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Elementary Techniques | Techniques of Function | Techniques of Recursion |Techniques of Number

Recycle numerical functions

Sample Code 1

a(X,T):XXa(sX,T-1)XX
a(a(,3)a(r,9)r,1)

Sample Code 2

a(X,T):a(sX,T-1)XX
a(ra(r,6),100)

IF statement

Sample Code 1

a(T):rsrrsr
b(T):a(2-T)b(T-5)
c(T):b(T)sc(T-1)
c(20)

In this code, b(T) equals "rsrrsr" if T≡1 mod 5, and no moves otherwise.

Examples

Rational Growth

Sample Code

a(T):sa(T-5)
b(T):a(T)rb(T+7)
b(1)

The speed of growth is "7/5".

Examples

12B method

Sample Code

f(T):sf(T-4)rf(T+7)
f(8)

This code realizes the loop

a:ssrsssrsssrsssra
a

In this loop, the number of "s" equals 4 + 7, and the number of "r" equals 7.
In generally, the code

f(T):[1]f(T-A)[2]f(T+B)

implies a loop with (A+B) times of "[1]" and B times of "[2]".

Sample Code 2

a(T):sa(T-37)ra(T+83)
a(1)

Since 83/37 approximately equals 9/4, this code is similar to

a(T):sa(T-4)ra(T+9)
a(1)

but the small difference changes the direction of the movement.
Therefore, "square minus square" shape can be drawn by a 12B code.

Sample Code 3

f(T):sf(T-15)rf(T+T+63)
f(1)

Some new sequence can be obtained by changing the coefficient of degree = 1.
In this case, the periodic sequence

1,[5,5,6,7],[5,5,6,7],[5,5,6,7],...

appears.

Examples

Random walk by a numerical function

Sample Code

f(T):sf(T-4)rf(T-7)
f(255)

Examples

Probably, no problems in HOJ requires this method (even for "best solution") at this moment.

Compress long statement by numbers

Sample Code 1

a(T,A):ra(T-A,A)
f(T):a(T,64)sa(T,16)sa(T,4)sa(T,1)s

By f(1 to 255), you can make all patterns of four step move, except "ssss".

Sample Code 2

a(T,X):X
b(A,B,X):b(A-127,B,s)a(128-A,Xb(A+A,B-1,r))
f(T):b(T,8,r)

All strings of length=8, made of "s" and "r" can be made by f(1 to 255), but for "srrrrrrr" ans "rrrrrrrr".

Sample Code 3

a(T,X):X
b(A,B):lb(A-81,B)a(82-A,llsb(A+A+A,B-1))
f(T):b(T,5)

Examples

Truncate a multiple recusion

Sample Code 1

f(X,T):rXf(f(sX,T-1),10)
f(,1)

Sample Code 2

f(X,T):Xf(rf(sX,T-1),10)
f(,1)

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Last-modified: 2013-02-13 (水) 23:43:58 (2015d)