[CTSC1997]选课

题面

题解

树形背包板子题。

设\(f[i][j]\)表示在以\(x\)为根的子树选\(j\)门课（包括\(x\)）能够获得的最高学分，用分组背包转移即可。

代码

#include<cstdio>
#include<vector>
#define RG register

inline int read()
{
	int data = 0, w = 1;
	char ch = getchar();
	while(ch != '-' && (ch < '0' || ch > '9')) ch = getchar();
	if(ch == '-') w = -1, ch = getchar();
	while(ch >= '0' && ch <= '9') data = data * 10 + (ch ^ 48), ch = getchar();
	return data*w;
}

const int maxn(310);
std::vector<int> g[maxn];
typedef std::vector<int>::iterator iter;
int s[maxn], f[maxn][maxn], n, m;

void dfs(int x)
{
	f[x][0] = 0;
	for(RG iter it = g[x].begin(); it != g[x].end(); ++it)
	{
		int to = *it; dfs(to);
		for(RG int v = m + 1; v; --v)
			for(RG int j = 0; j < v; ++j)
				f[x][v] = std::max(f[x][v], f[x][v - j] + f[to][j]);
	}
}

int main()
{
	n = read(); m = read();
	for(RG int i = 1; i <= n; i++)
		g[read()].push_back(i), f[i][1] = s[i] = read();
	dfs(0); printf("%d\n", f[0][m + 1]);
	return 0;
}