Find the rank of a given combination from an Array of String
Last Updated :
07 Jul, 2023
Given an array of string and a string K, the task is to find the rank of the given string if we generate all the combinations of the given array of strings.
Examples:
Input: string = ['ab', 'pq', 'nm'], K = 'pqnm'
Output: 7
Explanation: All combination generated are :-
'' -------------------> rank 1
'ab' -----------------> rank 2
'pq' -----------------> rank 3
'nm' ----------------> rank 4
'abpq' --------------> rank 5
'abnm' --------------> rank 6
'pqnm' --------------> rank 7
'abpqnm' ------------> rank 8
'pqnm' is at rank is generated at rank 7
Input: string = ['a', 'b'], K = 'aa'
Output: -1
Explanation: 'aa' cannot be generated by any combination of given element.
Approach: To solve the problem follow the below idea:
Generates the powerset of a given list of strings using the combinations function from the itertools module and a nested loop. It then calculates the rank of a target string in that powerset using the index function and returns -1 if the target string is not in the powerset. The code defines a list of strings and a target string, calls the get_rank function, and prints the rank.
Below are the steps for the above approach:
- Import the combinations function from the itertools module.
- Define a function to generate the powerset of a given list of strings.
- Initialize the powerset with an empty string.
- Loop over all possible lengths of subsets from 1 to the length of the input list.
- Use the combinations function to generate all possible subsets of the current length.
- Join the elements of each combination into a single string and append it to the powerset.
- Return the final powerset.
- Define a function to get the rank of a given string in the powerset of a list of strings.
- Generate the powerset of the input string list using the get_powerset function.
- If the target string is not in the powerset, return -1.
- Otherwise, return the index of the target string in the sorted powerset, plus 1.
- Get the rank of the target string in the powerset of the input string list using the get_rank function.
- Print the rank.
Below is the code for the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
// Define a function to generate the
// powerset of a given list of strings
vector<string> get_powerset(vector<string> string_list)
{
// Initialize the powerset with
// the empty string
vector<string> powerset = { "" };
// Loop over all possible
// lengths of subsets
for (int i = 1; i <= string_list.size(); i++) {
// Generate all combinations
// of subsets of length i
vector<bool> bitmask(i, true);
bitmask.resize(string_list.size(), false);
do {
string subset = "";
for (int j = 0; j < string_list.size(); j++) {
if (bitmask[j]) {
subset += string_list[j];
}
}
// Add the generated subset to the powerset
powerset.push_back(subset);
} while (prev_permutation(bitmask.begin(),
bitmask.end()));
}
// Return the final powerset
return powerset;
}
// Define a function to get the rank
// of a given string in the powerset
// of a list of strings
int get_rank(vector<string> string_list, string k)
{
// Generate the powerset of
// the input string list
vector<string> powerset = get_powerset(string_list);
// If the target string is not
// in the powerset, return -1
if (find(powerset.begin(), powerset.end(), k)
== powerset.end()) {
return -1;
}
// Otherwise, return the index of
// the target string in the
// sorted powerset, plus 1
return distance(powerset.begin(),
lower_bound(powerset.begin(),
powerset.end(), k))
+ 1;
}
int main()
{
vector<string> string_list = { "ab", "pq", "nm" };
string k = "pqnm";
// Get the rank of the target string
// in the powerset of the
// input string list
int rank = get_rank(string_list, k);
// Print the rank
cout << rank << endl;
return 0;
}
// Java code for the approach
import java.util.*;
public class GFG {
// Define a function to generate the
// powerset of a given list of strings
public static List<String> get_powerset(List<String> string_list) {
// Initialize the powerset with
// the empty string
List<String> powerset = new ArrayList<>();
powerset.add("");
// Loop over all possible
// lengths of subsets
for (int i = 1; i <= string_list.size(); i++) {
for (List<String> combination : combinations(string_list, i)) {
String subset = String.join("", combination);
powerset.add(subset);
}
}
// Return the final powerset
return powerset;
}
// Define a function to get the rank
// of a given string in the powerset
// of a list of strings
public static int get_rank(List<String> string_list, String k) {
// Generate the powerset of
// the input string list
List<String> powerset = get_powerset(string_list);
// If the target string is not
// in the powerset, return -1
if (!powerset.contains(k)) {
return -1;
}
// Otherwise, return the index of
// the target string in the
// sorted powerset, plus 1
return powerset.indexOf(k) + 1;
}
public static <T> Iterable<List<T>> combinations(List<T> items, int n) {
if (n == 0) {
return Collections.singletonList(Collections.emptyList());
} else {
List<List<T>> result = new ArrayList<>();
for (int i = 0; i <= items.size() - n; i++) {
T item = items.get(i);
for (List<T> combination : combinations(items.subList(i+1, items.size()), n-1)) {
List<T> list = new ArrayList<>();
list.add(item);
list.addAll(combination);
result.add(list);
}
}
return result;
}
}
public static void main(String[] args) {
List<String> string_list = Arrays.asList("ab", "pq", "nm");
