Optimization of N digits all permutations sum algorithm - python

[Note: Programming Challenge]
Challenge description:
Input: List of Digits 1, 5, 6, 2, 7, 4
Non-repeated and no zeros(digits 1-9 are all valid). The goal is to create all permutations and sum them all. I used itertools permutations for this. I was able to do some test assertions with 7,8, and 9digits on my local machine. At 9 digits the time increases quite a bit to where the server times out at 12seconds, but my computer doesn't take that long. It just says to optmize my algorithm.
Below is an example of how arrays are formed, and itertools does this in each iteration of the inner loop.
array for the list sum (terms of arrays)
[1] 1 # arrays with only one term (7 different arrays)
[5] 5
[6] 6
[2] 2
[7] 7
[3] 3
[4] 4
[1, 5] 6 # arrays with two terms (42 different arrays)
[1, 6] 7
[1, 2] 3
[1, 7] 8
[1, 3] 4
[1, 4] 5
..... ...
[1, 5, 6] 12 # arrays with three terms(210 different arrays)
[1, 5, 2] 8
[1, 5, 7] 13
[1, 5, 3] 9
........ ...
This is what I have so far, and it gets the job done but my main bottleneck is the sum, from 8 digits to 9 digits it increases exponentially. Below function passed two tests but on the server it times out.
for i in range(1, limit + 1):
for j in permutations(digits, i):
grandSum =+ grandSum + sum(j)
And below are the results from cProfile runs, 7, 8, 9:
13778 function calls in 0.011 seconds
Ordered by: standard name
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 0.011 0.011 <string>:1(<module>)
7 0.000 0.000 0.000 0.000 GreatTotalAdditions.py:25(removefirstindex)
1 0.006 0.006 0.011 0.011 GreatTotalAdditions.py:31(gta)
1 0.000 0.000 0.011 0.011 {built-in method builtins.exec}
21 0.000 0.000 0.000 0.000 {built-in method builtins.len}
8 0.000 0.000 0.000 0.000 {built-in method builtins.print}
13699 0.004 0.000 0.004 0.000 {built-in method builtins.sum}
25 0.000 0.000 0.000 0.000 {method 'append' of 'list' objects}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
7 0.000 0.000 0.000 0.000 {method 'insert' of 'list' objects}
7 0.000 0.000 0.000 0.000 {method 'pop' of 'list' objects}
109701 function calls in 0.086 seconds
Ordered by: standard name
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 0.085 0.085 <string>:1(<module>)
11 0.000 0.000 0.000 0.000 GreatTotalAdditions.py:25(removefirstindex)
1 0.047 0.047 0.085 0.085 GreatTotalAdditions.py:31(gta)
1 0.000 0.000 0.086 0.086 {built-in method builtins.exec}
27 0.000 0.000 0.000 0.000 {built-in method builtins.len}
9 0.000 0.000 0.000 0.000 {built-in method builtins.print}
109600 0.038 0.000 0.038 0.000 {built-in method builtins.sum}
28 0.000 0.000 0.000 0.000 {method 'append' of 'list' objects}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
11 0.000 0.000 0.000 0.000 {method 'insert' of 'list' objects}
11 0.000 0.000 0.000 0.000 {method 'pop' of 'list' objects}
986553 function calls in 0.701 seconds
Ordered by: standard name
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 0.701 0.701 <string>:1(<module>)
16 0.000 0.000 0.000 0.000 GreatTotalAdditions.py:25(removefirstindex)
1 0.374 0.374 0.701 0.701 GreatTotalAdditions.py:31(gta)
1 0.000 0.000 0.701 0.701 {built-in method builtins.exec}
34 0.000 0.000 0.000 0.000 {built-in method builtins.len}
10 0.000 0.000 0.000 0.000 {built-in method builtins.print}
986409 0.327 0.000 0.327 0.000 {built-in method builtins.sum}
48 0.000 0.000 0.000 0.000 {method 'append' of 'list' objects}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
16 0.000 0.000 0.000 0.000 {method 'insert' of 'list' objects}
16 0.000 0.000 0.000 0.000 {method 'pop' of 'list' objects}
Below is where I would like some help:
Knowing the sum is taking most of the computation time. I came up across this math formula, example for a 3 digit number:
(3-1)! * (1 + 2 + 3) * (111)
And my implementation is below, bare in mind I'm new to python:
def sum_them_quick(digits):
ones = ""
digitsSum = 0
# if 3 digits then form 111
for i in range(len(digits)):
ones += "1"
for j in digits:
digitsSum = digitsSum + j
return factorial(len(digits)-1) * (digitsSum) * (int(ones))
However the results from this last function are wrong, and doesn't correspond with good results from passed tests. I'm not entirely sure if the number of permutations is different than itertools permutations method, but I'll confirm tomorrow for sure.

