10

为像这样的字符串找到第一个非重复字符的最佳空间和时间效率解决方案是aabccbdcbe什么?

这里的答案是d。所以让我印象深刻的一点是,它可以通过两种方式完成:

  1. 对于每个索引,我循环 i-1 次并检查该字符是否再次出现。但这不是有效的:这种方法的增长是 O(N^2) 其中 N 是字符串的长度。
  2. 另一种可能的好方法是,如果我可以形成一棵树或任何其他 ds,以便我可以根据权重(出现次数)对角色进行排序。这可能只需要我一个长度为 N 的循环通过字符串来形成结构。这只是 O(N) + O(构建树或任何 ds 的时间)。
4

7 回答 7

18

这是一个非常简单的O(n)解决方案:

def fn(s):
  order = []
  counts = {}
  for x in s:
    if x in counts:
      counts[x] += 1
    else:
      counts[x] = 1 
      order.append(x)
  for x in order:
    if counts[x] == 1:
      return x
  return None

我们遍历字符串一次。当我们遇到一个新字符时,我们将其存储counts1,并将其附加到order。当我们遇到以前见过的字符时,我们会在counts. 最后,我们循环order直到找到一个值为1in的字符counts并返回它。

于 2013-03-19T17:34:56.650 回答
8

如果字符只出现一次,列表推导会按照它们出现的顺序为您提供字符:

In [61]: s = 'aabccbdcbe'

In [62]: [a for a in s if s.count(a) == 1]
Out[62]: ['d', 'e']

然后只返回这个的第一个条目:

In [63]: [a for a in s if s.count(a) == 1][0]
Out[63]: 'd'

如果您只需要第一个条目,生成器也可以工作:

In [69]: (a for a in s if s.count(a) == 1).next()
Out[69]: 'd'
于 2013-03-19T09:40:11.227 回答
7

我认为从字符串中删除重复字符可能会显着减少操作次数。例如:

s = "aabccbdcbe"
while s != "":
    slen0 = len(s)
    ch = s[0]
    s = s.replace(ch, "")
    slen1 = len(s)
    if slen1 == slen0-1:
        print ch
        break;
else:
    print "No answer"
于 2013-03-19T10:03:51.517 回答
5

搜索速度取决于几个因素:

  • 字符串的长度
  • 之前没有一次性字符的位置
  • 此位置之后的字符串大小
  • 字符串中出现的不同字符的数量

.

在下面的代码中,我首先在 两个字符串s
的帮助下定义了一个字符串random.choice()和一组名为 的一次性出现的字符unik ,并将其连接起来: 其中:
s1s2s1 + s2

  • s1是一个长度字符串,nwo其中没有任何一次性出现的字符
  • s2是一个长度字符串,nwi其中有一次性出现的字符

.

#### creation of s from s1 and s2 #########

from random import choice

def without(u,n):
    letters = list('abcdefghijklmnopqrstuvwxyz')
    for i in xrange(n):
        c = choice(letters)
        if c not in unik:
            yield c

def with_un(u,n):
    letters = list('abcdefghijklmnopqrstuvwxyz')
    ecr = []
    for i in xrange(n):
        c = choice(letters)
        #ecr.append('%d %s  len(letters) == %d' % (i,c,len(letters)))
        yield c
        if c in unik:
            letters.remove(c)
    #print '\n'.join(ecr)

unik = 'ekprw'
nwo,nwi = 0,500
s1 = ''.join(c for c in without(unik,nwo))
s2 = ''.join(c for c in with_un(unik,nwi))
s = s1 + s2

if s1:
    print '%-27ss2 : %d chars' % ('s1 : %d chars' % len(s1),len(s2))
    for el in 'ekprw':
        print ('s1.count(%s) == %-12ds2.count(%s) == %d'
               % (el,s1.count(el),el,s2.count(el)))
    others = [c for c in 'abcdefghijklmnopqrstuvwxyz' if c not in unik]
    print 's1.count(others)>1 %s' % all(s1.count(c)>1 for c in others)
else:
    print "s1 == ''     len(s2) == %d" % len(s2)
    for el in 'ekprw':
        print ('   -         s2.count(%s) == %d'
               % (el,s2.count(el)))
print 'len of s  == %d\n' % len(s)

