// COCI 2017-2018 - Dostavljac
// Lúcio Cardoso
// Solution:
// 1. Let dp[0][u][k] be the greatest amount we can achieve by starting our path at vertex u and
// finishing it inside the subtree of u, using a cost k. Similarly, let dp[1][u][k] be the same as
// the greatest amount in a path starting at u and ending at u with a cost of k.
// 2. At first, dp[0][u][k] = dp[1][u][k] = A[k], for all k > 0. Then, we can use "knapsack on trees".
// For each child v of u, we have:
// * dp[0][u][k] = max(dp[0][u][k], max(dp[0][v][j], dp[1][v][j]) + dp[1][u][i-j-1]), for 0 <= j < k (we end our path inside the subtree of v)
// * dp[0][u][k] = max(dp[0][u][k], dp[1][v][j] + dp[0][u][i-j-2]), for 0 <= j < k-1 (we end our path inside the subtree of another child)
// * dp[1][u][k] = max(dp[1][u][k], dp[1][v][j] + dp[1][u][i-j-2]), for 0 <= j < k-1 (we can go through v's subtree)
// 3. Final answer is max(dp[0][1][m], dp[1][1][m]). Overall complexity if O(n*m^2).
#include <bits/stdc++.h>
using namespace std;
const int maxn = 510;
int n, m;
int A[maxn];
// 0 - ending inside subtree
// 1 - coming back to vertex
int dp[2][maxn][maxn];
vector<int> grafo[maxn];
void dfs(int u, int p)
{
for (int i = 1; i <= m; i++)
dp[0][u][i] = dp[1][u][i] = A[u];
for (auto v: grafo[u])
{
if (v == p) continue;
dfs(v, u);
for (int i = m; i >= 1; i--)
{
for (int j = 0; j <= i; j++)
{
if (i >= j+1)
dp[0][u][i] = max(dp[0][u][i], max(dp[0][v][j], dp[1][v][j]) + dp[1][u][i-j-1]);
if (i >= j+2)
{
dp[0][u][i] = max(dp[0][u][i], dp[1][v][j] + dp[0][u][i-j-2]);
dp[1][u][i] = max(dp[1][u][i], dp[1][v][j] + dp[1][u][i-j-2]);
}
}
}
}
}
int main(void)
{
scanf("%d %d", &n, &m);
for (int i = 1; i <= n; i++)
scanf("%d", &A[i]);
for (int i = 1; i < n; i++)
{
int u, v;
scanf("%d %d", &u, &v);
grafo[u].push_back(v); grafo[v].push_back(u);
}
dfs(1, 0);
printf("%d\n", max(dp[0][1][m], dp[1][1][m]));
}
Compilation message
dostavljac.cpp: In function 'int main()':
dostavljac.cpp:63:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
63 | scanf("%d %d", &n, &m);
| ~~~~~^~~~~~~~~~~~~~~~~
dostavljac.cpp:66:8: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
66 | scanf("%d", &A[i]);
| ~~~~~^~~~~~~~~~~~~
dostavljac.cpp:71:8: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
71 | scanf("%d %d", &u, &v);
| ~~~~~^~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
396 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
340 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
468 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
580 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
6 ms |
676 KB |
Output is correct |
| 2 |
Correct |
2 ms |
724 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
2 ms |
836 KB |
Output is correct |
| 2 |
Correct |
30 ms |
920 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
54 ms |
1084 KB |
Output is correct |
| 2 |
Correct |
16 ms |
1132 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
18 ms |
1448 KB |
Output is correct |
| 2 |
Correct |
120 ms |
1524 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
101 ms |
1912 KB |
Output is correct |
| 2 |
Correct |
41 ms |
1908 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
201 ms |
2500 KB |
Output is correct |
| 2 |
Correct |
19 ms |
2252 KB |
Output is correct |