Related

Leetcode 1155. dictionary based memoization vs LRU Cache

I was solving leetcode 1155 which is about number of dice rolls with target sum. I was using dictionary-based memorization. Here's the exact code:
class Solution:
def numRollsToTarget(self, dices: int, faces: int, target: int) -> int:
dp = {}
def ways(t, rd):
if t == 0 and rd == 0: return 1
if t <= 0 or rd <= 0: return 0
if dp.get((t,rd)): return dp[(t,rd)]
dp[(t,rd)] = sum(ways(t-i, rd-1) for i in range(1,faces+1))
return dp[(t,rd)]
return ways(target, dices)
But this solution is invariably timing out for a combination of face and dices around 15*15
Then I found this solution which uses functools.lru_cache and the rest of it is exactly the same. This solution works very fast.
class Solution:
def numRollsToTarget(self, dices: int, faces: int, target: int) -> int:
from functools import lru_cache
#lru_cache(None)
def ways(t, rd):
if t == 0 and rd == 0: return 1
if t <= 0 or rd <= 0: return 0
return sum(ways(t-i, rd-1) for i in range(1,faces+1))
return ways(target, dices)
Earlier, I have compared and found that in most cases, lru_cache does not outperform dictionary-based cache by such a margin.
Can someone explain the reason why there is such a drastic performance difference between the two approaches?
First, running your OP code with cProfile and this is the report:
with print(numRollsToTarget2(4, 6, 20)) (OP version)
You can spot right away there're some heavy calls in ways genexpr and sum. That's prob. need close examinations and try to improve/reduce. Next posting is for similar memo version, but the calls is much less. And that version has passed w/o timeout.
35
2864 function calls (366 primitive calls) in 0.018 seconds
Ordered by: standard name
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 0.018 0.018 <string>:1(<module>)
1 0.000 0.000 0.001 0.001 dice_rolls.py:23(numRollsToTarget2)
1075/1 0.001 0.000 0.001 0.001 dice_rolls.py:25(ways)
1253/7 0.001 0.000 0.001 0.000 dice_rolls.py:30(<genexpr>)
1 0.000 0.000 0.018 0.018 dice_rolls.py:36(main)
21 0.000 0.000 0.000 0.000 rpc.py:153(debug)
3 0.000 0.000 0.017 0.006 rpc.py:216(remotecall)
3 0.000 0.000 0.000 0.000 rpc.py:226(asynccall)
3 0.000 0.000 0.016 0.005 rpc.py:246(asyncreturn)
3 0.000 0.000 0.000 0.000 rpc.py:252(decoderesponse)
3 0.000 0.000 0.016 0.005 rpc.py:290(getresponse)
3 0.000 0.000 0.000 0.000 rpc.py:298(_proxify)
3 0.000 0.000 0.016 0.005 rpc.py:306(_getresponse)
3 0.000 0.000 0.000 0.000 rpc.py:328(newseq)
3 0.000 0.000 0.000 0.000 rpc.py:332(putmessage)
2 0.000 0.000 0.001 0.000 rpc.py:559(__getattr__)
3 0.000 0.000 0.000 0.000 rpc.py:57(dumps)
1 0.000 0.000 0.001 0.001 rpc.py:577(__getmethods)
2 0.000 0.000 0.000 0.000 rpc.py:601(__init__)
2 0.000 0.000 0.016 0.008 rpc.py:606(__call__)
4 0.000 0.000 0.000 0.000 run.py:412(encoding)
4 0.000 0.000 0.000 0.000 run.py:416(errors)
2 0.000 0.000 0.017 0.008 run.py:433(write)
6 0.000 0.000 0.000 0.000 threading.py:1306(current_thread)
3 0.000 0.000 0.000 0.000 threading.py:222(__init__)
3 0.000 0.000 0.016 0.005 threading.py:270(wait)
3 0.000 0.000 0.000 0.000 threading.py:81(RLock)
3 0.000 0.000 0.000 0.000 {built-in method _struct.pack}
3 0.000 0.000 0.000 0.000 {built-in method _thread.allocate_lock}
6 0.000 0.000 0.000 0.000 {built-in method _thread.get_ident}
1 0.000 0.000 0.018 0.018 {built-in method builtins.exec}
6 0.000 0.000 0.000 0.000 {built-in method builtins.isinstance}
9 0.000 0.000 0.000 0.000 {built-in method builtins.len}
1 0.000 0.000 0.017 0.017 {built-in method builtins.print}
179/1 0.000 0.000 0.001 0.001 {built-in method builtins.sum}
3 0.000 0.000 0.000 0.000 {built-in method select.select}
3 0.000 0.000 0.000 0.000 {method '_acquire_restore' of '_thread.RLock' objects}
3 0.000 0.000 0.000 0.000 {method '_is_owned' of '_thread.RLock' objects}
3 0.000 0.000 0.000 0.000 {method '_release_save' of '_thread.RLock' objects}
3 0.000 0.000 0.000 0.000 {method 'acquire' of '_thread.RLock' objects}
6 0.016 0.003 0.016 0.003 {method 'acquire' of '_thread.lock' objects}
3 0.000 0.000 0.000 0.000 {method 'append' of 'collections.deque' objects}
2 0.000 0.000 0.000 0.000 {method 'decode' of 'bytes' objects}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
3 0.000 0.000 0.000 0.000 {method 'dump' of '_pickle.Pickler' objects}
2 0.000 0.000 0.000 0.000 {method 'encode' of 'str' objects}
201 0.000 0.000 0.000 0.000 {method 'get' of 'dict' objects}
3 0.000 0.000 0.000 0.000 {method 'getvalue' of '_io.BytesIO' objects}
3 0.000 0.000 0.000 0.000 {method 'release' of '_thread.RLock' objects}
3 0.000 0.000 0.000 0.000 {method 'send' of '_socket.socket' objects}
Then I tried to run modified/simplified version, and compare the results.