然后是基准测试。
改变数字nwonwi我们可以看到对速度的影响:

### benchmark of three solutions #################

from time import clock


# Janne Karila
from collections import Counter, OrderedDict
class OrderedCounter(Counter, OrderedDict):
    pass
te = clock()
c = OrderedCounter(s)
rjk = (item for item, count in c.iteritems() if count == 1).next()
tf = clock()-te
print 'Janne Karila  %.5f    found: %s' % (tf,rjk)

# eyquem
te = clock()
candidates = set(s)
li = []
for x in s:
    if x in candidates:
        li.append(x)
        candidates.remove(x)
    elif x in li:
        li.remove(x)
rey = li[0]
tf = clock()-te
print 'eyquem        %.5f    found: %s' % (tf,rey)

# TyrantWave
te = clock()
rty = (a for a in s if s.count(a) == 1).next()
tf = clock()-te
print 'TyrantWave    %.5f    found: %s' % (tf,rty)

.

一些结果

对于s1空长度,nwo = 0 和 nwi = 50:

s1 == ''     len(s2) == 50
   -         s2.count(e) == 1
   -         s2.count(k) == 1
   -         s2.count(p) == 1
   -         s2.count(r) == 1
   -         s2.count(w) == 1
len of s  == 50

Janne Karila  0.00077    found: e
eyquem        0.00013    found: e
TyrantWave    0.00005    found: e

TyrantWave 的解决方案更快,因为第一个出现的字符会在字符串的第一个位置快速找到

.

使用 nwo = 300 和 nwi = 50
(以下为 401 个字符,s1因为在构造 of 期间未保留一次性出现的字符s1,请参阅函数 without() )

s1 : 245 chars             s2 : 50 chars
s1.count(e) == 0           s2.count(e) == 1
s1.count(k) == 0           s2.count(k) == 1
s1.count(p) == 0           s2.count(p) == 1
s1.count(r) == 0           s2.count(r) == 1
s1.count(w) == 0           s2.count(w) == 1
s1.count(others)>1 True
len of s  == 295

Janne Karila  0.00167    found: e
eyquem        0.00030    found: e
TyrantWave    0.00042    found: e

这次 TyrantWave 的解决方案比我的要长,因为它必须计算第一部分中所有字符的出现次数,s也就是说s1其中没有一次性出现的字符(它们在第二部分中s2
但是,要用我的解决方案获得更短的时间,nwo需要明显大于nwi

.

nwo = 300 和 nwi = 5000

s1 : 240 chars             s2 : 5000 chars
s1.count(e) == 0           s2.count(e) == 1
s1.count(k) == 0           s2.count(k) == 1
s1.count(p) == 0           s2.count(p) == 1
s1.count(r) == 0           s2.count(r) == 1
s1.count(w) == 0           s2.count(w) == 1
s1.count(others)>1 True
len of s  == 5240

Janne Karila  0.01510    found: p
eyquem        0.00534    found: p
TyrantWave    0.00294    found: p

如果增加了长度s2,那么 TyrantWave 的解决方案又会更好。

.

总结你想要的

.

编辑

罗马的好主意!
我在基准测试中添加了 Roman 的解决方案,它赢了!

