给定一个字符串s,打印出给定字符串的所有可能的子序列迭代的方式。我们已经讨论了递归方法来打印字符串的所有子序列。
例子:
Input : abc
Output : a, b, c, ab, ac, bc, abc
Input : aab
Output : a, b, aa, ab, aab
方法1:
在这里,我们讨论与Power Set相似的更容易,更简单的迭代方法。我们使用从1到2 ^ length – 1的二进制表示形式的位模式。
输入=“ abc”
考虑1到(2 ^ 3-1),即1到7的二进制表示形式。
从二进制表示形式的左(MSB)到右侧(LSB)开始,并将与二进制表示形式的位值1相对应的输入字符串中的字符追加到Final子序列字符串sub中。
例子:
001 => abc。只有c对应于比特1。因此,子序列= c。
101 => abc。 a和c对应于比特1。因此,子序列= ac。
binary_representation(1)= 001 => c
binary_representation(2)= 010 => b
binary_representation(3)= 011 => bc
binary_representation(4)= 100 =>一个
binary_representation(5)= 101 =>交流电
binary_representation(6)= 110 => ab
binary_representation(7)= 111 => abc
下面是上述方法的实现:
C++
// C++ program to print all Subsequences
// of a string in iterative manner
#include
using namespace std;
// function to find subsequence
string subsequence(string s, int binary, int len)
{
string sub = "";
for (int j = 0; j < len; j++)
// check if jth bit in binary is 1
if (binary & (1 << j))
// if jth bit is 1, include it
// in subsequence
sub += s[j];
return sub;
}
// function to print all subsequences
void possibleSubsequences(string s){
// map to store subsequence
// lexicographically by length
map > sorted_subsequence;
int len = s.size();
// Total number of non-empty subsequence
// in string is 2^len-1
int limit = pow(2, len);
// i=0, corresponds to empty subsequence
for (int i = 1; i <= limit - 1; i++) {
// subsequence for binary pattern i
string sub = subsequence(s, i, len);
// storing sub in map
sorted_subsequence[sub.length()].insert(sub);
}
for (auto it : sorted_subsequence) {
// it.first is length of Subsequence
// it.second is set
cout << "Subsequences of length = "
<< it.first << " are:" << endl;
for (auto ii : it.second)
// ii is iterator of type set
cout << ii << " ";
cout << endl;
}
}
// driver function
int main()
{
string s = "aabc";
possibleSubsequences(s);
return 0;
}
Java
// Java program to print all Subsequences
// of a String in iterative manner
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.SortedMap;
import java.util.TreeMap;
class Graph{
// Function to find subsequence
static String subsequence(String s,
int binary,
int len)
{
String sub = "";
for(int j = 0; j < len; j++)
// Check if jth bit in binary is 1
if ((binary & (1 << j)) != 0)
// If jth bit is 1, include it
// in subsequence
sub += s.charAt(j);
return sub;
}
// Function to print all subsequences
static void possibleSubsequences(String s)
{
// Map to store subsequence
// lexicographically by length
SortedMap> sorted_subsequence = new TreeMap>();
int len = s.length();
// Total number of non-empty subsequence
// in String is 2^len-1
int limit = (int) Math.pow(2, len);
// i=0, corresponds to empty subsequence
for(int i = 1; i <= limit - 1; i++)
{
// Subsequence for binary pattern i
String sub = subsequence(s, i, len);
// Storing sub in map
if (!sorted_subsequence.containsKey(sub.length()))
sorted_subsequence.put(
sub.length(), new HashSet<>());
sorted_subsequence.get(
sub.length()).add(sub);
}
for(Map.Entry> it : sorted_subsequence.entrySet())
{
// it.first is length of Subsequence
// it.second is set
System.out.println("Subsequences of length = " +
it.getKey() + " are:");
for(String ii : it.getValue())
// ii is iterator of type set
System.out.print(ii + " ");
System.out.println();
}
}
// Driver code
public static void main(String[] args)
{
String s = "aabc";
possibleSubsequences(s);
}
}
// This code is contributed by sanjeev2552
Python3
# Python3 program to print all Subsequences
# of a string in iterative manner
# function to find subsequence
def subsequence(s, binary, length):
sub = ""
for j in range(length):
# check if jth bit in binary is 1
if (binary & (1 << j)):
# if jth bit is 1, include it
# in subsequence
sub += s[j]