35
387 function calls (193 primitive calls) in 0.006 seconds
Ordered by: standard name
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 0.006 0.006 <string>:1(<module>)
1 0.000 0.000 0.006 0.006 dice_rolls.py:36(main)
1 0.000 0.000 0.000 0.000 dice_rolls.py:5(numRollsToTarget)
195/1 0.000 0.000 0.000 0.000 dice_rolls.py:8(dp)
21 0.000 0.000 0.000 0.000 rpc.py:153(debug)
3 0.000 0.000 0.006 0.002 rpc.py:216(remotecall)
3 0.000 0.000 0.000 0.000 rpc.py:226(asynccall)
3 0.000 0.000 0.006 0.002 rpc.py:246(asyncreturn)
3 0.000 0.000 0.000 0.000 rpc.py:252(decoderesponse)
3 0.000 0.000 0.006 0.002 rpc.py:290(getresponse)
3 0.000 0.000 0.000 0.000 rpc.py:298(_proxify)
3 0.000 0.000 0.006 0.002 rpc.py:306(_getresponse)
3 0.000 0.000 0.000 0.000 rpc.py:328(newseq)
3 0.000 0.000 0.000 0.000 rpc.py:332(putmessage)
2 0.000 0.000 0.001 0.000 rpc.py:559(__getattr__)
3 0.000 0.000 0.000 0.000 rpc.py:57(dumps)
1 0.000 0.000 0.001 0.001 rpc.py:577(__getmethods)
2 0.000 0.000 0.000 0.000 rpc.py:601(__init__)
2 0.000 0.000 0.005 0.003 rpc.py:606(__call__)
4 0.000 0.000 0.000 0.000 run.py:412(encoding)
4 0.000 0.000 0.000 0.000 run.py:416(errors)
2 0.000 0.000 0.006 0.003 run.py:433(write)
6 0.000 0.000 0.000 0.000 threading.py:1306(current_thread)
3 0.000 0.000 0.000 0.000 threading.py:222(__init__)
3 0.000 0.000 0.006 0.002 threading.py:270(wait)
3 0.000 0.000 0.000 0.000 threading.py:81(RLock)
3 0.000 0.000 0.000 0.000 {built-in method _struct.pack}
3 0.000 0.000 0.000 0.000 {built-in method _thread.allocate_lock}
6 0.000 0.000 0.000 0.000 {built-in method _thread.get_ident}
1 0.000 0.000 0.006 0.006 {built-in method builtins.exec}
6 0.000 0.000 0.000 0.000 {built-in method builtins.isinstance}
9 0.000 0.000 0.000 0.000 {built-in method builtins.len}
34 0.000 0.000 0.000 0.000 {built-in method builtins.max}
1 0.000 0.000 0.006 0.006 {built-in method builtins.print}
3 0.000 0.000 0.000 0.000 {built-in method select.select}
3 0.000 0.000 0.000 0.000 {method '_acquire_restore' of '_thread.RLock' objects}
3 0.000 0.000 0.000 0.000 {method '_is_owned' of '_thread.RLock' objects}
3 0.000 0.000 0.000 0.000 {method '_release_save' of '_thread.RLock' objects}
3 0.000 0.000 0.000 0.000 {method 'acquire' of '_thread.RLock' objects}
6 0.006 0.001 0.006 0.001 {method 'acquire' of '_thread.lock' objects}
3 0.000 0.000 0.000 0.000 {method 'append' of 'collections.deque' objects}
2 0.000 0.000 0.000 0.000 {method 'decode' of 'bytes' objects}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
3 0.000 0.000 0.000 0.000 {method 'dump' of '_pickle.Pickler' objects}
2 0.000 0.000 0.000 0.000 {method 'encode' of 'str' objects}
2 0.000 0.000 0.000 0.000 {method 'get' of 'dict' objects}
3 0.000 0.000 0.000 0.000 {method 'getvalue' of '_io.BytesIO' objects}
3 0.000 0.000 0.000 0.000 {method 'release' of '_thread.RLock' objects}
3 0.000 0.000 0.000 0.000 {method 'send' of '_socket.socket' objects}
The profiling codes are here:
import cProfile
from typing import List
def numRollsToTarget(d, f, target):
memo = {}
def dp(d, target):
if d == 0:
return 0 if target > 0 else 1
if (d, target) in memo:
return memo[(d, target)]
result = 0
for k in range(max(0, target-f), target):
result += dp(d-1, k)
memo[(d, target)] = result
return result
return dp(d, target) % (10**9 + 7)
def numRollsToTarget2(dices: int, faces: int, target: int) -> int:
dp = {}
def ways(t, rd):
if t == 0 and rd == 0: return 1
if t <= 0 or rd <= 0: return 0
if dp.get((t,rd)): return dp[(t,rd)]
dp[(t,rd)] = sum(ways(t-i, rd-1) for i in range(1,faces+1))
return dp[(t,rd)]
return ways(target, dices)
def numRollsToTarget3(dices: int, faces: int, target: int) -> int:
from functools import lru_cache
#lru_cache(None)
def ways(t, rd):
if t == 0 and rd == 0: return 1
if t <= 0 or rd <= 0: return 0
return sum(ways(t-i, rd-1) for i in range(1,faces+1))
return ways(target, dices)
def main():
print(numRollsToTarget(4, 6, 20))
#print(numRollsToTarget2(4, 6, 20))
#print(numRollsToTarget3(4, 6, 20)) # not faster than first
if __name__ == '__main__':
cProfile.run('main()')

Python Profiling - discrepancy between inlining and calling function

I have this code:
def getNeighbors(cfg, cand, adj):
c_nocfg = np.setdiff1d(cand, cfg)
deg = np.sum(adj[np.ix_(cfg, c_nocfg)], axis=0)
degidx = np.where(deg) > 0
nbs = c_nocfg[degidx]
deg = deg[degidx]
return nbs, deg
which retrieves neighbors (and their degree in a subgraph spanned by nodes in cfg) from an adjacency matrix.