我还做了一些微小的修改来改进他的解决方案。

# Roman Fursenko
srf = s[:]
te = clock()
while srf != "":
    slen0 = len(srf)
    ch = srf[0]
    srf = srf.replace(ch, "")
    slen1 = len(srf)
    if slen1 == slen0-1:
        rrf = ch
        break
else:
    rrf = "No answer"
tf = clock()-te
print 'Roman Fursenko %.6f    found: %s' % (tf,rrf)

# Roman Fursenko improved
srf = s[:]
te = clock()
while not(srf is ""):
    slen0 = len(srf)
    srf = srf.replace(srf[0], "")
    if len(srf) == slen0-1:
        rrf = ch
        break
else:
    rrf = "No answer"
tf = clock()-te
print 'Roman improved %.6f    found: %s' % (tf,rrf)

print '\nindex of %s in the string :  %d' % (rty,s.index(rrf))

.

结果是:

.

s1 == ''     len(s2) == 50
   -         s2.count(e) == 1
   -         s2.count(k) == 1
   -         s2.count(p) == 1
   -         s2.count(r) == 1
   -         s2.count(w) == 1
len of s  == 50

Janne Karila   0.0032538    found: r
eyquem         0.0001249    found: r
TyrantWave     0.0000534    found: r
Roman Fursenko 0.0000299    found: r
Roman improved 0.0000263    found: r

index of r in the string :  1

s1 == ''     len(s2) == 50
   -         s2.count(e) == 1
   -         s2.count(k) == 0
   -         s2.count(p) == 1
   -         s2.count(r) == 1
   -         s2.count(w) == 1
len of s  == 50

Janne Karila   0.0008183    found: a
eyquem         0.0001285    found: a
TyrantWave     0.0000550    found: a
Roman Fursenko 0.0000433    found: a
Roman improved 0.0000391    found: a

index of a in the string :  4

>

s1 : 240 chars             s2 : 50 chars
s1.count(e) == 0           s2.count(e) == 1
s1.count(k) == 0           s2.count(k) == 0
s1.count(p) == 0           s2.count(p) == 1
s1.count(r) == 0           s2.count(r) == 1
s1.count(w) == 0           s2.count(w) == 1
s1.count(others)>1 True
len of s  == 290

Janne Karila   0.0016390    found: e
eyquem         0.0002956    found: e
TyrantWave     0.0004112    found: e
Roman Fursenko 0.0001428    found: e
Roman improved 0.0001277    found: e

index of e in the string :  242

s1 : 241 chars             s2 : 5000 chars
s1.count(e) == 0           s2.count(e) == 1
s1.count(k) == 0           s2.count(k) == 1
s1.count(p) == 0           s2.count(p) == 1
s1.count(r) == 0           s2.count(r) == 1
s1.count(w) == 0           s2.count(w) == 1
s1.count(others)>1 True
len of s  == 5241

Janne Karila   0.0148231    found: r
eyquem         0.0053283    found: r
TyrantWave     0.0030166    found: r
Roman Fursenko 0.0007414    found: r
Roman improved 0.0007230    found: r

index of r in the string :  250

感谢 Roman 的代码,我学到了一些东西:
s.replace()创建一个新字符串,因此我认为这是一种缓慢的方法。
但是,我不知道是什么原因,这是一种非常快速的方法。

.

编辑 2

Oin 的解决方案是最糟糕的:

# Oin
from operator import itemgetter
seen = set()
only_appear_once = dict()
te = clock()
for i, x in enumerate(s):
  if x in seen and x in only_appear_once:
    only_appear_once.pop(x)
  else:
    seen.add(x)
    only_appear_once[x] = i
  fco = min(only_appear_once.items(),key=itemgetter(1))[0]
tf = clock()-te
print 'Oin            %.7f    found: %s' % (tf,fco)

