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| #include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
using namespace std;
struct Charm
{
int weight;
int desirability;
};
struct Node
{
int index;
int weight;
int desirability;
int evaluation;
int index2;
int weight2;
int evaluation2;
bool operator<(const Node a)const
{
return evaluation < a.evaluation;
}
};
vector<Charm>* v = NULL;
int Down(int n, int m)
{
int down = 0;
for (int i = n - 1; i >= 0; i--)
{
if (m >= (*v)[i].weight)
{
m -= (*v)[i].weight;
down += (*v)[i].desirability;
}
else
{
}
if (m == 0)
{
break;
}
}
return down;
}
int Up(int n, int m)
{
int up = 0;
for (int i = n - 1; i >= 0; i--)
{
if (m >= (*v)[i].weight)
{
m -= (*v)[i].weight;
up += (*v)[i].desirability;
}
else
{
up += m * (*v)[i].desirability / (*v)[i].weight;
break;
}
}
return up;
}
void Evaluation(Node& node)
{
int evaluation = node.evaluation2;
int weight = node.weight2;
int index = node.index2;
for (int i = index; i >= 0; i--)
{
if (weight >= (*v)[i].weight)
{
weight -= (*v)[i].weight;
evaluation += (*v)[i].desirability;
}
else
{
node.index2 = i;
node.weight2 = weight;
node.evaluation2 = evaluation;
evaluation += weight * (*v)[i].desirability / (*v)[i].weight;
break;
}
if (i == 0)
{
node.index2 = i - 1;
node.weight2 = weight;
node.evaluation2 = evaluation;
break;
}
}
node.evaluation = evaluation;
}
int BranchAndBound(int n, int m)
{
int down = Down(n, m);
int up = Up(n, m);
if (down == up)
{
return down;
}
priority_queue<Node> q;
Node root;
root.index = n - 1;
root.weight = m;
root.desirability = 0;
root.evaluation = 0;
root.index2 = n - 1;
root.weight2 = m;
root.evaluation2 = 0;
Evaluation(root);
q.push(root);
Node c1;
Node c2;
while (!q.empty())
{
Node top = q.top();
q.pop();
if (top.evaluation <= down)
{
break;
}
if (top.index < 0)
{
down = down > top.desirability ? down : top.desirability;
continue;
}
if (top.weight == 0)
{
down = down > top.desirability ? down : top.desirability;
continue;
}
if (top.desirability == top.evaluation)
{
down = down > top.desirability ? down : top.desirability;
continue;
}
if (top.weight >= (*v)[top.index].weight)
{
c1.index = top.index - 1;
c1.weight = top.weight - (*v)[top.index].weight;
c1.desirability = top.desirability + (*v)[top.index].desirability;
c1.evaluation = top.evaluation;
c1.index2 = top.index2;
c1.weight2 = top.weight2;
c1.evaluation2 = top.evaluation2;
q.push(c1);
c2.index = top.index - 1;
c2.weight = top.weight;
c2.desirability = top.desirability;
c2.evaluation = top.evaluation;
c2.index2 = top.index2 <= c2.index ? top.index2 : c2.index;
if (top.index2 < top.index)
{
c2.index2 = top.index2;
c2.weight2 = top.weight2 + (*v)[top.index].weight;
c2.evaluation2 = top.evaluation2 - (*v)[top.index].desirability;
}
else
{
c2.index2 = top.index - 1;
c2.weight2 = top.weight2;
c2.evaluation2 = top.evaluation2;
}
Evaluation(c2);
if (c2.evaluation > down)
{
q.push(c2);
}
}
else
{
top.index = top.index - 1;
q.push(top);
}
}
return down;
}
bool cmp(Charm c1, Charm c2)
{
if (c1.desirability * c2.weight == c2.desirability * c1.weight)
{
return c1.weight < c2.weight;
}
else
{
return 1.0f * c1.desirability / c1.weight < 1.0f * c2.desirability / c2.weight;
}
}
int CharmBracelet(vector<Charm>* v, int n, int m)
{
sort(v->begin(), v->end(), cmp);
int ans = BranchAndBound(n, m);
return ans;
}
int main()
{
int n, m;
cin >> n >> m;
v = new vector<Charm>(n);
for (int i = 0; i < n; i++)
{
cin >> (*v)[i].weight;
cin >> (*v)[i].desirability;
}
int result = CharmBracelet(v, n, m);
delete v;
v = NULL;
cout << result << endl;
return 0;
}
|