codeforces Vacations 动态规划 划水 (`- -)_u
http://codeforces.com/problemset/problem/698/A
题目大意：
瓦西亚同学每天将面对四种情况：
0：健身房关门，没有编程比赛
1：健身房关门，有编程比赛
2：健身房开门，没有编程比赛
3：健身房开门，有编程比赛
求这n天当中，最少能休息几天。
瓦西亚唯一的要求是：不能连续两天健身，或连续两天比赛。
思路：
瓦西亚同学每天有三种状态：躺着等死，健身，编程比赛。
设二位数组 day[第几天][干啥]，表示第i天，干j事，最多不休息的天数。
状态转移方程则可由题目推出：
① day[i][等死] = max( day[i-1][等死] , day[i-1][健身] , day[i-1][编程] ) ;
② if(今天健身房开门) day[i][健身] = max( day[i-1][等死] , day[i-1][编程] ) + 1;
③ if(今天有编程比赛) day[i][编程] = max( day[i-1][等死] , day[i-1][健身] ) + 1;
最终取 day[n][等死]，day[n][健身]，day[n][编程] 中最大的那个，就是最多不休息几天。
可求得最少休息几天。
注：代码中首先将每天不能干的事设为 -1 ，方便判断。
代码：
#include
#define N 105
using namespace std;
int d[N][3];
int main()
{
int n,a,i,ans;
cin>>n;
for(i=1;i<=n;i++)
{
cin>>a;
if(a==0) d[i][1]=d[i][2]=-1;
else if(a==1) d[i][1]=-1;
else if(a==2) d[i][2]=-1;
}
for(i=1;i<=n;i++)
{
d[i][0]=max(d[i-1][0],max(d[i-1][1],d[i-1][2]));
if(d[i][1]!=-1) d[i][1]=max(d[i-1][0],d[i-1][2])+1;
if(d[i][2]!=-1) d[i][2]=max(d[i-1][0],d[i-1][1])+1;
}
ans=max(d[n][0],max(d[n][1],d[n][2]));
cout<
题目描述：
A. Vacations
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
Vasya has n days of vacations! So he decided to improve his IT skills and do sport. Vasya knows the following information about each of this n days: whether that gym opened and whether a contest was carried out in the Internet on that day. For the i-th day there are four options:
- on this day the gym is closed and the contest is not carried out;
- on this day the gym is closed and the contest is carried out;
- on this day the gym is open and the contest is not carried out;
- on this day the gym is open and the contest is carried out.
On each of days Vasya can either have a rest or write the contest (if it is carried out on this day), or do sport (if the gym is open on this day).
Find the minimum number of days on which Vasya will have a rest (it means, he will not do sport and write the contest at the same time). The only limitation that Vasya has — he does not want to do the same activity on two consecutive days: it means, he will not do sport on two consecutive days, and write the contest on two consecutive days.
Input
The first line contains a positive integer n (1 ≤ n ≤ 100) — the number of days of Vasya's vacations.
The second line contains the sequence of integers a1, a2, ..., an (0 ≤ ai ≤ 3) separated by space, where:
- ai equals 0, if on the i-th day of vacations the gym is closed and the contest is not carried out;
- ai equals 1, if on the i-th day of vacations the gym is closed, but the contest is carried out;
- ai equals 2, if on the i-th day of vacations the gym is open and the contest is not carried out;
- ai equals 3, if on the i-th day of vacations the gym is open and the contest is carried out.
Output
Print the minimum possible number of days on which Vasya will have a rest. Remember that Vasya refuses:
- to do sport on any two consecutive days,
- to write the contest on any two consecutive days.
Examples
input
Copy
4
1 3 2 0
output
Copy
2
input
Copy
7
1 3 3 2 1 2 3
output
Copy
0
input
Copy
2
2 2
output
Copy
1
Note
In the first test Vasya can write the contest on the day number 1 and do sport on the day number 3. Thus, he will have a rest for only 2 days.
In the second test Vasya should write contests on days number 1, 3, 5 and 7, in other days do sport. Thus, he will not have a rest for a single day.
In the third test Vasya can do sport either on a day number 1 or number 2. He can not do sport in two days, because it will be contrary to the his limitation. Thus, he will have a rest for only one day.