Inlining the code gives reasonable performance (~10kx10k adjacency matrix as boolean array, 10k candidates in cand, subgraph cfg spanning 500 nodes): 0.02s
However, calling the function getNeighbors results in an overhead of roughly 0.5s.
Mocking
deg = np.sum(adj[np.ix_(cfg, c_nocfg)], axis=0)
with
deg = np.random.randint(500, size=c_nocfg.shape[0])
drives down the runtime of the function call to 0.002s.
Could someone explain me what causes the enormous overhead in my case - after all, the sum-operation itself is not all too costly.
Profiling output
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.466 0.466 0.488 0.488 /home/x/x/x/utils/benchmarks.py:15(getNeighbors)
1 0.000 0.000 0.019 0.019 /usr/local/lib/python2.7/dist-packages/numpy/core/fromnumeric.py:1621(sum)
1 0.000 0.000 0.019 0.019 /usr/local/lib/python2.7/dist-packages/numpy/core/_methods.py:23(_sum)
1 0.019 0.019 0.019 0.019 {method 'reduce' of 'numpy.ufunc' objects}
1 0.000 0.000 0.002 0.002 /usr/local/lib/python2.7/dist-packages/numpy/lib/arraysetops.py:410(setdiff1d)
1 0.000 0.000 0.001 0.001 /usr/local/lib/python2.7/dist-packages/numpy/lib/arraysetops.py:284(in1d)
2 0.001 0.000 0.001 0.000 {method 'argsort' of 'numpy.ndarray' objects}
2 0.000 0.000 0.001 0.000 /usr/local/lib/python2.7/dist-packages/numpy/lib/arraysetops.py:93(unique)
2 0.000 0.000 0.000 0.000 {method 'sort' of 'numpy.ndarray' objects}
1 0.000 0.000 0.000 0.000 {numpy.core.multiarray.where}
4 0.000 0.000 0.000 0.000 {numpy.core.multiarray.concatenate}
2 0.000 0.000 0.000 0.000 {method 'flatten' of 'numpy.ndarray' objects}
1 0.000 0.000 0.000 0.000 /usr/local/lib/python2.7/dist-packages/numpy/lib/index_tricks.py:26(ix_)
5 0.000 0.000 0.000 0.000 /usr/local/lib/python2.7/dist-packages/numpy/core/numeric.py:392(asarray)
5 0.000 0.000 0.000 0.000 {numpy.core.multiarray.array}
1 0.000 0.000 0.000 0.000 {isinstance}
2 0.000 0.000 0.000 0.000 {method 'reshape' of 'numpy.ndarray' objects}
1 0.000 0.000 0.000 0.000 {range}
2 0.000 0.000 0.000 0.000 {method 'append' of 'list' objects}
2 0.000 0.000 0.000 0.000 {issubclass}
2 0.000 0.000 0.000 0.000 {method 'ravel' of 'numpy.ndarray' objects}
6 0.000 0.000 0.000 0.000 {len}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
inline version:
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 0.019 0.019 /usr/local/lib/python2.7/dist-packages/numpy/core/fromnumeric.py:1621(sum)
1 0.000 0.000 0.019 0.019 /usr/local/lib/python2.7/dist-packages/numpy/core/_methods.py:23(_sum)
1 0.019 0.019 0.019 0.019 {method 'reduce' of 'numpy.ufunc' objects}
1 0.000 0.000 0.002 0.002 /usr/local/lib/python2.7/dist-packages/numpy/lib/arraysetops.py:410(setdiff1d)
1 0.000 0.000 0.001 0.001 /usr/local/lib/python2.7/dist-packages/numpy/lib/arraysetops.py:284(in1d)
2 0.001 0.000 0.001 0.000 {method 'argsort' of 'numpy.ndarray' objects}
2 0.000 0.000 0.000 0.000 /usr/local/lib/python2.7/dist-packages/numpy/lib/arraysetops.py:93(unique)
2 0.000 0.000 0.000 0.000 {method 'sort' of 'numpy.ndarray' objects}
1 0.000 0.000 0.000 0.000 {numpy.core.multiarray.where}
4 0.000 0.000 0.000 0.000 {numpy.core.multiarray.concatenate}
2 0.000 0.000 0.000 0.000 {method 'flatten' of 'numpy.ndarray' objects}
1 0.000 0.000 0.000 0.000 /usr/local/lib/python2.7/dist-packages/numpy/lib/index_tricks.py:26(ix_)
5 0.000 0.000 0.000 0.000 /usr/local/lib/python2.7/dist-packages/numpy/core/numeric.py:392(asarray)
5 0.000 0.000 0.000 0.000 {numpy.core.multiarray.array}
1 0.000 0.000 0.000 0.000 {isinstance}
2 0.000 0.000 0.000 0.000 {method 'reshape' of 'numpy.ndarray' objects}
1 0.000 0.000 0.000 0.000 {range}
2 0.000 0.000 0.000 0.000 {method 'ravel' of 'numpy.ndarray' objects}
2 0.000 0.000 0.000 0.000 {method 'append' of 'list' objects}
2 0.000 0.000 0.000 0.000 {issubclass}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
6 0.000 0.000 0.000 0.000 {len}
sample data for testing:
np.random.seed(0)
adj = np.zeros(10000*10000, dtype=np.bool)
adj[np.random.randint(low=0, high=10000*10000+1, size=100000)] = True
adj = adj.reshape((10000, 10000))
cand = np.arange(adj.shape[0])
cfgs = np.random.choice(cand, size=500)

Characters in Strings in Python

Implement a function with signature find_chars(string1, string2) that
takes two strings and returns a string that contains only the
characters found in string1 and string two in the order that they are
found in string1. Implement a version of order N*N and one of order N.
