Codeforces 833B
来源:互联网 发布:淘宝电热水器 编辑:程序博客网 时间:2024/05/16 13:46
B. The Bakery
time limit per test 2.5seconds
memory limit per test 256megabytes
Some time ago Slastyona the Sweetmaid decided to open her ownbakery! She bought required ingredients and a wonder-oven which can bakeseveral types of cakes, and opened the bakery.
Soon the expenses started to overcome the income, so Slastyonadecided to study the sweets market. She learned it's profitable to pack cakesin boxes, and that the moredistinct cake types a box contains (let's denote this number as the value of the box), the higherprice it has.
She needs to change the production technology! The problem isthat the oven chooses the cake types on its own and Slastyona can't affect it.However, she knows the types and order ofn 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 oneright after another (in other words, shehas to put in a box a continuous segment of cakes).
Slastyona wants to maximize the total value of all boxes withcakes. Help her determine this maximum possible total value.
Input
The first line contains two integersn and k (1 ≤ n ≤ 35000,1 ≤ k ≤ min(n, 50)) –the number of cakes and the number of boxes, respectively.
The second line containsn 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
4 1
1 2 2 1
Output
2
Input
7 2
1 3 3 1 4 4 4
Output
5
Input
8 3
7 7 8 7 7 8 1 7
Output
6
Note
In the first example Slastyona has only one box. She has to putall cakes in it, so that there are two types of cakes in the box, so the valueis equal to2.
In the second example it is profitable to put the first two cakes in the firstbox, and all the rest in the second. There are two distinct types in the firstbox, and three in the second box then, so the total value is5.
【题意】
把n个数分成k段,每段的价值为这一段数里不同数字的个数,问价值和最大为多少。
【思路】
显然需要用到动态规划。我们用dp[i][j]表示前j个数分成i段价值和的最大值。容易得到状态转移方程为
dp[i][j]=max{dp[i-1][x]+剩下数的贡献} {1<=x< j}
过程用线段树维护一下区间最大值即可。
#include <cstdio>#include <vector>#include <cstring>#include <algorithm>using namespace std;#define mst(a,b) memset((a),(b),sizeof(a))#define rush() int T;scanf("%d",&T);while(T--)#define lson l,m,rt<<1#define rson m+1,r,rt<<1|1typedef long long ll;const int maxn = 35005;const ll mod = 1e9+7;const int INF = 0x3f3f3f;const double eps = 1e-9;int n,k;int dp[55][maxn]; //表示到第j个数分成了i段的最大价值int tree[maxn<<2],lazy[maxn<<2];int a[maxn],pre[maxn],pos[maxn];void init(){ mst(tree,0),mst(pos,0); mst(pre,0),mst(dp,0);}void pushup(int rt){ tree[rt]=max(tree[rt<<1|1],tree[rt<<1]);}void pushdown(int rt){ tree[rt<<1]+=lazy[rt]; tree[rt<<1|1]+=lazy[rt]; lazy[rt<<1]+=lazy[rt]; lazy[rt<<1|1]+=lazy[rt]; lazy[rt]=0;}void build(int pos,int l,int r,int rt){ lazy[rt]=0; if(l==r) { tree[rt]=dp[pos][l-1]; return; } int m=(l+r)>>1; build(pos,lson); build(pos,rson); pushup(rt);}void update(int L,int R,int l,int r,int rt){ if(L<=l&&r<=R) { tree[rt]++; lazy[rt]++; return; } pushdown(rt); int m=(l+r)>>1; if(L<=m) update(L,R,lson); if(R>m) update(L,R,rson); pushup(rt);}int query(int L,int R,int l,int r,int rt){ if(L<=l&&r<=R) { return tree[rt]; } pushdown(rt); int m=(l+r)>>1; int ans=0; if(L<=m) ans=max(ans,query(L,R,lson)); if(R>m) ans=max(ans,query(L,R,rson)); pushup(rt); return ans;}int main(){ while(~scanf("%d%d",&n,&k)) { init(); for(int i=1; i<=n; i++) { scanf("%d",&a[i]); pre[i]=pos[a[i]]+1; //相同数字前一次出现的数字+1 pos[a[i]]=i; } for(int i=1;i<=k;i++) { build(i-1,1,n,1); //在线段树中更新前一层dp的值 for(int j=1;j<=n;j++) { update(pre[j],j,1,n,1); dp[i][j]=query(1,j,1,n,1); } } printf("%d\n",dp[k][n]); } return 0;}
- Codeforces 833B
- Codeforces 833B
- CodeForces 833 B.The Bakery
- codeforces B
- codeforces B
- codeforces B
- codeforces B
- CodeForces 626B CodeForces 626B【暴力】
- CodeForces 841B (B) 博弈
- codeforces 134B
- codeforces#98 b
- codeforces 105 div2 B
- Codeforces 166B - Polygons
- codeforces B. Coins
- codeforces----193B Xor
- codeforces----208B Solitaire
- Codeforces 1B - Spreadsheet
- codeforces 214B Hometask
- 多线程和MsgWaitForMultipleObjects
- 深度学习之Windows下安装caffe及配置Python和matlab接口
- vue环境搭建
- Maven实战(一)--Why Maven
- 【css3】变形
- Codeforces 833B
- 时间转换c++题解
- String类型数字始终保留两位小数
- C语言入门第五篇,输入
- String转成Date类型,操作年月加减
- 算法学习记录三(C++)--->从尾到头打印链表每个节点的值
- 【设计模式】适配器模式
- C#的Winform多语言实现(resx文件)
- 士兵杀敌(五)NSOJ