1 model (6) day1

Question 1:

Question:

A [I] of N is a single peak. if and only when an x exists, a [1] <A [2] <... <A [x]> A [x + 1]>...> A [n]. Try to calculate the total number of n single-peaks in mod 1234567. N <= 2 000 000 000

 

Problem solving process:

1. first of all, the so-called "peak" must be the number N, so according to the N position to discuss, we can find that the number of N in the I position is C (n-1, I-1 ); therefore, the total number of solutions is sum {C (n-1, 0... n-1 )};

According to the binary theorem sum {C (n-1, 0... N-1)} = (1 + 1) ^ (n-1) = 2 ^ (n-1); Use A Rapid power calculation.

 

Question 2:

Question:

There is a dot matrix of m rows and n columns, and two adjacent points can be connected. A vertical line takes one unit, and a horizontal line takes two units. Some vertices are connected. How many units are required to connect all vertices at least. M, n <= 1000

 

Problem solving process:

1. Since it is necessary to connect, we naturally think of the smallest spanning tree, but there will be a lot of edges, and the Kruskal algorithm uses (eloge) time sorting. It must have timed out.

2. for further consideration, there are only three edge values: 0, 1, and 2, the sequential number of edge sets can be obtained after 2 is stored, and then the traditional Kruskal.

 

Question 3:

N pairs are given, indicating that the letters X and Y must be adjacent (that is, "XY" or "Yx" must appear in the string) and the string with the smallest Lexicographic Order is obtained, the given n pairs are satisfied and the length is n + 1;

 

Problem solving process:

1. Virtualize a letter into a dot and describe the link to an edge. This question is actually an Euler's path.

2. Obtain the number CNT of the singularity. If it is not 0 or 2, no solution is output.

3. If CNT = 0, you can search for a small-coded letter. If CNT = 2, you must start from the singularity.

 

1 model (6) day1