Codeforces Round #277 (Div. 2)D（樹形DP計數類）_html/css_WEB-ITnose
Jun 24, 2016 am 11:54 AM
D. Valid Sets
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
As you know, an undirected connected graph with?n?nodes and?n?-?1?edges is called a?tree. You are given an integer?d?and a tree consisting of?n?nodes. Each node?i?has a value?ai?associated with it.
We call a set?S?of tree nodes?valid?if following conditions are satisfied:
- S?is non-empty.
- S?is connected. In other words, if nodes?u?and?v?are in?S, then all nodes lying on the simple path between?u?and?v?should also be presented in?S.
- .
Your task is to count the number of valid sets. Since the result can be very large, you must print its remainder modulo?1000000007(109?+?7).
Input
The first line contains two space-separated integers?d?(0?≤?d?≤?2000) and?n?(1?≤?n?≤?2000).
The second line contains?n?space-separated positive integers?a1,?a2,?...,?an(1?≤?ai?≤?2000).
Then the next?n?-?1?line each contain pair of integers?u?and?v?(1?≤?u,?v?≤?n) denoting that there is an edge between?u?and?v. It is guaranteed that these edges form a tree.
Output
Print the number of valid sets modulo?1000000007.
Sample test(s)
input
1 42 1 3 21 21 33 4
output
input
0 31 2 31 22 3
output
input
4 87 8 7 5 4 6 4 101 61 25 81 33 56 73 4
output
41
Note
In the first sample, there are exactly 8 valid sets:?{1},?{2},?{3},?{4},?{1,?2},?{1,?3},?{3,?4}?and?{1,?3,?4}. Set?{1,?2,?3,?4}?is not valid, because the third condition isn't satisfied. Set?{1,?4}?satisfies the third condition, but conflicts with the second condition.
題意：RT
思路：樹形DP，dp[u]表示以u為根，且它的所有子樹的點v的權值都不超過它，且滿足 w[u]-w[v]
? ? ? ? ? ? 對于每個點為根這樣算一遍就好了，注意減去算重的情況，即相鄰多個點的權值相等，可以用點的代號去重（即規(guī)定只能從代號大的往小的DP）
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