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(M4) CHAPTER 2 - Coggle Diagram
(M4) CHAPTER 2
MATHEMATICAL ANALYSIS
RECURSIVE
CONSIDER THE COMPARISON AS THE INITIAL CONDITION
DECIDE A PARAMETER
IDENTIFY THE BASIC OPERATION
BASIC OPERATION DEPENDS ON THE INPUT'S SIZE?
SET UP A RECURRENCE RELATION
SOLVE THE RECURRENCE
MATHEMATICAL ANALYSIS
NONRECURSIVE
CONSIDER THE COMPARISON AS THE BASIC OPERATION
DECIDE A PARAMETER
IDENTIFY THE BASIC OPERATION
BASIC OPERATION DEPENDS ON THE INPUT'S SIZE?
STUDY THE THREE CASES OF EFFICIENCY
SET UP A SUM EXPRESSION
ASYMPTOTIC NOTATIONS
O (BIG OH)
LOWER OR SAME ORDER OF GROWTH
Ω (BIG OMEGA)
HIGHER OR SAME ORDER OF GROWTH
θ (BIG THETA)
SAME ORDER OF GROWTH
EMPIRICAL ANALYSIS
INSERT A COUNTER IN THE BASIC OPERATION
VERIFY IF THE VARIABLE WAS PUT IN THE RIGHT PLACE
VERIFY IF THE PROGRAM IS RUNNING CORRETLY AS IT SHOULD
MEASURE THE APPLICATION TIME WITH BUILT-IN FUCTION
START - FINISH
COMPUTER TIME IS NOT SO ACURATE
CREATE, ON PROPOSE, LOOPS TO GET THE AVERAGE TIME OF THEM
TIME IS SHARED WITH OTHER APPS IN THE COMPUTER
RANDOM NUMBERS IS A NEED
VISUAL ALGORITHMS
STATIC ALGORITHM
PROGRESS THROUGH SERIES OF IMAGES
DYNAMIC ALGORITHM
ANIMATIONS
IT IS A GOOD WAY TO SEE HOW A ALGORITHM WORKS
SOME IMPROVIMENTS OF ALGORITHM WAS DEVELOPED
BY OBSERVATING ITS RUNNING IN MOVIES-LIKE
THE ANALYSIS FRAMEWORK
TIME EFFICIENCY OR TIME COMPLEXITY
MAJOR OPPORTUNITY TO IMPROVE THAN SPACE COMPLEXITY
MEASURE RUNNING TIME
COUNT BASIC OPERATION
ORDER OF GROWTH (MAY IGNORE MULTIPLICATIVA CONSTANTS)
WORST, BEST AND AVERAGE CASES EFFICIENCIES
SPACE EFFICIENCY OR SPACE COMPLEXITY
MEASURE THE INPUT'S SIZE
TWO RESOURCES: RUNNING TIME AND MEMORY SPACE
O, θ, Ω
SUM ALGORITHM'S RUNNING TIME AND SIMPLIFY THE SUM