POJ 2385 Apple Catching

Posted 2020-10-04

It is a little known fact that cows love apples. Farmer John has two apple trees (which are conveniently numbered 1 and 2) in his field, each full of apples. Bessie cannot reach the apples when they are on the tree, so she must wait for them to fall. However, she must catch them in the air since the apples bruise when they hit the ground (and no one wants to eat bruised apples). Bessie is a quick eater, so an apple she does catch is eaten in just a few seconds. 

Each minute, one of the two apple trees drops an apple. Bessie, having much practice, can catch an apple if she is standing under a tree from which one falls. While Bessie can walk between the two trees quickly (in much less than a minute), she can stand under only one tree at any time. Moreover, cows do not get a lot of exercise, so she is not willing to walk back and forth between the trees endlessly (and thus misses some apples). 

Apples fall (one each minute) for T (1 <= T <= 1,000) minutes. Bessie is willing to walk back and forth at most W (1 <= W <= 30) times. Given which tree will drop an apple each minute, determine the maximum number of apples which Bessie can catch. Bessie starts at tree 1.

Input

* Line 1: Two space separated integers: T and W 

* Lines 2..T+1: 1 or 2: the tree that will drop an apple each minute.

Output

* Line 1: The maximum number of apples Bessie can catch without walking more than W times.

Sample Input

7 2
2
1
1
2
2
1
1

Sample Output

6

Hint

INPUT DETAILS: 

Seven apples fall - one from tree 2, then two in a row from tree 1, then two in a row from tree 2, then two in a row from tree 1. Bessie is willing to walk from one tree to the other twice. 

OUTPUT DETAILS: 

Bessie can catch six apples by staying under tree 1 until the first two have dropped, then moving to tree 2 for the next two, then returning back to tree 1 for the final two.

 

设计状态dp[i][j]代表到I时间转换了j次的最大收益，那么状态显然可以由之前的状态转还是不转转移过来，注意加上一段区间的值可以用前缀和来优化。

 

 1 #include<cstdio>
 2 #include<cstdlib>
 3 #include<cstring>
 4 #include<iostream>
 5 #include<cmath>
 6 #include<algorithm>
 7 #include<vector>
 8 #include<stack>
 9 #include<queue>
10 #include<map>
11 #define RG register
12 #define IL inline
13 #define pi acos(-1.0)
14 #define ll long long 
15 using namespace std;
16 int tree1[1005],tree2[1005];
17 int dp[1005][35];
18 int T,W;
19 int main() {
20   scanf("%d%d",&T,&W);
21   for(int i=1;i<=T;i++){
22     int type;
23     scanf("%d",&type);
24     if(type==1) tree1[i]=1;
25     else tree2[i]=1;
26     tree1[i]+=tree1[i-1];
27     tree2[i]+=tree2[i-1];
28   }
29   for(int i=1;i<=T;i++)
30     for(int j=0;j<i;j++){
31       for(int w=0;w<=W;w++){
32         if(w%2==0){
33        dp[i][w]=max(dp[i][w],dp[j][w]+tree1[i]-tree1[j]);
34        if(w+1<=W) dp[i][w+1]=max(dp[i][w+1],dp[j][w]+tree2[i]-tree2[j]);
35     } else{
36        dp[i][w]=max(dp[i][w],dp[j][w]+tree2[i]-tree2[j]);
37        if(w+1<=W) dp[i][w+1]=max(dp[i][w+1],dp[j][w]+tree1[i]-tree1[j]);
38     }
39       }
40     }
41   int maxn=0;
42   for(int i=0;i<=W;i++) maxn=max(maxn,dp[T][i]);
43   cout<<maxn;
44   return 0;
45 }