(Source: http://thereq.com/q/138/python-software-interview-question/characters-in-strings)
Here are my solutions:
Order N*N:
def find_chars_slow(string1, string2):
res = []
for char in string1:
if char in string2:
res.append(char)
return ''.join(res)
So the for loop goes through N elements, and each char in string2 check is another N operations so this gives N*N.
Order N:
from collections import defaultdict
def find_char_fast(string1, string2):
d = defaultdict(int)
for char in string2:
d[char] += 1
res = []
for char in string1:
if char in d:
res.append(char)
return ''.join(res)
First store the characters of string2 as a dictionary (O(N)). Then scan string1 (O(N)) and check if it is in the dict (O(1)). This gives a total runtime of O(2N) = O(N).
Is the above correct? Is there a faster method?
Your solution is algorithmically correct (the first is O(n**2), and the second is O(n)) but you're doing some things that are going to be possible red flags to an interviewer.
The first function is basically okay. You might get bonus points for writing it like this:
''.join([c for c in string1 if c in string2])
..which does essentially the same thing.
My problem (if I'm wearing my interviewer pants) with how you've written the second function is that you use a defaultdict where you don't care at all about the count - you only care about membership. This is the classic case for when to use a set.
seen = set(string2)
''.join([c for c in string1 if c in seen])
The way I've written these functions are going to be slightly faster than what you wrote, since list comprehensions loop in native code rather than in python bytecode. They are algorithmically the same complexity.
Your method is sound, and there is no method with time complexity less than O(N), since you obviously need to go through each character at least once.
That is not to say that there's no method that runs faster. There's no need to actually increment the numbers in the dictionary. You could, for example, use a set. You could also make further use of python's features, such as list comprehensions/generators:
def find_char_fast2(string1, string2):
s= set(string2)
return "".join( (x for x in string1 if x in s) )
The algorithms you have used are perfectly fine. There are few improvements you can do
Since you are converting the second string to a dictionary, I would recommend using set, like this
d = set(string2)
Apart from that you can use list comprehension, as a filter, like this
return "".join([char for char in string1 if char in d])
If the order of the characters in the output doesn't matter, you can simply convert both the strings to sets and simply find set difference, like this
return "".join(set(string1) - set(string2))
Hi, I am trying to profiling the various solution given here:
In my snippet, I am using a module called faker to generate fake words so i can test on very long string more than 20k characters:
Snippet:
from faker import Faker
from timeit import Timer
from collections import defaultdict
def first(string1, string2):
sets = set(string2)
return ''.join((c for c in string1 if c in sets))
def second(s1, s2):
res = []
for char in string1:
if char in string2:
res.append(char)
return ''.join(res)
def third(s1, s2):
d = defaultdict(int)
for char in string2:
d[char] += 1
res = []
for char in string1:
if char in d:
res.append(char)
return ''.join(res)
f = Faker()
string1 = ''.join(f.paragraph(nb_sentences=10000).split())
string2 = ''.join(f.paragraph(nb_sentences=10000).split())
funcs = [first, second, third]
import cProfile
print 'Length of String1: ', len(string1)
print 'Length of String2: ', len(string2)
print 'Time taken to execute:'
for f in funcs:
t = Timer(lambda: f(string1, string2))
print f.__name__, cProfile.run('t.timeit(number=100)')
Output:
Length of String1: 525133
Length of String2: 501050
Time taken to execute:
first 52513711 function calls in 18.169 seconds
Ordered by: standard name
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 0.000 0.000 <string>:1(<module>)
100 0.001 0.000 18.164 0.182 s.py:39(<lambda>)
100 1.723 0.017 18.163 0.182 s.py:5(first)
52513400 9.442 0.000 9.442 0.000 s.py:7(<genexpr>)
1 0.000 0.000 0.000 0.000 timeit.py:143(setup)
1 0.000 0.000 18.169 18.169 timeit.py:178(timeit)
1 0.005 0.005 18.169 18.169 timeit.py:96(inner)
1 0.000 0.000 0.000 0.000 {gc.disable}
1 0.000 0.000 0.000 0.000 {gc.enable}
1 0.000 0.000 0.000 0.000 {gc.isenabled}
