Codeforces Round #200 (Div. 2) Rational Resistance

Oct 7, 2013#CodeForce #math26

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The Codeforces Round #200 (Div. 2) Rational Resistance problem involves using the properties of resistors to calculate the minimum number of resistors needed to form a given ratio. By breaking down the ratio into integer and decimal parts, and using a method similar to finding the greatest common divisor (gcd), the problem can be solved.

This problem is a bit difficult to think about 0.0

Using the characteristics of resistors

1/R1+1/Re=1/Rans

The integer part can be connected in series, and the decimal part can be connected in parallel

There is a key point that if we can use at least N resistors to form a/b, then we can also use N resistors to form b/a

So as long as b>a, we can switch them and turn it into a>b, then we can decompose it into an integer and a decimal

And the integer part is naturally the number of resistors

The decimal part can be further decomposed using the method above

It feels like gcd

//  
//        GGGGGGGGGGGGG        CCCCCCCCCCCCC               AAA  
//     GGG::::::::::::G     CCC::::::::::::C              A:::A  
//   GG:::::::::::::::G   CC:::::::::::::::C             A:::::A  
//  G:::::GGGGGGGG::::G  C:::::CCCCCCCC::::C            A:::::::A  
// G:::::G       GGGGGG C:::::C       CCCCCC           A:::::::::A  
//G:::::G              C:::::C                        A:::::A:::::A  
//G:::::G              C:::::C                       A:::::A A:::::A  
//G:::::G    GGGGGGGGGGC:::::C                      A:::::A   A:::::A  
//G:::::G    G::::::::GC:::::C                     A:::::A     A:::::A  
//G:::::G    GGGGG::::GC:::::C                    A:::::AAAAAAAAA:::::A  
//G:::::G        G::::GC:::::C                   A:::::::::::::::::::::A  
// G:::::G       G::::G C:::::C       CCCCCC    A:::::AAAAAAAAAAAAA:::::A  
//  G:::::GGGGGGGG::::G  C:::::CCCCCCCC::::C   A:::::A             A:::::A  
//   GG:::::::::::::::G   CC:::::::::::::::C  A:::::A               A:::::A  
//     GGG::::::GGG:::G     CCC::::::::::::C A:::::A                 A:::::A  
//        GGGGGG   GGGG        CCCCCCCCCCCCCAAAAAAA                   AAAAAAA  
#include <iostream>  
#include <cstdio>  
#include <cstring>  
#include <algorithm>  
#include <cmath>  
#include <climits>  
#include <vector>  
#include <set>  
#include <map>  
#include <queue>  
#include <cctype>  
#include <utility>  
#include <ctime>  
using namespace std;  
#ifdef DEBUG  
#define VAR(a,b) decltype(b) a=(b)  
#define debug(...) printf("DEBUG: "),printf(\_\_VA\_ARGS\_\_)  
#define gettime() end\_time=clock();printf("now running time is %.7f\\n",(float)(end\_time - start\_time)/CLOCKS\_PER\_SEC);  
#else  
#define VAR(a,b) \_\_typeof(b) a=(b)  
#define debug(...)  
#define gettime()  
#endif  
typedef unsigned int uint;  
typedef long long int Int;  
typedef unsigned long long int UInt;  
#define Set(a,s) memset(a,s,sizeof(a))  
#define Write(w) freopen(w,"w",stdout)  
#define Read(r) freopen(r,"r",stdin)  
#define Pln() printf("\\n")  
#define I\_de(x,n)for(int i=0;i<n;i++)printf("%d ",x\[i\]);Pln()  
#define De(x)printf(#x"%d\\n",x)  
#define For(i,x)for(int i=0;i<x;i++)  
#define CON(x,y) x##y  
#define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\\  
    printf("%d ",dp\[htx\]\[hty\]);}Pln();}  
#define M 30005  
#define PII pair<int,int\>  
#define PB push\_back  
#define oo INT\_MAX  
#define Set\_oo 0x3f  
#define FOR(a,b) for(VAR(a,(b).begin());a!=(b).end();++a)  
#define eps 1e-6  
#define X first  
#define Y second  
clock\_t start\_time=clock(), end\_time;  
bool xdy(double x,double y){return x>y+eps;}  
bool xddy(double x,double y){return x>y-eps;}  
bool xcy(double x,double y){return x<y-eps;}  
bool xcdy(double x,double y){return x<y+eps;}  
int min3(int x,int y,int z){  
    int tmp=min(x,y);  
    return min(tmp,z);  
}  
int max3(int x,int y,int z){  
    int tmp=max(x,y);  
    return max(tmp,z);  
}  
  
