Equilibrium situation of the main divide and conquer theorem
gives the asymptotic complexity of the subproblem balanced with the cost of merging.
symbols, variables and units
a≥1: number of sub-problems; b>1: reduction ratio; n: scale. An illustration of the interdisciplinary principle of
applicable conditions and boundaries
Only the k=0 case of type 2 of the main theorem; rounding does not change the regular asymptotic order.
formula source code
The following is a copyable LaTeX expression.
T(n)=aT(n/b)+\Theta(n^{\log_b a})=\Theta(n^{\log_b a}\log n)Reference and Extended Learning
MIT OpenCourseWare · Introduction to Algorithms ↗is organized according to model definition and assumptions. Please check actual conditions and original literature before engineering, research and clinical use.
master theoremDivide and Conquer