Background
"KO-RE-A, KO-RE-A" shout 54.000 happy football fans after their
team has reached the semifinals of the FIFA World Cup in their home
country. But although their excitement is real, the Korean people are
still very organized by nature. For example, they have organized huge
trumpets (that sound like blowing a ship's horn) to support their team
playing on the field. The fans want to keep the level of noise constant
throughout the match.
The trumpets are operated by compressed gas. However, if you blow
the trumpet for 2 seconds without stopping it will break. So when the
trumpet makes noise, everything is okay, but in a pause of the
trumpet,the fans must chant "KO-RE-A"!
Before the match, a group of fans gathers and decides on a
chanting pattern. The pattern is a sequence of 0's and 1's which is
interpreted in the following way: If the pattern shows a 1, the trumpet
is blown. If it shows a 0, the fans chant "KO-RE-A". To ensure that the
trumpet will not break, the pattern is not allowed to have two
consecutive 1's in it.
Problem
Given a positive integer n, determine the number of different
chanting patterns of this length, i.e., determine the number of n-bit
sequences that contain no adjacent 1's. For example, for n = 3 the
answer is 5 (sequences 000, 001, 010, 100, 101 are acceptable while
011, 110, 111 are not).
The first line contains the number of scenarios.
For each scenario, you are given a single positive integer less than 45 on a line by itself.
The output for every scenario begins with a line containing "Scenario #i:", where i is the number of the scenario starting at 1. Then print a single line containing the number of n-bit sequences which have no adjacent 1's. Terminate the output for the scenario with a blank line.
2 3 1
Scenario #1: 5 Scenario #2: 2
Migrated from old NTUJ.
| No. | Testdata Range | Score |
|---|