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 guaranteed to produce the correct output
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
min = 0
tmax = 0
max = int(len(numlist) - 1)
while (max - min) > 1:
if numlist[max] > value:
tmax = max
max = int((min + max) / 2)
if max % 1 != 0:
max += .5
else:
min = max
max = tmax
for R in range (int(min), int(tmax)):
if numlist[R] == value:
exists = "True"
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')
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,
'RanchoBernardo':50
},
'Westview':{
'DelNorte':15,
'MtCarmel':35,
'Poway':25,
'RanchoBernardo': 45
},
'MtCarmel':{
'Westview':35,
'DelNorte':20,
'Poway':40,
'RanchoBernardo':30
},
'Poway':{
'Westview':25,
'MtCarmel':40,
'DelNorte':35,
'RanchoBernardo':15
},
'RanchoBernardo':{
'Westview':45,
'MtCarmel':30,
'Poway':15,
'DelNorte':50
}
}
def fastestroute(start,data):
path = []
unused = ['DelNorte','Westview','MtCarmel','Poway','RanchoBernardo']
cd = {} #current dictionary, sub dictionary of current school
current = start #current school
plen = 0 #path length
for a in unused: # set first school
if start == a:
path.append(a)
unused.remove(a)
while len(unused) > 0: # find next school with smallest path that hasnt been visited yet.\
min = 60
mname = ''
cd = data[current]
for b in unused:
if cd[b] < min:
min = cd[b]
mname = b
plen += min
path.append(mname)
unused.remove(mname)
current = mname
plen += data[path[4]][path[0]] # add starting school to the end
path.append(path[0])
print(path)
print("path length: " + str(plen))
fastestroute('DelNorte',dataset)