1 0.000 0.000 0.000 0.000 {globals}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
100 6.998 0.070 16.440 0.164 {method 'join' of 'str' objects}
2 0.000 0.000 0.000 0.000 {time.time}
None
second 52513611 function calls in 22.280 seconds
Ordered by: standard name
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 22.280 22.280 <string>:1(<module>)
100 0.121 0.001 22.275 0.223 s.py:39(<lambda>)
100 16.957 0.170 22.153 0.222 s.py:9(second)
1 0.000 0.000 0.000 0.000 timeit.py:143(setup)
1 0.000 0.000 22.280 22.280 timeit.py:178(timeit)
1 0.005 0.005 22.280 22.280 timeit.py:96(inner)
1 0.000 0.000 0.000 0.000 {gc.disable}
1 0.000 0.000 0.000 0.000 {gc.enable}
1 0.000 0.000 0.000 0.000 {gc.isenabled}
1 0.000 0.000 0.000 0.000 {globals}
52513300 4.018 0.000 4.018 0.000 {method 'append' of 'list' objects}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
100 1.179 0.012 1.179 0.012 {method 'join' of 'str' objects}
2 0.000 0.000 0.000 0.000 {time.time}
None
third 52513611 function calls in 28.184 seconds
Ordered by: standard name
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 28.184 28.184 <string>:1(<module>)
100 22.847 0.228 28.059 0.281 s.py:16(third)
100 0.120 0.001 28.179 0.282 s.py:39(<lambda>)
1 0.000 0.000 0.000 0.000 timeit.py:143(setup)
1 0.000 0.000 28.184 28.184 timeit.py:178(timeit)
1 0.005 0.005 28.184 28.184 timeit.py:96(inner)
1 0.000 0.000 0.000 0.000 {gc.disable}
1 0.000 0.000 0.000 0.000 {gc.enable}
1 0.000 0.000 0.000 0.000 {gc.isenabled}
1 0.000 0.000 0.000 0.000 {globals}
52513300 4.032 0.000 4.032 0.000 {method 'append' of 'list' objects}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
100 1.180 0.012 1.180 0.012 {method 'join' of 'str' objects}
2 0.000 0.000 0.000 0.000 {time.time}
None
Conclusion:
So, the first function with comprehension is the fastest.
But when you run on strings size around 25K characters second functions wins.
Length of String1: 22959
Length of String2: 452919
Time taken to execute:
first 2296311 function calls in 2.216 seconds
Ordered by: standard name
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 0.000 0.000 <string>:1(<module>)
100 0.000 0.000 2.216 0.022 s.py:39(<lambda>)
100 1.530 0.015 2.216 0.022 s.py:5(first)
2296000 0.402 0.000 0.402 0.000 s.py:7(<genexpr>)
1 0.000 0.000 0.000 0.000 timeit.py:143(setup)
1 0.000 0.000 2.216 2.216 timeit.py:178(timeit)
1 0.000 0.000 2.216 2.216 timeit.py:96(inner)
1 0.000 0.000 0.000 0.000 {gc.disable}
1 0.000 0.000 0.000 0.000 {gc.enable}
1 0.000 0.000 0.000 0.000 {gc.isenabled}
1 0.000 0.000 0.000 0.000 {globals}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
100 0.284 0.003 0.686 0.007 {method 'join' of 'str' objects}
2 0.000 0.000 0.000 0.000 {time.time}
None
second 2296211 function calls in 0.939 seconds
Ordered by: standard name
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 0.939 0.939 <string>:1(<module>)
100 0.003 0.000 0.939 0.009 s.py:39(<lambda>)
100 0.729 0.007 0.936 0.009 s.py:9(second)
1 0.000 0.000 0.000 0.000 timeit.py:143(setup)
1 0.000 0.000 0.939 0.939 timeit.py:178(timeit)
1 0.000 0.000 0.939 0.939 timeit.py:96(inner)
1 0.000 0.000 0.000 0.000 {gc.disable}
1 0.000 0.000 0.000 0.000 {gc.enable}
1 0.000 0.000 0.000 0.000 {gc.isenabled}
1 0.000 0.000 0.000 0.000 {globals}
2295900 0.165 0.000 0.165 0.000 {method 'append' of 'list' objects}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
100 0.042 0.000 0.042 0.000 {method 'join' of 'str' objects}
2 0.000 0.000 0.000 0.000 {time.time}
None
third 2296211 function calls in 8.361 seconds
Ordered by: standard name
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 8.361 8.361 <string>:1(<module>)
100 8.145 0.081 8.357 0.084 s.py:16(third)
100 0.004 0.000 8.361 0.084 s.py:39(<lambda>)
1 0.000 0.000 0.000 0.000 timeit.py:143(setup)
1 0.000 0.000 8.361 8.361 timeit.py:178(timeit)
1 0.000 0.000 8.361 8.361 timeit.py:96(inner)
1 0.000 0.000 0.000 0.000 {gc.disable}
1 0.000 0.000 0.000 0.000 {gc.enable}
1 0.000 0.000 0.000 0.000 {gc.isenabled}
1 0.000 0.000 0.000 0.000 {globals}
2295900 0.169 0.000 0.169 0.000 {method 'append' of 'list' objects}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
100 0.043 0.000 0.043 0.000 {method 'join' of 'str' objects}
2 0.000 0.000 0.000 0.000 {time.time}
None

Testing whether a tuple has all distinct elements

I was seeking for a way to test whether a tuple has all distinct elements - so to say, it is a set and ended up with this quick and dirty solution.
