vijos-p1543 extremum Problem (Fibonacci series + formula derivation + python)

P1543Extremum Problem accepted Tags: [show tags]<textarea id="code" class="textbox"></textarea>Background

Xiao Ming's Math Tour 2.

Descriptive narrative

M, N is known as an integer, and the following two conditions are met:
①m, n∈1,2. ..., K
② (n^ 2-mn-m^2) ^2=1
Compile a procedure. For a given k, a set of M, N, which satisfies the above two conditions, and the maximum value of the m^2+n^2 is obtained. For example, if k=1995. m=987,n=1597, the M, n satisfies the condition, and the m^2+n^2 value is the largest.

Format input Format

Enter the value of only one row, K.

Output format

Outputs only one row, m^2+n^2 the value.

Example 1 example input 1[copy]

1995

Example output 1[copy]

3524578

Limit

1 seconds for each test pilot.

Tips

Source:
Shantou Fxoi Group
Phoeagon
ThanX2 Sivon
For Tripley

First of all, we have to find the relationship between the item and the column.

So you can get a[i] = 3 * A[i-1]-The number of items in the Fibonacci sequence is represented by I in a[i-2]{}

So that we can solve this problem.

#!/usr/bin/env python3#-*-coding:utf-8-*-k = Int (raw_input ()) A = 1b = 1ans = 2cnt = 2if k = = 1:    print 2elif k = = 2 :    print 5else: While    True:        if ans > k:break        t = a        a = a + b        b = t        ans + a        cnt + = 1
   
    c = 1    d = 1 for    i in range (CNT):        t = c        c = c *        d = t    print C        
   

vijos-p1543 extremum Problem (Fibonacci series + formula derivation + python)