Created
March 28, 2019 14:26
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#!/usr/bin/env python3 | |
import math | |
import time | |
def isPrime(n): | |
max_divisor = math.floor(math.sqrt(n)) | |
for d in range(2, max_divisor+1): | |
if n % d == 0: | |
return False | |
return True | |
def getNextSmallerPrime(n): | |
for i in range(n-1, 0, -1): | |
if isPrime(i): | |
return i | |
return 0 | |
def bfs_dynamic(leftOver, currentNumber, dynamicResults, dynamicNextN): # breadth first search | |
# We solve the same problem over and over again, therefore solve it using | |
# references. | |
# Get dynamic data of current number | |
dynamicDataForCurrentNumber = dynamicResults.get(currentNumber) | |
if dynamicDataForCurrentNumber is None: | |
dynamicDataForCurrentNumber = dict() | |
dynamicResults[currentNumber] = dynamicDataForCurrentNumber | |
# If we already computed the result, return it | |
dynamicResult = dynamicDataForCurrentNumber.get(leftOver) | |
if dynamicResult is not None: | |
return dynamicResult | |
# Get next smaller prime, also dynamic | |
nextN = dynamicNextN.get(currentNumber) | |
if nextN is None: | |
nextN = getNextSmallerPrime(currentNumber) | |
dynamicNextN[currentNumber] = nextN | |
# Compute all possible results for currentNumber in leftover: | |
resultList = [] | |
numResults = 0 | |
subLeftOver = leftOver - currentNumber | |
# If adding one of the current number makes it complete, add it to the results | |
if subLeftOver == 0: | |
resultList.append([currentNumber]) | |
numResults += 1 | |
# Otherwise, try with another number of the same type | |
elif subLeftOver > 0: | |
subResult, numSubResults = bfs_dynamic(subLeftOver, | |
currentNumber, | |
dynamicResults, | |
dynamicNextN) | |
resultList.append([currentNumber, subResult]) | |
numResults += numSubResults | |
# Iterate down to next prime | |
if nextN != 0: | |
subResult, numSolutions = bfs_dynamic(leftOver, | |
nextN, | |
dynamicResults, | |
dynamicNextN) | |
nextResult = [subResult] | |
resultList.append(nextResult) | |
numResults += numSolutions | |
# Store result in dynamic array | |
dynamicResult = (resultList, numResults) | |
dynamicDataForCurrentNumber[leftOver] = dynamicResult | |
return dynamicResult | |
def convertDynamicStructureToArrays(results, parentPrefix=[], arrayResults=[]): | |
for result in results: | |
prefix = [] | |
hadList = False | |
for resultElement in result: | |
if isinstance(resultElement, list): | |
hadList = True | |
convertDynamicStructureToArrays(resultElement, | |
parentPrefix + prefix, | |
arrayResults) | |
else: | |
prefix += [resultElement] | |
if not hadList: | |
arrayResults.append(parentPrefix + prefix) | |
return arrayResults | |
def main(): | |
n = 5 | |
start_time = time.perf_counter() | |
dynamicResults = dict() | |
dynamicNextN = dict() | |
results, numSolutions = bfs_dynamic(n, | |
getNextSmallerPrime(n+1), | |
dynamicResults, | |
dynamicNextN) | |
end_time = time.perf_counter() | |
print("Num Solutions:", numSolutions) | |
# Converting the result to actual arrays takes the longest time. | |
# If you just need to iterate through the result, you don't need to convert, | |
# you can directly work on the dynamic structure. | |
# But it's quite complicated. | |
arrayResults = convertDynamicStructureToArrays(results) | |
for result in arrayResults: | |
print(result) | |
print("--- %s milliseconds ---" % (1000*(end_time - start_time))) | |
if __name__ == "__main__": | |
main() |
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