Techniques of Recursion
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開始行:
[[English Page]]~
[[Elementary Techniques]] | [[Techniques of Function]] | ...
#contents
*Replace in a recursive function [#eb7b48e9]
**Sample Code 1 [#e3a7c461]
a(X):XXXXrXXXXla(srslX)
a(r)
(20B)
The code above can be compressed by replacing XXXX by ano...
a(X,Y):YrYla(srslX,XXXX)
a(r,)
(19B)
**Examples [#o5494688]
-[[Problem 0441]]
*Special first term [#m9d39ab4]
**Sample Code 1 [#e3a7c461]
a(X,Y):YrYla(srslX,XXXX)
a(r,sss)
Even if you replace something by Y, the rule of Y isn't a...
Thus, you can use "1st Y" freely.
**Sample Code 2 [#v5560bd3]
a(X,Y):XYXa(XX,l)
a(srsl,r)
**Sample Code 3 [#p1575461]
a(X,Y):XXXXYa(sX,YYl)
a(r,)
In this code, "1st Y" and "2nd Y" is special.
**Examples [#x97b838b]
-[[Problem 0651]]
*Controll the spped of growth [#xe4dbfff]
**Sample Code 1 [#ab7d95e0]
a(X,Y):XXXXra(sY,X)
a(r,r)
X grows with a spped of 1/2.
**Sample Code 2 [#n4d973bf]
a(X,Y,Z):Xra(ssY,sZ,X)
a(,,)
This code gives a sequence [0,2,3][3,5,6][6,8,9][9,11,12]...
**Sample Code 3 [#w85e28fe]
a(X,Y,Z):Xra(sYX,Z,Y)
a(,,s)
This code gives a sequence [0,1][3,4][6,7]...~
"s" and "" appar at Y alternatively.
**Examples [#ld1a4eec]
-[[Problem 0544]]
-[[Problem 0547]]
*Change of variables [#d5ec0183]
**Sample Code [#o3fadcb7]
a(X):XrXrXrXra(XrXlX)
a(s)
Put Y = Xr, then this code can be transformed to the foll...
b(Y):YYYYb(newY = [newX]r = XrXlXr = YYllY)
b(sr)
b(Y):YYYYb(YYllY)
b(sr)
**Examples [#h19a3f89]
-[[Problem 1309]]
-[[Problem 1720]]
*Multiple recursion [#z2d43815]
**Sample Code 1 [#i62107f5]
f(X):ssXlssf(sX)
f()
[12B]
This code can be compressed by recycling "ss"：
f(X):ssXlf(f(sX))
f()
[11B]
**Sample Code 2 [#pd3c6df3]
f(X):srslXf(f(ss))
f()
**Examples [#c51fb1eb]
-[[Problem 0090]]
-[[Problem 1687]]
**Examples [#s1d10173]
-[[Problem 1687]]
-[[Problem 0090]]
-[[Problem 0710]]
*Recursion with many functions [#je2c6d23]
f(X):[1]
a(X):[2]a(f(X))
a(f([3]))
This code can be compressed by using two recursive functi...
f(X):a([1])
a(X):[2]f(X)
f([3])
終了行:
[[English Page]]~
[[Elementary Techniques]] | [[Techniques of Function]] | ...
#contents
*Replace in a recursive function [#eb7b48e9]
**Sample Code 1 [#e3a7c461]
a(X):XXXXrXXXXla(srslX)
a(r)
(20B)
The code above can be compressed by replacing XXXX by ano...
a(X,Y):YrYla(srslX,XXXX)
a(r,)
(19B)
**Examples [#o5494688]
-[[Problem 0441]]
*Special first term [#m9d39ab4]
**Sample Code 1 [#e3a7c461]
a(X,Y):YrYla(srslX,XXXX)
a(r,sss)
Even if you replace something by Y, the rule of Y isn't a...
Thus, you can use "1st Y" freely.
**Sample Code 2 [#v5560bd3]
a(X,Y):XYXa(XX,l)
a(srsl,r)
**Sample Code 3 [#p1575461]
a(X,Y):XXXXYa(sX,YYl)
a(r,)
In this code, "1st Y" and "2nd Y" is special.
**Examples [#x97b838b]
-[[Problem 0651]]
*Controll the spped of growth [#xe4dbfff]
**Sample Code 1 [#ab7d95e0]
a(X,Y):XXXXra(sY,X)
a(r,r)
X grows with a spped of 1/2.
**Sample Code 2 [#n4d973bf]
a(X,Y,Z):Xra(ssY,sZ,X)
a(,,)
This code gives a sequence [0,2,3][3,5,6][6,8,9][9,11,12]...
**Sample Code 3 [#w85e28fe]
a(X,Y,Z):Xra(sYX,Z,Y)
a(,,s)
This code gives a sequence [0,1][3,4][6,7]...~
"s" and "" appar at Y alternatively.
**Examples [#ld1a4eec]
-[[Problem 0544]]
-[[Problem 0547]]
*Change of variables [#d5ec0183]
**Sample Code [#o3fadcb7]
a(X):XrXrXrXra(XrXlX)
a(s)
Put Y = Xr, then this code can be transformed to the foll...
b(Y):YYYYb(newY = [newX]r = XrXlXr = YYllY)
b(sr)
b(Y):YYYYb(YYllY)
b(sr)
**Examples [#h19a3f89]
-[[Problem 1309]]
-[[Problem 1720]]
*Multiple recursion [#z2d43815]
**Sample Code 1 [#i62107f5]
f(X):ssXlssf(sX)
f()
[12B]
This code can be compressed by recycling "ss"：
f(X):ssXlf(f(sX))
f()
[11B]
**Sample Code 2 [#pd3c6df3]
f(X):srslXf(f(ss))
f()
**Examples [#c51fb1eb]
-[[Problem 0090]]
-[[Problem 1687]]
**Examples [#s1d10173]
-[[Problem 1687]]
-[[Problem 0090]]
-[[Problem 0710]]
*Recursion with many functions [#je2c6d23]
f(X):[1]
a(X):[2]a(f(X))
a(f([3]))
This code can be compressed by using two recursive functi...
f(X):a([1])
a(X):[2]f(X)
f([3])
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