Codeforces 815C. Karen and Supermarket【树形DP】

时间:2023-03-09 15:25:48
Codeforces 815C. Karen and Supermarket【树形DP】

LINK


思路

首先发现依赖关系是一个树形的结构

然后因为直接算花多少钱来统计贡献不是很好

因为数组开不下

那就可以算一个子树里面选多少个的最小代价就可以了

注意统计贡献的时候用优惠券的答案只能在1号点进行统计


//Author: dream_maker
#include<bits/stdc++.h>
using namespace std;
//----------------------------------------------
//typename
typedef long long ll;
//convenient for
#define fu(a, b, c) for (int a = b; a <= c; ++a)
#define fd(a, b, c) for (int a = b; a >= c; --a)
#define fv(a, b) for (int a = 0; a < (signed)b.size(); ++a)
//inf of different typename
const int INF_of_int = 1e9;
const ll INF_of_ll = 1e18;
//fast read and write
template <typename T>
void Read(T &x) {
bool w = 1;x = 0;
char c = getchar();
while (!isdigit(c) && c != '-') c = getchar();
if (c == '-') w = 0, c = getchar();
while (isdigit(c)) {
x = (x<<1) + (x<<3) + c -'0';
c = getchar();
}
if (!w) x = -x;
}
template <typename T>
void Write(T x) {
if (x < 0) {
putchar('-');
x = -x;
}
if (x > 9) Write(x / 10);
putchar(x % 10 + '0');
}
//----------------------------------------------
const int N = 5010;
struct Edge{
int v, nxt;
}E[N << 1];
int head[N], tot = 0;
ll c[N], d[N], siz[N], n;
ll dp[N][N][2], ans = 0, B;
void add(int u, int v) {
E[++tot] = (Edge){v, head[u]};
head[u] = tot;
}
void dfs(int u, int fa) {
siz[u] = 1;
dp[u][1][1] = c[u] - d[u];
dp[u][1][0] = c[u];
for (int i = head[u]; i; i = E[i].nxt) {
int v = E[i].v;
if (v == fa) continue;
dfs(v, u);
fd(j, siz[u], 0)
fd(k, siz[v], 0) {
dp[u][j + k][1] = min(dp[u][j + k][1], dp[u][j][1] + min(dp[v][k][0], dp[v][k][1]));
dp[u][j + k][0] = min(dp[u][j + k][0], dp[u][j][0] + dp[v][k][0]);
}
siz[u] += siz[v];
}
fu(i, ans + 1, siz[u]) {
if (dp[u][i][0] <= B) ans = i;
else break;
}
}
int main() {
memset(dp, 0x3f, sizeof(dp));
Read(n); Read(B);
fu(i, 1, n) {
Read(c[i]); Read(d[i]);
dp[i][0][0] = 0;
if (i > 1) {
int u; Read(u);
add(i, u);
add(u, i);
}
}
dfs(1, 0);
fu(i, ans + 1, n) if (dp[1][i][1] <= B) ans = i;
Write(ans);
return 0;
}