Codeforces Round #426 (Div. 1) B The Bakery （线段树+dp）

B. The Bakery

time limit per test

2.5 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Some time ago Slastyona the Sweetmaid decided to open her own bakery! She bought required ingredients and a wonder-oven which can bake several types of cakes, and opened the bakery.

Soon the expenses started to overcome the income, so Slastyona decided to study the sweets market. She learned it's profitable to pack cakes in boxes, and that the more distinct cake types a box contains (let's denote this number as the value of the box), the higher price it has.

She needs to change the production technology! The problem is that the oven chooses the cake types on its own and Slastyona can't affect it. However, she knows the types and order of n cakes the oven is going to bake today. Slastyona has to pack exactly k boxes with cakes today, and she has to put in each box several (at least one) cakes the oven produced one right after another (in other words, she has to put in a box a continuous segment of cakes).

Slastyona wants to maximize the total value of all boxes with cakes. Help her determine this maximum possible total value.

Input

The first line contains two integers n and k (1 ≤ n ≤ 35000, 1 ≤ k ≤ min(n, 50)) – the number of cakes and the number of boxes, respectively.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ n) – the types of cakes in the order the oven bakes them.

Output

Print the only integer – the maximum total value of all boxes with cakes.

Examples

input

Copy

4 1
1 2 2 1

output

Copy

2

input

Copy

7 2
1 3 3 1 4 4 4

output

Copy

5

input

Copy

8 3
7 7 8 7 7 8 1 7

output

Copy

6

Note

In the first example Slastyona has only one box. She has to put all cakes in it, so that there are two types of cakes in the box, so the value is equal to 2.

In the second example it is profitable to put the first two cakes in the first box, and all the rest in the second. There are two distinct types in the first box, and three in the second box then, so the total value is 5.

思路：

dp[i][j]代表： 前j个数，分成i块的最大价值。

那么有状态转移方程： dp[i][j] = max(dp[i-1][k]+sum[k+1][j],dp[i][j])

记录下每个点上次出现的位置，存到last[]数组。

更新dp[i-1][1-n]，将上一个状态的值存进线段树维护，因为每次状态变化的范围都是  last[j]-j，区间更新下就好了

实现代码：

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define mid int m = (l + r) >> 1
const int M = 2e5+10;
//jmqayxtl
int mx[M<<2],lazy[M<<2],dp[60][M],a[M],last[M],vis[M];

void pushup(int rt){
    mx[rt] = max(mx[rt<<1],mx[rt<<1|1]);
}

void pushdown(int rt){
    if(lazy[rt]){
        lazy[rt<<1] += lazy[rt];
        lazy[rt<<1|1] += lazy[rt];
        mx[rt<<1] += lazy[rt];
        mx[rt<<1|1] += lazy[rt];
        lazy[rt] = 0;
    }
}

void build(int p,int l,int r,int rt){
    lazy[rt] = 0; mx[rt] = 0;
    if(l == r){
        mx[rt] = dp[p][l-1];
        return ;
    }
    mid;
    build(p,lson);
    build(p,rson);
    pushup(rt);
}

void update(int L,int R,int c,int l,int r,int rt){
    if(L <= l&&R >= r){
        mx[rt] += c;
        
        lazy[rt] += c;
        return ;
    }
    pushdown(rt);
    mid;
    if(L <= m) update(L,R,c,lson);
    if(R > m) update(L,R,c,rson);
    pushup(rt);
}

int query(int L,int R,int l,int r,int rt){
    if(L <= l&&R >= r){
        return mx[rt];
    }
    pushdown(rt);
    mid;
    int ret = 0;
    if(L <= m) ret = max(query(L,R,lson),ret);
    if(R > m) ret = max(query(L,R,rson),ret);
    return ret;
}

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    int n,k;
    cin>>n>>k;
    for(int i = 1;i <= n;i ++){
        cin>>a[i];
        last[i] = vis[a[i]];
        vis[a[i]] = i;
    }
    for(int i = 1;i <= k;i ++){
        build(i-1,1,n,1);
        for(int j = 1;j <= n;j ++){
            update(last[j]+1,j,1,1,n,1);
            dp[i][j] = query(1,j,1,n,1);
            cout<<i<<" "<<j<<" "<<dp[i][j]<<endl;
        }
    }
    cout<<dp[k][n]<<endl;
}