Search an array of abscissas
PROBLEM
Given an array of abscissas A.J, J=1,...,N, with the elements either monotically increasing or monotically decreasing, and given a number V, find an integer J such that V lies between A.J and A.Jp1, where Jp1=J+1.
ALGORITHM
Bisection (see
binary search) will find the right place in the table about
lgN tries.
IMPLEMENTATION
Unit:
internal function
Global variables:
ascending sequence of values A.1,...,A.N
Parameters:
positive integer N, number V
Returns:
a value J such that V is between A.J and A.Jp1, where Jp1=J+1. J=0 or J=N indicates that V is out of range.
LOCATE: procedure expose A.
parse arg N, V
L = 0; U = N + 1; Ascnd = (A.N >= A.1)
do while (U - L) > 1
M = (U + L) % 2
if (V >= A.M) = Ascnd then L = M
else U = M
end
if V = A.1 then return 1
if V = A.N then return N - 1
return L
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CONNECTIONS
Literature
Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. Numerical Recipes in C : the art of scientific computing
- 2nd ed. University Press, Cambridge, 1992
