Number Theory: High Precision --- ultraviolet A 10183: How many fibs?

How many fibs?

Description

Recall the definition of the Fibonacci numbers:

f1 := 1 
f2 := 2 
fn := f

N-1

 + f

N-2

     (n>=3) 

Given two numbers a and B, calculate how many Fibonacci numbers are in the range [a, B].

Input

The input contains several test cases. each test case consists of two non-negative integer numbers A and B. input is terminated by a = B = 0. otherwise, a <= B <= 10100. the numbers A and B are given with no superfluous leading zeros.

Output

For each test case output on a single line the number of Fibonacci numbers fi with a <= Fi <= B.

Sample Input

10 1001234567890 98765432100 0

Sample output

54

 

Mean: 

Given two integers A and B, the number of Fibonacci numbers in the statistical interval [a, B.

Analyze:

T because the input range of this question has reached 10 ^ 100, it must be accurate.

We first obtain all the Fibonacci numbers less than 10 ^ 100, then input the STA, en, and then perform the location search. Finally, we can see the answer when we see the positions of STA and en.

Time Complexity:O (N)

 

Source code:

 

/* _ Ooooo _ o8888888o 88 ". "88 (|-_-|) O \=/o ____/'---'\____. '\\| | //'. /\| |: | // _ | -: -| \-// | \ _ | ''\ ---/'' | \. -\__'-'___/-. /___'.. '/--. --\'.. __. "" '<'. ___ \_< |> _/___. '> '"". | :'-\'.; '\_/';. '/-': | \\'-. \___\/___/. -'// ====== '-. ____'-. ___\_____/___. -'____. -'= --- =' ^ ^ ......... .................................... The bug in the bucket of the bucket. When you wake up, you can only sit on the Internet, and get drunk and sleep. When you wake up, you can get online for the next year. I hope that the old computer room will not bow to the boss; Mercedes Benz and BMW are interesting, and the bus programmers are themselves. When others laugh at me, I laugh at myself, and my life is so cheap. If I don't see the beautiful girl on the street, which is my programmer? * // Memory time // 1347 K 0 Ms //: snarl_jsb # include <algorithm> # include <cstdio> # include <cstring> # include <cstdlib> # include <iostream> # include <vector> # include <queue> # include <Stack> # include <map> # include <string> # include <climits> # include <cmath> # define Max 1100 # define ll long longusing namespace STD; vector <string> maid; string maid (string F1, string F2) {string Buff; int carry = 0, len1 = f1.length (), len2 = f2.length (); for (INT I = 0; I <len1; I ++) {carry = (F1 [I]-'0') + (F2 [I]-'0 ') + carry; char c = carry % 10 + '0'; carry/= 10; buff. push_back (c) ;}for (INT I = len1; I <len2; I ++) {carry = (F2 [I]-'0') + carry; char c = carry % 10 + '0'; carry/= 10; buff. push_back (c);} If (carry) buff. push_back ('1'); Return Buff;} void fill_fibs () {string F1, F2; f1.push _ back ('1'); f2.push _ back ('1 '); fibs. push_back (F1); fibs. push_back (F2); While (f2.length () <105) {string TMP = fig (F1, F2); F1 = F2; F2 = TMP; fig. push_back (F2);} fibs [0] = "0"; int size = fibs. size (); For (INT I = 0; I <size; I ++) reverse (FIBS [I]. begin (), fibs [I]. end ();} int main () {// freopen ("C: \ Users \ Asus \ Desktop \ cout.txt", "W", stdout ); // freopen ("C: \ Users \ Asus \ Desktop \ cout.txt", "W", stdout); fill_fibs (); string STA, en; while (CIN> sta> en, Sta [0]-'0' | En [0]-'0') {int I = 1, ANS = 0; while (1) {If (FIBS [I]. length ()> Sta. length () break; else if (FIBS [I]. length () = Sta. length () & fibs [I]> = Sta) break; I ++;} while (1) {If (FIBS [I] = EN) {ans ++; break;} If (FIBS [I]. length ()> en. length () break; else if (FIBS [I]. length () = en. length () & fibs [I]> en) break; I ++; ans ++;} cout <ans <Endl;} return 0 ;}

　　

Number Theory: High Precision --- ultraviolet A 10183: How many fibs?