Homework 3.17 - 3.18
Vocabulary
- Problem: a general description of a task that can or cannot be solved algorithmically
- Decision Problem: A problem with a yes or no answer
- Organization Problem: a problem with a goal of finding the best answer
- Instance:a problem with a specific input
- Efficiency:amount of computing needed to solve a problem
- Polynomial Efficiency (Good): more work takes a proportional amount of time (1 job is +2 time)
- Exponential Efficiency (Bad): more work takes an exponential amount more time (1 job is 2x time)
- Heuristic Approach: When optimal solutions are inefficient, look for a possibly optimal solution that is more efficient
- Decidable Problem: A decision problem that has a clear solution that will always make a correct output
- Undecidable Problem: A decision problem with no solution that is not gaurenteed to produce the correct output
Notes
- Algorithm efficiency relates to how many resources a computer needs to expend to process an algorithm. The efficiency of an algorithm needs to be determined to ensure it can perform without the risk of crashes or severe delays. If an algorithm is not efficient, it is unlikely to be fit for its purpose.
- One way to measure the efficiency of an algorithm is to count how many operations it needs in order to find the answer across different input sizes.
- A good algorithm is correct, but a great algorithm is both correct and efficient. The most efficient algorithm is one that takes the least amount of execution time and memory usage possible while still yielding a correct answer.
- In computer science, algorithmic efficiency is a property of an algorithm which relates to the amount of computational resources used by the algorithm. An algorithm must be analyzed to determine its resource usage, and the efficiency of an algorithm can be measured based on the usage of different resources.
- Quicksort. Quicksort is one of the most efficient sorting algorithms, and this makes of it one of the most used as well. The first thing to do is to select a pivot number, this number will separate the data, on its left are the numbers smaller than it and the greater numbers on the right.
import time
numlist = [1,3,5,7,9,11,13,15,17,19]
valuelist = [0,3,6,9,12,15,18,21]
def isvalue(value,array):
#--------------------
exists = False
if exists == False:
return exists
#--------------------
starttime = time.time()
for i in range(100000):
for i in range(len(valuelist)):
x = isvalue(valuelist[i],numlist)
endtime = time.time()
print(endtime-starttime,'seconds')
import math as m
a = int(input("num:"))
b = int(input("num:"))
c = a **2 + b**2
if int(m.sqrt(c)) == m.sqrt(c):
print("sum is perfect")
else:
print("sum is not perfect")
Notes
- An undecidable problem is one that should give a "yes" or "no" answer, but yet no algorithm exists that can answer correctly on all inputs.
- In computability theory, an undecidable problem is a type of computational problem that requires a yes/no answer, but where there cannot possibly be any computer program that always gives the correct answer; that is, any possible program would sometimes give the wrong answer or run forever without giving any answer.
- An unsolvable problem is one for which no algorithm can ever be written to find the solution. An undecidable problem is one for which no algorithm can ever be written that will always give a correct true/false decision for every input value.
- There are some problems that a computer can never solve, even the world's most powerful computer with infinite time: the undecidable problems. An undecidable problem is one that should give a "yes" or "no" answer, but yet no algorithm exists that can answer correctly on all inputs.
Homework!
Make an algorithm that finds the fastest route that hits every location once starting and ending at Del Norte. Make sure to show your thinking. If you are strugling, try using a huristic approach. Remember, what matters more than having perfectly functioning code is that you tried your hardest.
dataset = {
'DelNorte':{
'Westview':15,
'MtCarmel':20,
'Poway':35,
'RanchoBernrdo':50
},
'Westview':{
'Del Norte':15,
'MtCarmel':35,
'Poway':25,
'RanchoBernrdo': 45
},
'MtCarmel':{
'Westview':35,
'Del Norte':20,
'Poway':40,
'RanchoBernrdo':30
},
'Poway':{
'Westview':25,
'MtCarmel':40,
'Del Norte':35,
'RanchoBernrdo':15
},
'RanchoBernardo':{
'Westview':45,
'MtCarmel':30,
'Poway':15,
'Del Norte':50
}
}
def fastestroute(start,data):
drivetime = 0
order = []
#CODE,CODE,CODE
return(drivetime,order)
start = 'DelNorte'
# 'dataset' is the name of the nested key value pair
# I was really confused with this code and when I did attempt it, my vscode kept freezing