结果

s1 == ''     len(s2) == 50
Oin            0.0007124    found: e
Janne Karila   0.0008057    found: e
eyquem         0.0001252    found: e
TyrantWave     0.0000712    found: e
Roman Fursenko 0.0000335    found: e
Roman improved 0.0000335    found: e

index of e in the string :  2


s1 : 237 chars             s2 : 50 chars
Oin            0.0029783    found: k
Janne Karila   0.0014714    found: k
eyquem         0.0002889    found: k
TyrantWave     0.0005598    found: k
Roman Fursenko 0.0001458    found: k
Roman improved 0.0001372    found: k

index of k in the string :  246


s1 : 236 chars             s2 : 5000 chars
Oin            0.0801739    found: e
Janne Karila   0.0155715    found: e
eyquem         0.0044623    found: e
TyrantWave     0.0027548    found: e
Roman Fursenko 0.0007255    found: e
Roman improved 0.0007199    found: e

index of e in the string :  244
于 2013-03-19T13:36:49.527 回答
3

collections.Counter有效计数(*)并collections.OrderedDict记住第一次看到项目的顺序。让我们使用多重继承来组合好处:

from collections import Counter, OrderedDict

class OrderedCounter(Counter, OrderedDict):
    pass

def first_unique(iterable):
    c = OrderedCounter(iterable)
    for item, count in c.iteritems():
        if count == 1:
            return item

print first_unique('aabccbdcbe')
#d            
print first_unique('abccbdcbe')            
#a

Counter使用它的超类dict来存储计数。定义方法解析顺序之间的class OrderedCounter(Counter, OrderedDict)插入,增加记住插入顺序的能力。OrderedDictCounterdict

(*) 从这个意义上说,这是 O(n) 和高效的,但不是最快的解决方案,如基准所示。

于 2013-03-19T10:09:21.053 回答
0

这是一种使用good一组字符和bad一组字符(出现多次)的方法:

import timeit
import collections
import operator
import random

s = [chr(i) for i in range(ord('a'), ord('z')) for j in range(100)] + ['z']

random.shuffle(s)
s = ''.join(s)

def good_bad_sets(s):
    setbad = set()
    setgood = set()
    for char in s:
        if(char not in setbad):
            if(char in setgood):
                setgood.remove(char)
                setbad.add(char)
            else:
                setgood.add(char)
    return s[min([s.index(char) for char in setgood])] if len(s) > 0 else None

def app_once(s):
    seen = set()
    only_appear_once = set()
    for i in s:
      if i in seen:
        only_appear_once.discard(i)
      else:
        seen.add(i)
        only_appear_once.add(i)
    return s[min([s.index(char) for char in only_appear_once])] if len(only_appear_once) > 0 else None

print('Good bad sets: %ss' % timeit.Timer(lambda : good_bad_sets(s)).timeit(100))
print('Oin\'s approach: %ss' % timeit.Timer(lambda : app_once(s)).timeit(100))
print('LC: %ss' % timeit.Timer(lambda : [a for a in s if s.count(a) == 1][0]).timeit(100))

我将它与 LC 方法进行了比较,大约 50 个字符,good并且bad设置方法变得更快。这种方法与Oin与 LC 的比较:

Good bad sets: 0.0419239997864s
Oin's approach: 0.0803039073944s
LC: 0.647999048233s
于 2013-03-19T10:04:20.233 回答
-1

所以从问题的定义来看,很明显你需要一个 O(n) 的解决方案,这意味着只遍历列表一次。所有使用计数形式的解决方案都是错误的,因为它们在该操作中再次遍历列表。因此,您需要自己跟踪计数。

如果您在该字符串中只有字符,那么您无需担心存储,您可以将字符用作字典中的键。该 dict 中的值将是字符串 s 中字符的索引。最后,我们必须通过计算字典值的最小值来查看哪个是第一个。这是一个(可能)比第一个更短的列表上的 O(n) 操作。

总数仍为 O(c*n),因此为 O(n)。

from operator import itemgetter

seen = set()
only_appear_once = dict()

for i, x in enumerate(s):
  if x in seen and x in only_appear_once:
    only_appear_once.pop(x)
  else:
    seen.add(x)
    only_appear_once[x] = i

first_count_of_one = only_appear_once[min(only_appear_once.values(), key=itemgetter(1))]
于 2013-03-19T09:56:18.137 回答