树形DP。用F[k][0]和F[k][1]表示某节点不选和选了之后子树的最大值。那么:
f[i][0]=sigma(max(f[k][0],f[k][1]))
f[i][1]=sigma(f[k][0])+v[i]
解题中用了备忘录。一开始要先找树根。
#include <cstdio> #include <iostream> #include <algorithm> #include <memory.h> #include <vector> #define MAX(a, b) a>b?a:b #define LEN 6005 using namespace std; int F[LEN][2]; // dp state, F[i][0] for i not selected, F[i][1] for i selected int R[LEN]; bool isRoot[LEN]; int opt(int x, int y, vector<vector<int> > &tree) { if (F[x][y] != -1) { return F[x][y]; } if (y == 0) { int sum = 0; for (int i = 0; i < tree[x].size(); i++) { sum += MAX(opt(tree[x][i], 0, tree), opt(tree[x][i], 1, tree)); } F[x][y] = sum; return sum; } else if (y == 1) { int sum = R[x]; for (int i = 0; i < tree[x].size(); i++) { sum += opt(tree[x][i], 0, tree); } F[x][y] = sum; return sum; } else return 0; } int main() { memset(F, 0, sizeof(F)); memset(R, 0, sizeof(R)); memset(isRoot, true, sizeof(isRoot)); int n; cin >> n; vector<vector<int> > tree(n+1); for (int i = 1; i <= n; i++) { cin >> R[i]; } int x, y; for (int i = 1; i <= n-1; i++) { cin >> x >> y; tree[y].push_back(x); isRoot[x] = false; } cin >> x >> y; // skip 0, 0 for (int i = 1; i <= n; i++) { for (int j = 0; j <= 1; j++) { F[i][j] = -1; } } int root = 0; for (int i = 1; i <= n; i++) { if (isRoot[i]) { root = i; break; } } int ans = MAX(opt(root, 0, tree), opt(root, 1, tree)); cout << ans << endl; return 0; }