[Beauty of programming] 2.6 precise expression of Floating Point Numbers

Question: Give a finite decimal or an infinite repeating decimal number, and use the smallest denominator to accurately express this number with a fraction. Parentheses indicate the cyclic part, for example:

0.3, 0.3 (3), 0.3 (0)

 

Thought: I saw it, dumb. After thinking twice and not thinking about it, I went online to find a round-robin decimal point to convert the score. The result was actually a primary school Olympics question! I'm depressed .....

Take 1.2 (34) as an example.

1.2 (34) * 10 = 12. 34343434...

1.2 (34) * 1000 = 1234. 3434...

1.2 (34) * 1000-1.2 (34) * 10 = 1234-12

990*1.2 (34) = 1222

1.2 (34) = 1222/990

 

Then, we can divide the denominator of the numerator by their maximum appointment.

The code input is a string. You need to determine whether there are loops and loops that are 0.

# Include <stdio. h> # include <string. h> typedef struct fraction {int numerator; int denominator;} fraction; // returns num * 10 ^ powint TENs (INT num, int POW) {for (INT I = POW; i! = 0; I --) {num * = 10;} return num;} // calculate the maximum common approx. Int Mod (INT num1, int num2) {int A, B; A = (num1> num2 )? Num1: num2; B = (num1 <num2 )? Num1: num2; int r = A % B; If (r = 0) return B; else {A = B; B = r; return Mod (, b) ;}} fraction getfractionexperssion (char * In) {int intefer = 0; // integer part int withoutloop = 0; // int withloop = 0; // int powwithoutloop = 0 in the loop part; // the nth decimal point int powofloop = 0 in the non-circular part; // the nth decimal point int Numerator = 0 in the loop part; // molecule int Denominator = 0; // denominator fraction ans; int TMP = 0; int tmppowwithoutloop = 0; int tmppowofloo P = 0; char * tmpin = In; bool bhasloop = false; while (* tmpin! = '\ 0') {If (* tmpin> = '0' & * tmpin <= '9') {TMP = TMP * 10 + (* tmpin) -'0'); tmppowwithoutloop ++; tmppowofloop ++;} else if (* tmpin = '. ') {tmppowwithoutloop = 0;} else if (* tmpin =' (') {powwithoutloop = tmppowwithoutloop; withoutloop = TMP; tmppowofloop = 0; TMP = 0; bhasloop = true;} else if (* tmpin = ') {powofloop = tmppowofloop; withloop = TMP; TMP = 0;} else {printf ("input error !! ");} Tmpin ++;} // If (! Bhasloop) {withoutloop = TMP; powwithoutloop = tmppowwithoutloop;} If (withloop = 0) // itself is not a circular decimal number {// obtain the numerator Numerator = withoutloop; denominator = TENs (1, powwithoutloop); // calculates the maximum common approx. Int GCD = Mod (numerator, denominator); // minimizes the molecular denominator ans of the answer. denominator = Denominator/GCD; ans. numerator = numerator/GCD; printf ("% s = % d/% d \ n", in, ans. numerator, ans. denominator); Return ans;} else // is a loop decimal point {Numerator = TENs (withoutloop, powofloop) + withloop-withoutloop; Denominator = TENs (1, powofloop + powwithoutloop) -Tens (1, powwithoutloop); int GCD = Mod (numerator, denominator); ans. denominator = Denominator/GCD; ans. numerator = numerator/GCD; printf ("% s = % d/% d \ n", in, ans. numerator, ans. denominator); Return ans ;}} int main () {char * in1 = "3.3 (3)"; char * in2 = "2.3 (12 )"; char * in3 = "0.300 (0)"; getfractionexperssion (in1); getfractionexperssion (in2); getfractionexperssion (in3); Return 0 ;}

 

[Beauty of programming] 2.6 precise expression of Floating Point Numbers