return sub
# function to print all subsequences
def possibleSubsequences(s):
# map to store subsequence
# lexicographically by length
sorted_subsequence = {}
length = len(s)
# Total number of non-empty subsequence
# in string is 2^len-1
limit = 2 ** length
# i=0, corresponds to empty subsequence
for i in range(1, limit):
# subsequence for binary pattern i
sub = subsequence(s, i, length)
# storing sub in map
if len(sub) in sorted_subsequence.keys():
sorted_subsequence[len(sub)] = \
tuple(list(sorted_subsequence[len(sub)]) + [sub])
else:
sorted_subsequence[len(sub)] = [sub]
for it in sorted_subsequence:
# it.first is length of Subsequence
# it.second is set
print("Subsequences of length =", it, "are:")
for ii in sorted(set(sorted_subsequence[it])):
# ii is iterator of type set
print(ii, end = ' ')
print()
# Driver Code
s = "aabc"
possibleSubsequences(s)
# This code is contributed by ankush_953
C++
// C++ code all Subsequences of a
// string in iterative manner
#include
using namespace std;
// function to find subsequence
string subsequence(string s, int binary)
{
string sub = "";
int pos;
// loop while binary is greater than 0
while(binary>0)
{
// get the position of rightmost set bit
pos=log2(binary&-binary)+1;
// append at beginning as we are
// going from LSB to MSB
sub=s[pos-1]+sub;
// resets bit at pos in binary
binary= (binary & ~(1 << (pos-1)));
}
reverse(sub.begin(),sub.end());
return sub;
}
// function to print all subsequences
void possibleSubsequences(string s){
// map to store subsequence
// lexicographically by length
map > sorted_subsequence;
int len = s.size();
// Total number of non-empty subsequence
// in string is 2^len-1
int limit = pow(2, len);
// i=0, corresponds to empty subsequence
for (int i = 1; i <= limit - 1; i++) {
// subsequence for binary pattern i
string sub = subsequence(s, i);
// storing sub in map
sorted_subsequence[sub.length()].insert(sub);
}
for (auto it : sorted_subsequence) {
// it.first is length of Subsequence
// it.second is set
cout << "Subsequences of length = "
<< it.first << " are:" << endl;
for (auto ii : it.second)
// ii is iterator of type set
cout << ii << " ";
cout << endl;
}
}
// driver function
int main()
{
string s = "aabc";
possibleSubsequences(s);
return 0;
}
Python3
# Python3 program to print all Subsequences
# of a string in an iterative manner
from math import log2, floor
# function to find subsequence
def subsequence(s, binary):
sub = ""
# loop while binary is greater than
while(binary > 0):
# get the position of rightmost set bit
pos=floor(log2(binary&-binary) + 1)
# append at beginning as we are
# going from LSB to MSB
sub = s[pos - 1] + sub
# resets bit at pos in binary
binary= (binary & ~(1 << (pos - 1)))
sub = sub[::-1]
return sub
# function to print all subsequences
def possibleSubsequences(s):
# map to store subsequence
# lexicographically by length
sorted_subsequence = {}
length = len(s)
# Total number of non-empty subsequence
# in string is 2^len-1
limit = 2 ** length
# i=0, corresponds to empty subsequence
for i in range(1, limit):
# subsequence for binary pattern i
sub = subsequence(s, i)
# storing sub in map
if len(sub) in sorted_subsequence.keys():
sorted_subsequence[len(sub)] = \
tuple(list(sorted_subsequence[len(sub)]) + [sub])
else:
sorted_subsequence[len(sub)] = [sub]
for it in sorted_subsequence:
# it.first is length of Subsequence
# it.second is set
print("Subsequences of length =", it, "are:")
for ii in sorted(set(sorted_subsequence[it])):
# ii is iterator of type set
print(ii, end = ' ')
print()
# Driver Code
s = "aabc"
possibleSubsequences(s)
# This code is contributed by ankush_953
输出:
Subsequences of length = 1 are:
a b c
