USACO 2018 February Contest, Bronze Problem 3. Taming the Herd

USACO 2018年2月赛铜级题3

Taming the Herd

Early in the morning, Farmer John woke up to the sound of splintering wood. It was the cows, and they were breaking out of the barn again!

Farmer John was sick and tired of the cows' morning breakouts, and he decided enough was enough: it was time to get tough. He nailed to the barn wall a counter tracking the number of days since the last breakout. So if a breakout occurred in the morning, the counter would be 00 that day; if the most recent breakout was 33 days ago, the counter would read 33. Farmer John meticulously logged the counter every day.

The end of the year has come, and Farmer John is ready to do some accounting. The cows will pay, he says! But lo and behold, some entries of his log are missing!

Farmer John is confident that the he started his log on the day of a breakout. Please help him determine, out of all sequences of events consistent with the log entries that remain, the minimum and maximum number of breakouts that may have take place over the course of the logged time.


The first line contains a single integer NN (1N1001≤N≤100), denoting the number of days since Farmer John started logging the cow breakout counter.The second line contains NN space-separated integers. The iith integer is either 1−1, indicating that the log entry for day ii is missing, or a non-negative integer aiai (at most 100100), indicating that on day ii the counter was at aiai.

OUTPUT FORMAT (file taming.out):

If there is no sequence of events consistent with Farmer John's partial log and his knowledge that the cows definitely broke out of the barn on the morning of day 11, output a single integer 1−1. Otherwise, output two space-separated integers mm followed by MM, where mm is the minimum number of breakouts of any consistent sequence of events, and MM is the maximum.


-1 -1 -1 1


2 3

In this example, we can deduce that a breakout had to occur on day 3. Knowing that a breakout also occurred on day 1, the only remaining bit of uncertainty is whether a breakout occurred on day 2. Hence, there were between 2 and 3 breakouts in total.

Problem credits: Dhruv Rohatgi