U587038 背包 题解

题解

传送门

70pts

树上 01 背包。

Code

#include <bits/stdc++.h>
#define int long long
using namespace std;
inline int read()
{
	int x = 0,p = 1;
	char c = getchar();
	while(c > '9' || c < '0')	p = c == '-' ? -1 : 1,c = getchar();
	while(c >= '0' && c <= '9')	x = (x << 1) + (x << 3) + (c ^ 48),c = getchar();
	return p * x;
}
template<typename _Tp> inline void _write(_Tp x) { if(x > 9) _write(x / 10); putchar(x % 10 | 48); }
template<typename _Tp> inline void write(_Tp x) { if(x < 0) putchar('-'),x = -x; _write(x); }
template<typename _Tp> inline void writeln(_Tp x) { write(x); puts(""); }
const int N = 1e5 + 10;
int n,Q,v[N],w[N],f[5010][5010];
struct query
{
	int u,L;
} q[N];
signed main()
{
	n = read();
	for(int i = 1;i <= n;i++)	v[i] = read(),w[i] = read();
	Q = read();
	int maxL = 0;
	for(int i = 1;i <= Q;i++)
		q[i].u = read(),q[i].L = read(),maxL = max(maxL,q[i].L);
	f[1][w[1]] = v[1];
	for(int i = 2;i <= n;i++)
	{
		int k = i >> 1;
		for(int j = 1;j < w[i];j++)
			f[i][j] = f[k][j];
		for(int j = w[i];j <= maxL;j++)
			f[i][j] = max(f[k][j],f[k][j - w[i]] + v[i]);
	}
	for(int i = 1;i <= Q;i++)
	{
		int ans = 0;
		for(int j = 1;j <= q[i].L;j++)
			ans = max(ans,f[q[i].u][j]);
		writeln(ans);
	}
	return 0;
}

100 pts

可以发现前 n \sqrt{n} n 个数被访问的次数比较多，所以考虑预计算这些数的 01 背包的 dp 值。

剩下的点用 dfs 暴力枚举即可，但是统计答案时要特别注意。

AC Code

#include <bits/stdc++.h>
#define int long long
using namespace std;
inline int read()
{
	int x = 0,p = 1;
	char c = getchar();
	while(c > '9' || c < '0')	p = c == '-' ? -1 : 1,c = getchar();
	while(c >= '0' && c <= '9')	x = (x << 1) + (x << 3) + (c ^ 48),c = getchar();
	return p * x;
}
template<typename _Tp> inline void _write(_Tp x) { if(x > 9) _write(x / 10); putchar(x % 10 | 48); }
template<typename _Tp> inline void write(_Tp x) { if(x < 0) putchar('-'),x = -x; _write(x); }
template<typename _Tp> inline void writeln(_Tp x) { write(x); puts(""); }
const int N = 1e5 + 10;
int n,Q,v[N],w[N],f[320][N];
int _sqrt;
int ans = 0;
struct query
{
	int u,L;
} q[N];
void dfs(int u,int L,int value = 0,int weight = 0)
{
	if(L - weight < 0)	return;
	if(u <= _sqrt)
	{
		ans = max(ans,value + f[u][L - weight]);
		return;
	}
	dfs(u >> 1,L,value + v[u],weight + w[u]);
	dfs(u >> 1,L,value,weight);
}
signed main()
{
	n = read();
	for(int i = 1;i <= n;i++)	v[i] = read(),w[i] = read();
	Q = read();
	int maxL = 0;
	for(int i = 1;i <= Q;i++)
		q[i].u = read(),q[i].L = read(),maxL = max(maxL,q[i].L);
	for(int i = w[1];i <= maxL;i++)	f[1][i] = v[1];
	_sqrt = sqrt(n); 
	for(int i = 2;i <= _sqrt;i++)
	{
		int k = i >> 1;
		for(int j = 1;j < w[i];j++)
			f[i][j] = f[k][j];
		for(int j = w[i];j <= maxL;j++)
			f[i][j] = max(f[k][j],f[k][j - w[i]] + v[i]);
	}
	for(int i = 1;i <= Q;i++)
	{
		ans = 0;
		if(q[i].u <= _sqrt)
			ans = max(ans,f[q[i].u][q[i].L]);
		else
			dfs(q[i].u,q[i].L);
		writeln(ans);
	}
	return 0;
}