def distinct ( tup):
n=0
for t in tup:
for k in tup:
#print t,k,n
if (t == k ):
n = n+1
if ( n != len(tup)):
return False
else :
return True
print distinct((1,3,2,10))
print distinct((3,3,4,2,7))
Any thinking error? Is there a builtin on tuples?
You can very easily do it as:
len(set(tup))==len(tup)
This creates a set of tup and checks if it is the same length as the original tup. The only case in which they would have the same length is if all elements in tup were unique
Examples
>>> a = (1,2,3)
>>> print len(set(a))==len(a)
True
>>> b = (1,2,2)
>>> print len(set(b))==len(b)
False
>>> c = (1,2,3,4,5,6,7,8,5)
>>> print len(set(c))==len(c)
False
In the majority of the cases, where all of the items in the tuple are hashable and support comparison (using == operator) with each other, #sshashank124's solution is what you're after:
len(set(tup))==len(tup)
For the example you posted, i.e. a tuple of ints, that would do.
Else, if the items are not hashable, but do have order defined on them (support '==', '<' operators, etc.), the best you can do is sorting them (O(NlogN) worst case), and then look for adjacent equal elements:
sorted_tup = sorted(tup)
all( x!=y for x,y in zip(sorted_tup[:-1],sorted_tup[1:]) )
Else, if the items only support equality comparison (==), the best you can do is the O(N^2) worst case algorithm, i.e. comparing every item to every other.
I would implement it this way, using itertools.combinations:
def distinct(tup):
for x,y in itertools.combinations(tup, 2):
if x == y:
return False
return True
Or as a one-liner:
all( x!=y for x,y in itertools.combinations(tup, 2) )
What about using early_exit:
This will be faster:
def distinct(tup):
s = set()
for x in tup:
if x in s:
return False
s.add(x)
return True
Ok: Here is the test and profiling with 1000 int:
#!/usr/bin/python
def distinct1(tup):
n=0
for t in tup:
for k in tup:
if (t == k ):
n = n+1
if ( n != len(tup)):
return False
else :
return True
def distinct2(tup):
return len(set(tup))==len(tup)
def distinct3(tup):
s = set()
for x in tup:
if x in s:
return False
s.add(x)
return True
import cProfile
from faker import Faker
from timeit import Timer
s = Faker()
func = [ distinct1, distinct2, distinct3 ]
tuples = tuple([ s.random_int(min=1, max=9999) for x in range(1000) ])
for fun in func:
t = Timer(lambda: fun(tuples))
print fun.__name__, cProfile.run('t.timeit(number=1000)')
Output: distinct 2 and distinct3 are almost the same.
distinct1 3011 function calls in 60.289 seconds
Ordered by: standard name
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 60.289 60.289 <string>:1(<module>)
1000 60.287 0.060 60.287 0.060 compare_tuple.py:3(distinct1)
1000 0.001 0.000 60.288 0.060 compare_tuple.py:34(<lambda>)
1 0.000 0.000 0.000 0.000 timeit.py:143(setup)
1 0.000 0.000 60.289 60.289 timeit.py:178(timeit)
1 0.001 0.001 60.289 60.289 timeit.py:96(inner)
1 0.000 0.000 0.000 0.000 {gc.disable}
1 0.000 0.000 0.000 0.000 {gc.enable}
1 0.000 0.000 0.000 0.000 {gc.isenabled}
1 0.000 0.000 0.000 0.000 {globals}
1000 0.000 0.000 0.000 0.000 {len}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
2 0.000 0.000 0.000 0.000 {time.time}
None
distinct2 4011 function calls in 0.053 seconds
Ordered by: standard name
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 0.053 0.053 <string>:1(<module>)
1000 0.052 0.000 0.052 0.000 compare_tuple.py:14(distinct2)
1000 0.000 0.000 0.053 0.000 compare_tuple.py:34(<lambda>)
1 0.000 0.000 0.000 0.000 timeit.py:143(setup)
1 0.000 0.000 0.053 0.053 timeit.py:178(timeit)
1 0.000 0.000 0.053 0.053 timeit.py:96(inner)
1 0.000 0.000 0.000 0.000 {gc.disable}
1 0.000 0.000 0.000 0.000 {gc.enable}
1 0.000 0.000 0.000 0.000 {gc.isenabled}
1 0.000 0.000 0.000 0.000 {globals}
2000 0.000 0.000 0.000 0.000 {len}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
2 0.000 0.000 0.000 0.000 {time.time}
None
distinct3 183011 function calls in 0.072 seconds
Ordered by: standard name
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.000 0.000 0.072 0.072 <string>:1(<module>)
1000 0.051 0.000 0.070 0.000 compare_tuple.py:17(distinct3)
1000 0.002 0.000 0.072 0.000 compare_tuple.py:34(<lambda>)
1 0.000 0.000 0.000 0.000 timeit.py:143(setup)
1 0.000 0.000 0.072 0.072 timeit.py:178(timeit)
1 0.000 0.000 0.072 0.072 timeit.py:96(inner)
1 0.000 0.000 0.000 0.000 {gc.disable}
1 0.000 0.000 0.000 0.000 {gc.enable}
1 0.000 0.000 0.000 0.000 {gc.isenabled}
1 0.000 0.000 0.000 0.000 {globals}
181000 0.019 0.000 0.019 0.000 {method 'add' of 'set' objects}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
2 0.000 0.000 0.000 0.000 {time.time}
None
a = (1,2,3,4,5,6,7,8,9)
b = (1,2,3,4,5,6,6,7,8,9)
def unique(tup):
i = 0
while i < len(tup):
if tup[i] in tup[i+1:]:
return False
i = i + 1
return True
unique(a)
True
unique(b)
False
Readable and works with hashable items. People seem adverse to "while". This also allows for "special cases" and filtering on attributes.

