Count ways to partition a Binary String such that each substring contains exactly two 0s
Given a binary string str, the task is to find the count of ways to partition the string such that each partitioned substring contains exactly two 0s.
Examples:
Input: str = “00100”
Output:
Explanation:
Possible ways to partition the string such that each partition contains exactly two 0s are: { {“00”, “100”}, {“001”, “00”} }.
Therefore, the required output is 2.Input: str = “000”
Output: 0
Approach: The idea is to calculate the count of 1s between every two consecutive 0s of the given string. Follow the steps below to solve the problem:
- Initialize an array, say IdxOf0s[], to store the indices of 0s in the given string.
- Iterate over the characters of the given string and store the indices of the 0s into IdxOf0s[].
- Initialize a variable, say cntWays, to store the count of ways to partition the string such that each partition contains exactly two 0s.
- If count of 0s in the given string is odd, then update cntWays = 0.
- Otherwise, traverse the array IdxOf0s[] and calculate the count of ways to partition the array having each partition exactly two 0s using cntWays *= (IdxOf0s[i] – IdxOf0s[i – 1])
- Finally, print the value of cntWays.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Function to find count of ways to partition// the string such that each partition// contains exactly two 0s.int totalWays(int n, string str){ // Stores indices of 0s in // the given string. vector<int> IdxOf0s; // Store the count of ways to partition // the string such that each partition // contains exactly two 0s. int cntWays = 1; // Iterate over each characters // of the given string for (int i = 0; i < n; i++) { // If current character is '0' if (str[i] == '0') { // Insert index IdxOf0s.push_back(i); } } // Stores total count of 0s in str int M = IdxOf0s.size(); if (M == 0 or M % 2) { return 0; } // Traverse the array, IdxOf0s[] for (int i = 2; i < M; i += 2) { // Update cntWays cntWays = cntWays * (IdxOf0s[i] - IdxOf0s[i - 1]); } return cntWays;}// Driver Codeint main(){ string str = "00100"; int n = str.length(); cout << totalWays(n, str); return 0;} |
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Java
// Java program for the above approach import java.util.*;class GFG{ // Function to find count of ways to partition // the string such that each partition // contains exactly two 0s. static int totalWays(int n, String str) { // Stores indices of 0s in // the given string. ArrayList<Integer> IdxOf0s = new ArrayList<Integer>(); // Store the count of ways to partition // the string such that each partition // contains exactly two 0s. int cntWays = 1; // Iterate over each characters // of the given string for (int i = 0; i < n; i++) { // If current character is '0' if (str.charAt(i) == '0') { // Insert index IdxOf0s.add(i); } } // Stores total count of 0s in str int M = IdxOf0s.size(); if ((M == 0) || ((M % 2) != 0)) { return 0; } // Traverse the array, IdxOf0s[] for (int i = 2; i < M; i += 2) { // Update cntWays cntWays = cntWays * (IdxOf0s.get(i) - IdxOf0s.get(i - 1)); } return cntWays; } // Driver codepublic static void main(String[] args){ String str = "00100"; int n = str.length(); System.out.print(totalWays(n, str)); }}// This code is contributed by sanjoy_62. |
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Python3
# Python3 program for the above approach# Function to find count of ways to partition# thesuch that each partition# contains exactly two 0s.def totalWays(n, str): # Stores indices of 0s in # the given string. IdxOf0s = [] # Store the count of ways to partition # the such that each partition # contains exactly two 0s. cntWays = 1 # Iterate over each characters # of the given string for i in range(n): # If current character is '0' if (str[i] == '0'): # Insert index IdxOf0s.append(i) # Stores total count of 0s in str M = len(IdxOf0s) if (M == 0 or M % 2): return 0 # Traverse the array, IdxOf0s[] for i in range(2, M, 2): # Update cntWays cntWays = cntWays * (IdxOf0s[i] - IdxOf0s[i - 1]) return cntWays# Driver Codeif __name__ == '__main__': str = "00100" n = len(str) print(totalWays(n, str))# This code is contributed by mohit kumar 29 |
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C#
// C# program for the above approach using System;using System.Collections; using System.Collections.Generic; class GFG { // Function to find count of ways to partition // the string such that each partition // contains exactly two 0s. static int totalWays(int n, string str) { // Stores indices of 0s in // the given string. ArrayList IdxOf0s = new ArrayList(); // Store the count of ways to partition // the string such that each partition // contains exactly two 0s. int cntWays = 1; // Iterate over each characters // of the given string for (int i = 0; i < n; i++) { // If current character is '0' if (str[i] == '0') { // Insert index IdxOf0s.Add(i); } } // Stores total count of 0s in str int M = IdxOf0s.Count; if ((M == 0) || ((M % 2) != 0)) { return 0; } // Traverse the array, IdxOf0s[] for (int i = 2; i < M; i += 2) { // Update cntWays cntWays = cntWays * (Convert.ToInt32(IdxOf0s[i]) - Convert.ToInt32(IdxOf0s[i - 1])); } return cntWays; } // Driver code static public void Main() { string str = "00100"; int n = str.Length; Console.Write(totalWays(n, str)); }}// This code is contributed by Dharanendra L V |
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Output:
2
Time Complexity: O(N)
Auxiliary Space: O(N)
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