Codeforces Round #334 (603A) Alternative Thinking [貪心]

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Kevin has just recevied his disappointing results on the USA Identification of Cows Olympiad (USAICO) in the form of a binary string of length n. Each character of Kevin's string represents Kevin's score on one of the n questions of the olympiad—'1' for a correctly identified cow and '0' otherwise.

However, all is not lost. Kevin is a big proponent of alternative thinking and believes that his score, instead of being the sum of his points, should be the length of the longest alternating subsequence of his string. Here, we define an alternating subsequence of a string as a not-necessarily contiguous subsequence where no two consecutive elements are equal. For example, {0, 1, 0, 1}{1, 0, 1}, and{1, 0, 1, 0} are alternating sequences, while {1, 0, 0} and {0, 1, 0, 1, 1} are not.

Kevin, being the sneaky little puffball that he is, is willing to hack into the USAICO databases to improve his score. In order to be subtle, he decides that he will flip exactly one substring—that is, take a contiguous non-empty substring of his score and change all '0's in that substring to '1's and vice versa. After such an operation, Kevin wants to know the length of the longest possible alternating subsequence that his string could have.


題意:

給出一個01串,先在你可以取反其中一個Substring(0變1,1變0),問這樣操作後最長的0,1間隔子序列最長是多少。

解法:

顯然,如果其中含有一個“11”或者“00”,最長序列實在原序列的基礎上+1,例如10010 可以變成 10101,將右邊的數字其以後的都取反即可。

然後,如果含有2個或更多的“11”或者“00”,其答案爲原來的最長序列長度+2,例如1001011 可以變成 1010101,只需要把其中兩個的靠近部分的那個數與中間所有數都取反即可。

至於求原來的最長串,就是相鄰兩個不同的數量,即間隔的0,1塊的快數,例如(0000)(11111)(000)(1111),最長串就是4

代碼:

略 ^  ^

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