Algorithm notes

2013/03/31 Confirming a point is in a triangle （2D）

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Directed area formula :

|  x0 y0 1  |

|  x1 y1 1  |    =  2A  =  x0*y1 + y0*x2 + y2*x1 - y1*x2 - y0*x1 - x0*y2

|  x2 y2 1  |

("A" represents the area, (x0,y0) & (x1,y1) & (x2, y2) are points of the triangle.)

Assuming that (x,y) is the point we want to confirm, calculate area "B":

          |  x   y  1  |             |  x0 y0 1  |             |  x0 y0 1  |

2B =   |  x1 y1 1 |     +      |  x   y   1  |     +      |  x1 y1 1  |           Then judge if 2B == 2A.

          |  x2 y2 1 |             |  x2 y2 1  |             |  x   y   1  |

2013/03/30  Finding the longest palindrome substring

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Manacher algorithm :

The core idea is to fill the string with '#' like:

source string :     abcccba

filled string     :     #a#b#c#c#c#b#a#

Then you can find the length of the filled string is always odd, so you needn't to consider the condition of even.

Store the middle position in the substring you are to judge and the radious the substring contains.

2013/03 Fibonacci solution by martix

2013/03 Hanoi recursion

2013/03 Binary GCD(Greatest common divisor)