String k = "pqnm";
// Get the rank of the target string
// in the powerset of the
// input string list
int rank = get_rank(string_list, k);
System.out.println(rank); // Output: 7
}
}
# Import the combinations function
# from the itertools module
from itertools import combinations
# Define a function to generate the
# powerset of a given list of strings
def get_powerset(string_list):
# Initialize the powerset with
# the empty string
powerset = ['']
# Loop over all possible
# lengths of subsets
for i in range(1, len(string_list)+1):
# Generate all combinations
# of subsets of length i
for combination in combinations(string_list, i):
# Join the elements of each
# combination into a single string
powerset.append(''.join(combination))
# Return the final powerset
return powerset
# Define a function to get the rank
# of a given string in the powerset
# of a list of strings
def get_rank(string_list, k):
# Generate the powerset of
# the input string list
powerset = get_powerset(string_list)
# If the target string is not
# in the powerset, return -1
if k not in powerset:
return -1
# Otherwise, return the index of
# the target string in the
# sorted powerset, plus 1
return powerset.index(k) + 1
# Define a list of strings
# and a target string
string_list = ['ab', 'pq', 'nm']
k = 'pqnm'
# Get the rank of the target string
# in the powerset of the
# input string list
rank = get_rank(string_list, k)
# Print the rank
print(rank)
// C# code for the approach
using System;
using System.Collections.Generic;
using System.Linq;
public class GFG
{
// Define a function to generate the
// powerset of a given list of strings
public static List<string>
get_powerset(List<string> string_list)
{
// Initialize the powerset with
// the empty string
List<string> powerset = new List<string>();
powerset.Add("");
// Loop over all possible
// lengths of subsets
for (int i = 1; i <= string_list.Count; i++) {
foreach(List<string> combination in
combinations(string_list, i))
{
string subset
= string.Join("", combination);
powerset.Add(subset);
}
}
// Return the final powerset
return powerset;
}
// Define a function to get the rank
// of a given string in the powerset
// of a list of strings
public static int get_rank(List<string> string_list,
string k)
{
// Generate the powerset of
// the input string list
List<string> powerset = get_powerset(string_list);
// If the target string is not
// in the powerset, return -1
if (!powerset.Contains(k)) {
return -1;
}
// Otherwise, return the index of
// the target string in the
// sorted powerset, plus 1
return powerset.IndexOf(k) + 1;
}
public static IEnumerable<IEnumerable<T> >
combinations<T>(IEnumerable<T> items, int n)
{
if (n == 0) {
return new[] { Enumerable.Empty<T>() };
}
else {
List<List<T> > result = new List<List<T> >();
for (int i = 0; i <= items.Count() - n; i++) {
T item = items.ElementAt(i);
foreach(IEnumerable<T> combination in
combinations(items.Skip(i + 1),
n - 1))
{
List<T> list = new List<T>();
list.Add(item);
list.AddRange(combination);
result.Add(list);
}
}
return result;
}
}
public static void Main()
{
List<string> string_list
= new List<string>() { "ab", "pq", "nm" };
string k = "pqnm";
// Get the rank of the target string
// in the powerset of the
// input string list
int rank = get_rank(string_list, k);
Console.WriteLine(rank); // Output: 7
}
}
// This code is contributed by user_dtewbxkn77n
// Define a function to generate the
// powerset of a given list of strings
function getPowerset(stringList) {
// Initialize the powerset with
//the empty string
let powerset = [""];
// Loop over all possible
//lengths of subsets
for (let i = 1; i <= stringList.length; i++) {
// Generate all combinations
// of subsets of length i
let bitmask = new Array(i).fill(true);
bitmask = bitmask.concat(new Array(stringList.length - i).fill(false));
do {
let subset = "";
for (let j = 0; j < stringList.length; j++) {
if (bitmask[j]) {
subset += stringList[j];
}
}
// Add the generated subset to the powerset
powerset.push(subset);
} while (prevPermutation(bitmask));
}
// Return the final powerset
return powerset;
}
// Helper function to generate
// the previous permutation
function prevPermutation(array) {
let i = array.length - 1;
while (i > 0 && array[i - 1] <= array[i]) {
i--;
}
if (i <= 0) {
return false;
}
let j = array.length - 1;
while (array[j] >= array[i - 1]) {
j--;
}
let temp = array[i - 1];
array[i - 1] = array[j];
array[j] = temp;
j = array.length - 1;
while (i < j) {
temp = array[i];
array[i] = array[j];
array[j] = temp;
i++;
j--;
}
return true;
}
// Define a function to get the rank
// of a given string in the powerset
// of a list of strings
function getRank(stringList, k) {
// Generate the powerset of
// the input string list
let powerset = getPowerset(stringList);
// If the target string is not
// in the powerset, return -1
if (!powerset.includes(k)) {
return -1;
}
// Otherwise, return the index of
// the target string in the
// sorted powerset, plus 1
return powerset.indexOf(k) + 1;
}
// Main
let stringList = ["ab", "pq", "nm"];
let k = "pqnm";
// Get the rank of the target string
// in the powerset of the
// input string list
let rank = getRank(stringList, k);
// Print the rank
console.log(rank);
Time complexity: O(n * 2n * log(n)) to generate the power set O(2n), sorting the power set O(n * 2n * log(n)) and finding the index O(n * 2n).
Auxiliary space: O(2n) to store all generated combinations.
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