left : 0ll, static_cast<long long>(target) - 1);
result = max(result, mn * partial + (static_cast<long long>(size(flowers)) - right) * full);
}
return result;
}
};
// Time: O(nlogn)
// Space: O(n)
// sort, prefix sum, greedy, binary search
class Solution4 {
public:
long long maximumBeauty(vector<int>& flowers, long long newFlowers, int target, int full, int partial) {
const auto& check = [](const auto& prefix, const auto& total, auto x) {
return (prefix[x] - prefix[x - 1]) * x - prefix[x] <= total;
};
const auto& binary_search_right = [&check](const auto& prefix, const auto& total, auto left, auto right) {
while (left <= right) {
const auto mid = left + (right - left) / 2;
if (!check(prefix, total, mid)) {
right = mid - 1;
} else {
left = mid + 1;
}
}
return right;
};
const auto it = partition(begin(flowers), end(flowers), [&target](int x) { return x < target; });
sort(begin(flowers), it);
const long long n = distance(begin(flowers), it);
vector<long long> prefix(n + 1);
for (int i = 0; i < n; ++i) {
prefix[i + 1] = prefix[i] + flowers[i];
}
long long result = 0, suffix = 0;
for (long long right = n; right >= 0; --right) {
if (right != n) {
suffix += flowers[right];
}
const auto total = newFlowers - (static_cast<long long>(n - right) * target - suffix);
if (total < 0) {
break;
}
const auto left = binary_search_right(prefix, total, 1, right);
const auto mn = min(left ? (total + prefix[left]) / left : 0ll, static_cast<long long>(target) - 1);
result = max(result, mn * partial + (static_cast<long long>(size(flowers)) - right) * full);
}
return result;
}
};