int main() {  
    ios\_base::sync\_with\_stdio(0);  
    Int a,b;  
    while(~scanf("%I64d%I64d",&a,&b)){  
        Int ans=0;  
        while(a){  
            if(b>a)swap(a,b);  
            ans+=a/b;  
            a%=b;  
        }  
        printf("%I64d\\n",ans);  
    }  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
}

// // GGGGGGGGGGGGG CCCCCCCCCCCCC AAA // GGG::::::::::::G CCC::::::::::::C A:::A // GG:::::::::::::::G CC:::::::::::::::C A:::::A // G:::::GGGGGGGG::::G C:::::CCCCCCCC::::C A:::::::A // G:::::G GGGGGG C:::::C CCCCCC A:::::::::A //G:::::G C:::::C A:::::A:::::A //G:::::G C:::::C A:::::A A:::::A //G:::::G GGGGGGGGGGC:::::C A:::::A A:::::A //G:::::G G::::::::GC:::::C A:::::A A:::::A //G:::::G GGGGG::::GC:::::C A:::::AAAAAAAAA:::::A //G:::::G G::::GC:::::C A:::::::::::::::::::::A // G:::::G G::::G C:::::C CCCCCC A:::::AAAAAAAAAAAAA:::::A // G:::::GGGGGGGG::::G C:::::CCCCCCCC::::C A:::::A A:::::A // GG:::::::::::::::G CC:::::::::::::::C A:::::A A:::::A // GGG::::::GGG:::G CCC::::::::::::C A:::::A A:::::A // GGGGGG GGGG CCCCCCCCCCCCCAAAAAAA AAAAAAA #include <iostream> #include <cstdio> #include <cstring> #include <algorithm> #include <cmath> #include <climits> #include <vector> #include <set> #include <map> #include <queue> #include <cctype> #include <utility> #include <ctime> using namespace std; #ifdef DEBUG #define VAR(a,b) decltype(b) a=(b) #define debug(...) printf("DEBUG: "),printf(\_\_VA\_ARGS\_\_) #define gettime() end\_time=clock();printf("now running time is %.7f\\n",(float)(end\_time - start\_time)/CLOCKS\_PER\_SEC); #else #define VAR(a,b) \_\_typeof(b) a=(b) #define debug(...) #define gettime() #endif typedef unsigned int uint; typedef long long int Int; typedef unsigned long long int UInt; #define Set(a,s) memset(a,s,sizeof(a)) #define Write(w) freopen(w,"w",stdout) #define Read(r) freopen(r,"r",stdin) #define Pln() printf("\\n") #define I\_de(x,n)for(int i=0;i<n;i++)printf("%d ",x\[i\]);Pln() #define De(x)printf(#x"%d\\n",x) #define For(i,x)for(int i=0;i<x;i++) #define CON(x,y) x##y #define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\\ printf("%d ",dp\[htx\]\[hty\]);}Pln();} #define M 30005 #define PII pair<int,int\> #define PB push\_back #define oo INT\_MAX #define Set\_oo 0x3f #define FOR(a,b) for(VAR(a,(b).begin());a!=(b).end();++a) #define eps 1e-6 #define X first #define Y second clock\_t start\_time=clock(), end\_time; bool xdy(double x,double y){return x>y+eps;} bool xddy(double x,double y){return x>y-eps;} bool xcy(double x,double y){return x<y-eps;} bool xcdy(double x,double y){return x<y+eps;} int min3(int x,int y,int z){ int tmp=min(x,y); return min(tmp,z); } int max3(int x,int y,int z){ int tmp=max(x,y); return max(tmp,z); } int main() { ios\_base::sync\_with\_stdio(0); Int a,b; while(~scanf("%I64d%I64d",&a,&b)){ Int ans=0; while(a){ if(b>a)swap(a,b); ans+=a/b; a%=b; } printf("%I64d\\n",ans); } }