Slow conversion of binary data

I have a binary file with a particular format, described here for those that are interested. The format isn't the import thing. I can read and convert this data into the form that I want but the problem is these binary files tend to have a lot of information in them. If I am just returning the bytes as read, this is very quick (less than 1 second), but I can't do anything useful with those bytes, they need to be converted into genotypes first and that is the code that appears to be slowing things down.
The conversion for a series of bytes into genotypes is as follows
h = ['%02x' % ord(b) for b in currBytes]
b = ''.join([bin(int(i, 16))[2:].zfill(8)[::-1] for i in h])[:nBits]
genotypes = [b[i:i+2] for i in range(0, len(b), 2)]
map = {'00': 0, '01': 1, '11': 2, '10': None}
return [map[i] for i in genotypes]
What I am hoping is that there is a faster way to do this? Any ideas? Below are the results of running python -m cProfile test.py where test.py is calling a reader object I have written to read these files.
vlan1711:src davykavanagh$ python -m cProfile test.py
183, 593483, 108607389, 366, 368, 46
that took 93.6410450935
86649088 function calls in 96.396 seconds
Ordered by: standard name
ncalls tottime percall cumtime percall filename:lineno(function)
1 1.248 1.248 2.753 2.753 plinkReader.py:13(__init__)
1 0.000 0.000 0.000 0.000 plinkReader.py:47(plinkReader)
1 0.000 0.000 0.000 0.000 plinkReader.py:48(__init__)
1 0.000 0.000 0.000 0.000 plinkReader.py:5(<module>)
1 0.000 0.000 0.000 0.000 plinkReader.py:55(__iter__)
593484 77.634 0.000 91.477 0.000 plinkReader.py:58(next)
1 0.000 0.000 0.000 0.000 plinkReader.py:71(SNP)
593483 1.123 0.000 1.504 0.000 plinkReader.py:75(__init__)
1 0.000 0.000 0.000 0.000 plinkReader.py:8(plinkFiles)
1 0.000 0.000 0.000 0.000 plinkReader.py:85(Person)
183 0.000 0.000 0.001 0.000 plinkReader.py:89(__init__)
1 2.166 2.166 96.396 96.396 test.py:5(<module>)
27300218 5.909 0.000 5.909 0.000 {bin}
593483 0.080 0.000 0.080 0.000 {len}
1 0.000 0.000 0.000 0.000 {math.ceil}
1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}
2 0.000 0.000 0.000 0.000 {method 'format' of 'str' objects}
593483 0.531 0.000 0.531 0.000 {method 'join' of 'str' objects}
593485 0.588 0.000 0.588 0.000 {method 'read' of 'file' objects}
593666 0.257 0.000 0.257 0.000 {method 'rsplit' of 'str' objects}
593666 0.125 0.000 0.125 0.000 {method 'rstrip' of 'str' objects}
27300218 4.098 0.000 4.098 0.000 {method 'zfill' of 'str' objects}
3 0.000 0.000 0.000 0.000 {open}
27300218 1.820 0.000 1.820 0.000 {ord}
593483 0.817 0.000 0.817 0.000 {range}
2 0.000 0.000 0.000 0.000 {time.time}
You are slowing things down by creating lists and large strings you don't need. You are just examining bits of the bytes and convert two-bit groups into numbers. That can be achieved much simpler, e. g. by this code:
def convert(currBytes, nBits):
for byte in currBytes:
for p in range(4):
bits = (ord(byte) >> (p*2)) & 3
yield None if bits == 1 else 1 if bits == 2 else 2 if bits == 3 else 0
nBits -= 2
if nBits <= 0:
raise StopIteration()
In case you really need a list in the end, just use
list(convert(currBytes, nBits))
But I guess there can be cases in which you just want to iterate over the results:
for blurp in convert(currBytes, nBits):
# handle your blurp (0, 1, 2, or None)

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