数学 SRM 690 Div1 WolfCardGame 300

Problem Statement

Wolf Sothe and Cat Snuke are playing a card game. The game is played with exactly 100 cards. The cards are numbered from 1 to 100. The game is played as follows:

1. First, Cat Snuke chooses the goal: an integer N between 1 and 100, inclusive.
2. Then, Wolf Sothe chooses exactly K of the 100 cards and gives the chosen cards to Snuke.
3. Next, Cat Snuke may throw some of those K cards away. He may choose any subset of cards he was given, possibly none or all of them.
4. Finally, Cat Snuke may write minus signs onto any subset of the cards he still holds. For example, if he currently has the cards {1,3,4,7}, he may alter them to {-1,3,4,-7}.

At the end of the game, Snuke computes the sum of the numbers on his cards (with the added minus signs). Snuke wins the game if the sum is exactly equal to the goal number N. Otherwise, Sothe wins.

Your task is to help Wolf Sothe win the game. We are now in step 2 of the game. You are given the int N chosen by Snuke and the int K that specifies the number of cards you have to give to Snuke. Choose those K cards in such a way that Snuke will be unable to win the game. If you can do that, return a vector <int> with K elements: the numbers on the chosen cards. If there are multiple solutions, you may return any of them. If there is no solution, return an empty vector <int> instead.

Definition

Class:	WolfCardGame
Method:	createAnswer
Parameters:	int, int
Returns:	vector <int>
Method signature:	vector <int> createAnswer(int N, int K)
(be sure your method is public)

Limits

Time limit (s):	2.000
Memory limit (MB):	256
Stack limit (MB):	256

Constraints

-

N will be between 1 and 100, inclusive.

-

K will be between 1 and 15, inclusive.

Examples

0)

20

4

Returns: {1, 2, 3, 4 }

If we give Snuke cards with numbers 1, 2, 3, and 4 on them, the largest sum he can form is 1+2+3+4 = 10. Thus, he cannot reach N=20 and we win.

1)

40

1

Returns: {39 }

2)

97

6

Returns: {7, 68, 9, 10, 62, 58 }

3)

2

12

Returns: {33, 69, 42, 45, 96, 15, 57, 12, 93, 9, 54, 99 }

题意：从１到１００挑出Ｋ个数字，挑出的数字可正可负，求一种总和不为Ｎ的方案．

分析：如果Ｎ为奇数，那么选前Ｋ个最小的偶数一定不会组成奇数．类似的，如果Ｎ不是３的倍数，那么选择前Ｋ个最小的３的倍数的数字；４，５，６同理，但７的时候，如果Ｋ＝１５，最后一个数字是１０５不在１００内，满足该特殊情况的数字是６０，那么前面添加一个１，结果是{1,7,14,21,28,35,42,49,56,63,70,77,84,91,98}

官方题解

class WolfCardGame {
    public:
        vector <int> createAnswer( int N, int K ) {
            vector<int> ret;
            if (N == 60 && K == 15) {
            	ret.push_back (1);
            	K = 14;
            }
            for (int i=2; i<=7; ++i) {
            	if (N % i != 0) {
            		for (int j=0, v=i; j<K; ++j, v+=i) {
            			ret.push_back (v);
            		}
                    break;
            	}
            }
            return ret;
        }
};