#include <iostream>
#include <vector>
using int64 = long long;
const int64 kMinInt64 = -2'000'000'000'000'000'000;
class PopAmplifier {
public:
PopAmplifier() {
std::cin >> n_ >> m_;
A_[0] = 0LL;
ps[0] = 0;
for (int i = 0; i < n_; i++) {
std::cin >> A_[i];
ps[i + 1] = ps[i] + A_[i];
}
}
void compute_optimal_trees() {
// First, compute the trees of height 1.
for (int a = 0; a < n_; a++) {
full_tree_[1][a][a] = 0;
full_tree_[1][a][a + 1] = 0;
part_tree_[1][a][a] = 0;
part_tree_[1][a][a + 1] = 0;
}
int64 full_leaves = 1LL;
int64 part_leaves = 1LL;
int h = 2;
for (int64 m = m_; m > 0; h++) {
bool right = (m % 2LL) == 1LL;
const int64 right_leaves = part_leaves;
const int64 child_leaves = full_leaves;
if (right) {
part_leaves += full_leaves;
}
full_leaves *= 2LL;
m /= 2LL;
for (int64 a = 0; a < n_; a++) {
full_tree_[h][a][a] = part_tree_[h][a][a] = 0LL;
for (int64 b = a + 1; b <= n_ && b <= a + full_leaves; b++) {
full_tree_[h][a][b] = kMinInt64;
// [a,s) goes to the left subtree. [s,b) goes to the right.
for (int s = std::max(a, b - child_leaves);
s <= std::min(b, child_leaves + a); s++) {
// The right subtree has an additional 1-bit everyone
// needs to be multiplied by.
full_tree_[h][a][b] =
std::max(full_tree_[h][a][b],
full_tree_[h - 1][a][s] +
full_tree_[h - 1][s][b] + sum(s, b));
}
// std::cerr << " - full_tree_["<<h << ","<< a << ","<< b << "] = " << full_tree_[h][a][b] << std::endl;
}
for (int64 b = a + 1; b <= n_ && b <= a + part_leaves; b++) {
if (!right) {
part_tree_[h][a][b] = part_tree_[h - 1][a][b];
continue;
}
part_tree_[h][a][b] = kMinInt64;
// [a,s) goes to the left subtree. [s,b) goes to the right.
for (int s = std::max(a, b - right_leaves);
s <= std::min(b, child_leaves + a); s++) {
// The right subtree has an additional 1-bit everyone
// needs to be multiplied by.
part_tree_[h][a][b] =
std::max(part_tree_[h][a][b],
full_tree_[h - 1][a][s] +
part_tree_[h - 1][s][b] + sum(s, b));
}
// std::cerr << " - part_tree_["<<h << ","<< a << ","<< b << "] = " << part_tree_[h][a][b] << std::endl;
}
}
}
std::cout << part_tree_[h - 1][0][n_] << std::endl;
}
// Returns sum of A_ in interval [a,b).
inline int64 sum(int a, int b) { return ps[b] - ps[a]; }
private:
int64 n_, m_;
int64 A_[256];
// ps contains prefix sums of A_.
int64 ps[256];
// full_tree_ contains optimum beat values for intervals of a and given full
// tree height.
int64 full_tree_[64][256][256];
// part_tree_ contains optimum beat values for intervals on a tree with cut
// off part.
int64 part_tree_[64][256][256];
};
int main() {
PopAmplifier A;
A.compute_optimal_trees();
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 | #include <iostream> #include <vector> using int64 = long long; const int64 kMinInt64 = -2'000'000'000'000'000'000; class PopAmplifier { public: PopAmplifier() { std::cin >> n_ >> m_; A_[0] = 0LL; ps[0] = 0; for (int i = 0; i < n_; i++) { std::cin >> A_[i]; ps[i + 1] = ps[i] + A_[i]; } } void compute_optimal_trees() { // First, compute the trees of height 1. for (int a = 0; a < n_; a++) { full_tree_[1][a][a] = 0; full_tree_[1][a][a + 1] = 0; part_tree_[1][a][a] = 0; part_tree_[1][a][a + 1] = 0; } int64 full_leaves = 1LL; int64 part_leaves = 1LL; int h = 2; for (int64 m = m_; m > 0; h++) { bool right = (m % 2LL) == 1LL; const int64 right_leaves = part_leaves; const int64 child_leaves = full_leaves; if (right) { part_leaves += full_leaves; } full_leaves *= 2LL; m /= 2LL; for (int64 a = 0; a < n_; a++) { full_tree_[h][a][a] = part_tree_[h][a][a] = 0LL; for (int64 b = a + 1; b <= n_ && b <= a + full_leaves; b++) { full_tree_[h][a][b] = kMinInt64; // [a,s) goes to the left subtree. [s,b) goes to the right. for (int s = std::max(a, b - child_leaves); s <= std::min(b, child_leaves + a); s++) { // The right subtree has an additional 1-bit everyone // needs to be multiplied by. full_tree_[h][a][b] = std::max(full_tree_[h][a][b], full_tree_[h - 1][a][s] + full_tree_[h - 1][s][b] + sum(s, b)); } // std::cerr << " - full_tree_["<<h << ","<< a << ","<< b << "] = " << full_tree_[h][a][b] << std::endl; } for (int64 b = a + 1; b <= n_ && b <= a + part_leaves; b++) { if (!right) { part_tree_[h][a][b] = part_tree_[h - 1][a][b]; continue; } part_tree_[h][a][b] = kMinInt64; // [a,s) goes to the left subtree. [s,b) goes to the right. for (int s = std::max(a, b - right_leaves); s <= std::min(b, child_leaves + a); s++) { // The right subtree has an additional 1-bit everyone // needs to be multiplied by. part_tree_[h][a][b] = std::max(part_tree_[h][a][b], full_tree_[h - 1][a][s] + part_tree_[h - 1][s][b] + sum(s, b)); } // std::cerr << " - part_tree_["<<h << ","<< a << ","<< b << "] = " << part_tree_[h][a][b] << std::endl; } } } std::cout << part_tree_[h - 1][0][n_] << std::endl; } // Returns sum of A_ in interval [a,b). inline int64 sum(int a, int b) { return ps[b] - ps[a]; } private: int64 n_, m_; int64 A_[256]; // ps contains prefix sums of A_. int64 ps[256]; // full_tree_ contains optimum beat values for intervals of a and given full // tree height. int64 full_tree_[64][256][256]; // part_tree_ contains optimum beat values for intervals on a tree with cut // off part. int64 part_tree_[64][256][256]; }; int main() { PopAmplifier A; A.compute_optimal_trees(); } |
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