Subsequences of length = 2 are:
aa ab ac bc
Subsequences of length = 3 are:
aab aac abc
Subsequences of length = 4 are:
aabc
时间复杂度: ,其中n是查找子序列的字符串的长度,l是二进制字符串的长度。
方法2:
方法是获取最右边的设置位的位置,并在将给定字符串中的相应字符附加到子序列后重置该位,并将重复相同的操作,直到相应的二进制模式没有设置位为止。
如果输入为s =“ abc”
考虑1到(2 ^ 3-1),即1到7的二进制表示形式。
001 => abc。只有c对应于比特1。因此,子序列= c
101 => abc。 a和c对应于比特1。因此,子序列= ac。
让我们使用5的二进制表示形式,即101。
最右边的位在位置1,在sub = c的开头附加字符,重置位置1 => 100
最右边的位在位置3,在sub = ac的开头附加字符,重置位置3 => 000
由于现在我们没有剩余的设置位,因此我们将停止计算子序列。
例子 :
binary_representation(1)= 001 => c
binary_representation(2)= 010 => b
binary_representation(3)= 011 => bc
binary_representation(4)= 100 =>一个
binary_representation(5)= 101 =>交流电
binary_representation(6)= 110 => ab
binary_representation(7)= 111 => abc
下面是上述方法的实现:
C++
// C++ code all Subsequences of a
// string in iterative manner
#include
using namespace std;
// function to find subsequence
string subsequence(string s, int binary)
{
string sub = "";
int pos;
// loop while binary is greater than 0
while(binary>0)
{
// get the position of rightmost set bit
pos=log2(binary&-binary)+1;
// append at beginning as we are
// going from LSB to MSB
sub=s[pos-1]+sub;
// resets bit at pos in binary
binary= (binary & ~(1 << (pos-1)));
}
reverse(sub.begin(),sub.end());
return sub;
}
// function to print all subsequences
void possibleSubsequences(string s){
// map to store subsequence
// lexicographically by length
map > sorted_subsequence;
int len = s.size();
// Total number of non-empty subsequence
// in string is 2^len-1
int limit = pow(2, len);
// i=0, corresponds to empty subsequence
for (int i = 1; i <= limit - 1; i++) {
// subsequence for binary pattern i
string sub = subsequence(s, i);
// storing sub in map
sorted_subsequence[sub.length()].insert(sub);
}
for (auto it : sorted_subsequence) {
// it.first is length of Subsequence
// it.second is set
cout << "Subsequences of length = "
<< it.first << " are:" << endl;
for (auto ii : it.second)
// ii is iterator of type set
cout << ii << " ";
cout << endl;
}
}
// driver function
int main()
{
string s = "aabc";
possibleSubsequences(s);
return 0;
}
Python3
# Python3 program to print all Subsequences
# of a string in an iterative manner
from math import log2, floor
# function to find subsequence
def subsequence(s, binary):
sub = ""
# loop while binary is greater than
while(binary > 0):
# get the position of rightmost set bit
pos=floor(log2(binary&-binary) + 1)
# append at beginning as we are
# going from LSB to MSB
sub = s[pos - 1] + sub
# resets bit at pos in binary
binary= (binary & ~(1 << (pos - 1)))
sub = sub[::-1]
return sub
# function to print all subsequences
def possibleSubsequences(s):
# map to store subsequence
# lexicographically by length
sorted_subsequence = {}
length = len(s)
# Total number of non-empty subsequence
# in string is 2^len-1
limit = 2 ** length
# i=0, corresponds to empty subsequence
for i in range(1, limit):
# subsequence for binary pattern i
sub = subsequence(s, i)
# storing sub in map
if len(sub) in sorted_subsequence.keys():
sorted_subsequence[len(sub)] = \
tuple(list(sorted_subsequence[len(sub)]) + [sub])
else:
sorted_subsequence[len(sub)] = [sub]
for it in sorted_subsequence:
# it.first is length of Subsequence
# it.second is set
print("Subsequences of length =", it, "are:")
for ii in sorted(set(sorted_subsequence[it])):
# ii is iterator of type set
print(ii, end = ' ')
print()
# Driver Code
s = "aabc"
possibleSubsequences(s)
# This code is contributed by ankush_953
输出:
Subsequences of length = 1 are:
a b c
Subsequences of length = 2 are:
aa ab ac bc
Subsequences of length = 3 are:
aab aac abc
Subsequences of length = 4 are:
aabc
时间复杂度: ,其中n是查找子序列的字符串的长度,b是二进制字符串中设置的位数。
如果您希望与行业专家一起参加现场课程,请参阅《 Geeks现场课程》和《 Geeks现场课程美国》。