CF1252J Tiling Terrace

CF1252J Tiling Terrace

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Title Description

Talia has just bought an abandoned house in the outskirt of Jakarta. The house has a nice and long yard which can be represented as a one-dimensional grid containing 1 \times N1×N cells. To beautify the house, Talia is going to build a terrace on the yard by tiling the cells. Each cell on the yard contains either soil (represented by the character '.') or rock (represented by the character '#'), and there are at most 5050 cells containing rocks.

Being a superstitious person, Talia wants to tile the terrace with mystical tiles that have the power to repel ghosts. There are three types of mystical tiles:

• Type-1: Covers 1 \times 11×1 cell and can only be placed on a soil cell (".").
• Type-2: Covers 1 \times 21×2 cells and can only be placed on two consecutive soil cells ("..").
• Type-3: Covers 1 \times 31×3 cells and can only be placed on consecutive soil-rock-soil cells (".#.").

Each tile of Type-1, Type-2, and Type-3 has the power to repel G_1G1 , G_2G2 , and G_3G3 ghosts per day, respectively. There are also some mystical rules which must be followed for the power to be effective:

• There should be no overlapping tiles, i.e. each cell is covered by at most one tile.
• There should be at most KK tiles of Type-1, while there are no limitations for tiles of Type-2 and Type-3.

Talia is scared of ghosts, thus, the terrace (which is tiled by mystical tiles) should be able to repel as many ghosts as possible. Help Talia to find the maximum number of ghosts that can be repelled per day by the terrace. Note that Talia does not need to tile all the cells on the yard as long as the number of ghosts that can be repelled by the terrace is maximum.

Input Format

Input begins with a line containing five integers: NN KK G_1G1 G_2G2 G_3G3 ( 1 \le N \le 100,0001≤N≤100000 ; 0 \le K \le N0≤K≤N ; 0 \le G_1, G_2, G_3 \le 10000≤G1,G2,G3≤1000 ) representing the number of cells, the maximum number of tiles of Type-1, the number of ghosts repelled per day by a tile of Type-1, the number of ghosts repelled per day by a tile of Type-2, and the number of ghosts repelled by a tile of Type-3, respectively. The next line contains a string of NN characters representing the yard. Each character in the string is either '.' which represents a soil cell or '#' which represents a rock cell. There are at most 5050 rock cells.

Output Format

Output in a line an integer representing the maximum number of ghosts that can be repelled per day.

Sample input and output

Input # 1 copy

Output # 1 copy

Input # 2 Copy

Output # 2 Copy

Input # 3 Copy

Output # 3 Copy

Description / Tips

Explanation for the sample input/output #1

Let "A" be a tile of Type-1, "BB" be a tile of Type-2, and "CCC" be a tile of Type-3. The tiling "ACCCBB" in this case produces the maximum number of ghosts that can be repelled, i.e. 10 + 40 + 25 = 7510+40+25=75

Explanation for the sample input/output #2

This sample input has the same yard with the previous sample input, but each tile of Type-2 can repel more ghosts per day. The tiling "BB#BBA" or "BB#ABB" produces the maximum number of ghosts that can be repelled, i.e. 100 + 100 + 10 = 210100+100+10=210 . Observe that the third cell is left untiled.

Explanation for the sample input/output #3

The tiling "ACCCA.#", "ACCC.A#", or ".CCCAA#" produces the maximum number of ghosts that can be repelled, i.e. 30 + 100 + 30 = 16030+100+30=160 . Observe that there is no way to tile the last cell.

answer:

It is very easy to judge a \ (DP \) title.

Think about the question head: CF358D Dima and Hares

So we divided the way decisions can be seen: the first and second options are included only, only the third option of "#", then we can consider staging decisions. "": The whole sequence into order "#" spaced apart sections, and with \ (a [i] \) array holds \ (I \) paragraph "." number.

We then set the state \ (dp [i] [j ] [0/1] \) represents the former \ (J \) section with the \ (I \) views embodiment \ (1 \) , behind \ (0/1 \) indicates that the last "#" is there a way to \ (3 \) maximum value obtained.

So we only need to consider the transfer of frequency use two.

Transfer equation need to be classified discussions. Additionally, there is a situation that is not finished selecting \ (n \) characters. This thing can be when enumerating 1 divided by two with automatic rounding to achieve.

It is understood in conjunction with the code:

#include<cstdio>
#include<cstring>
#include<algorithm>
#define int long long
using namespace std;
const int maxn=1e5+10;
int n,k,g1,g2,g3,tot,ans;
char s[maxn];
int a[maxn],dp[60][maxn][5];
//dp[i][j][0/1]表示前j段使用i次方式1，最后一个"#"是否选用方式3所得的最大利益。
signed main()
{
    scanf("%I64d%I64d%I64d%I64d%I64d",&n,&k,&g1,&g2,&g3);
    scanf("%s",s+1);
    tot=1;
    for(int i=1;i<=n;i++)
    {
        if(s[i]=='#')
            tot++;
        else
            a[tot]++;
    }
    while(tot && !a[tot])
        tot--;
    if(!tot)
    {
        puts("0");
        return 0;
    }
    memset(dp,0xcf,sizeof(dp));
    dp[0][0][0]=0;
    for(int i=1;i<=tot;i++)
        for(int j=0;j<=k;j++)
        {
            int t=min(a[i],j);
            for(int l=0;l<=t;l++)
            {
                if(l<=a[i])
                    dp[i][j][0]=max(dp[i][j][0],dp[i-1][j-l][0]+(a[i]-l)/2*g2+l*g1);
                if(l<=a[i]-1)
                {
                    dp[i][j][0]=max(dp[i][j][0],dp[i-1][j-l][1]+(a[i]-l-1)/2*g2+g3+l*g1);
                    dp[i][j][1]=max(dp[i][j][1],dp[i-1][j-l][0]+(a[i]-l-1)/2*g2+l*g1);
                }
                if(l<=a[i]-2)
                    dp[i][j][1]=max(dp[i][j][1],dp[i-1][j-l][1]+(a[i]-l-2)/2*g2+g3+l*g1);
            }
        }
    for(int i=0;i<=k;i++)
        ans=max(ans,dp[tot][i][0]);
    printf("%I64d",ans);
    return 0;
}