IOI '14 P6 - Holiday

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Points: 40
Time limit: 1.8s
Memory limit: 256M

Problem type
Allowed languages
C, C++

Jian-Jia is planning his next holiday in Taiwan. During his holiday, Jian-Jia moves from city to city and visits attractions in the cities.

There are n cities in Taiwan, all located along a single highway. The cities are numbered consecutively from 0 to n-1. For city i, where 0 < i < n-1, the adjacent cities are i-1 and i+1. The only city adjacent to city 0 is city 1, and the only city adjacent to city n-1 is city n-2.

Each city contains some number of attractions. Jian-Jia has d days of holiday and plans to visit as many attractions as possible. Jian-Jia has already selected a city in which to start his holiday. In each day of his holiday Jian-Jia can either move to an adjacent city, or else visit all the attractions of the city he is staying, but not both. Jian-Jia will never visit the attractions in the same city twice even if he stays in the city multiple times. Please help Jian-Jia plan his holiday so that he visits as many different attractions as possible.


Suppose Jian-Jia has 7 days of holiday, there are 5 cities (listed in the table below), and he starts from city 2. On the first day Jian-Jia visits the 20 attractions in city 2. On the second day Jian-Jia moves from city 2 to city 3, and on the third day visits the 30 attractions in city 3. Jian-Jia then spends the next three days moving from city 3 to city 0, and visits the 10 attractions in city 0 on the seventh day. The total number of attractions Jian-Jia visits is 20 + 30 + 10 = 60, which is the maximum number of attractions Jian-Jia can visit in 7 days when he starts from city 2.

citynumber of attractions
1visit the attractions in city 2
2move from city 2 to city 3
3visit the attractions in city 3
4move from city 3 to city 2
5move from city 2 to city 1
6move from city 1 to city 0
7visit the attractions in city 0


Please implement a function findMaxAttraction that computes the maximum number of attractions Jian-Jia can visit.

  • findMaxAttraction(n, start, d, attraction)
    • n: the number of cities.
    • start: the index of the starting city.
    • d: the number of days.
    • attraction: array of length n; attraction[i] is the number of attractions in city i, for 0 \le i \le n-1.
    • The function should return the maximum number of attractions Jian-Jia can visit.


In all subtasks 0 \le d \le 2n+\lfloor n/2\rfloor, and the number of attractions in each city is non-negative.

Additional constraints:
subtaskpointsnmaximum number of attractions in a citystarting city
172 \le n \le 201\,000\,000\,000no constraints
2232 \le n \le 100\,000100city 0
3172 \le n \le 3\,0001\,000\,000\,000no constraints
4532 \le n \le 100\,0001\,000\,000\,000no constraints

Implementation details

Your submission should implement the subprogram described above using the following signatures.

Note that the result may be large, and the return type of findMaxAttraction is a 64-bit integer.

C/C++ program
long long int findMaxAttraction(int n, int start, int d, int attraction[]);
Pascal program
function findMaxAttraction(n, start, d : longint; attraction : array of longint): int64;


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