1. NumberSolitaire (feat.PYTHON)

A game for one player is played on a board consisting of N consecutive squares, numbered from 0 to N − 1. There is a number written on each square. A non-empty array A of N integers contains the numbers written on the squares. Moreover, some squares can be marked during the game.

At the beginning of the game, there is a pebble on square number 0 and this is the only square on the board which is marked. The goal of the game is to move the pebble to square number N − 1.

During each turn we throw a six-sided die, with numbers from 1 to 6 on its faces, and consider the number K, which shows on the upper face after the die comes to rest. Then we move the pebble standing on square number I to square number I + K, providing that square number I + K exists. If square number I + K does not exist, we throw the die again until we obtain a valid move. Finally, we mark square number I + K.

After the game finishes (when the pebble is standing on square number N − 1), we calculate the result. The result of the game is the sum of the numbers written on all marked squares.

For example, given the following array:

A[0] = 1 A[1] = -2 A[2] = 0 A[3] = 9 A[4] = -1 A[5] = -2

one possible game could be as follows:

• the pebble is on square number 0, which is marked;
• we throw 3; the pebble moves from square number 0 to square number 3; we mark square number 3;
• we throw 5; the pebble does not move, since there is no square number 8 on the board;
• we throw 2; the pebble moves to square number 5; we mark this square and the game ends.

The marked squares are 0, 3 and 5, so the result of the game is 1 + 9 + (−2) = 8. This is the maximal possible result that can be achieved on this board.

Write a function:

def solution(A)

that, given a non-empty array A of N integers, returns the maximal result that can be achieved on the board represented by array A.

For example, given the array

A[0] = 1 A[1] = -2 A[2] = 0 A[3] = 9 A[4] = -1 A[5] = -2

the function should return 8, as explained above.

Write an efficient algorithm for the following assumptions:

• N is an integer within the range [2..100,000];
• each element of array A is an integer within the range [−10,000..10,000].

- 소스

def solution(A):
    N = len(A)
    answer = [A[0]] * (N + 6)

    for i in range(1, N):
        answer[i + 6] = max(answer[i : i + 6]) + A[i]

    return answer[-1]

print(solution([1, -2, 0, 9, -1, -2]))

- 문제풀이

0 ~ N-1 까지 사각형이 주어지는 문제로

시작위치 I = 0에서 시작해서 N-1로 가면 끝나는 문제입니다.

 

주사위의 값은 K로 가정하였을 때 I+K인덱스가 존재하면 옮겨가는 방식으로 이동합니다.

이 때 지나간 요소의 합이 최대값을 구하는 문제로 주사위의 범위 1~6까지의 배열을 추가로 만들어 놓고

6의 범위 안에서 최댓값만을 취하여 이동하는 방식으로 루프를 돌며 마지막에 최댓값을 반환합니다.