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C++ Program to Find Maximum number of 0s placed consecutively at the start and end in any rotation of a Binary String

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  • Last Updated : 27 Jan, 2022

Given a binary string S of size N, the task is to maximize the sum of the count of consecutive 0s present at the start and end of any of the rotations of the given string S.

Examples:

Input: S = “1001”
Output: 2
Explanation:
All possible rotations of the string are:
“1001”: Count of 0s at the start = 0; at the end = 0. Sum= 0 + 0 = 0.
“0011”: Count of 0s at the start = 2; at the end = 0. Sum = 2 + 0=2
“0110”: Count of 0s at the start = 1; at the end = 1. Sum= 1 + 1 = 2.
“1100”: Count of 0s at the start = 0; at the end = 2. Sum = 0 + 2 = 2
Therefore, the maximum sum possible is 2.

Input: S = “01010”
Output: 2
Explanation: 
All possible rotations of the string are:
“01010”: Count of 0s at the start = 1; at the end = 1. Sum= 1+1=1
“10100”: Count of 0s at the start = 0; at the end = 2. Sum= 0+2=2
“01001”: Count of 0s at the start = 1; at the end = 0. Sum= 1+0=1
“10010”: Count of 0s at the start = 0; at the end = 1. Sum= 0+1=1
“00101”: Count of 0s at the start = 2; at the end = 0. Sum= 2+0=2
Therefore, the maximum sum possible is 2.

 

Naive Approach: The simplest idea is to generate all rotations of the given string and for each rotation, count the number of 0s present at the beginning and end of the string and calculate their sum. Finally, print the maximum sum obtained.  

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 the maximum sum of
// consecutive 0s present at the start
// and end of a string present in any
// of the rotations of the given string
void findMaximumZeros(string str, int n)
{
    // Check if all the characters
    // in the string are 0
    int c0 = 0;
  
    // Iterate over characters
    // of the string
    for (int i = 0; i < n; ++i) {
        if (str[i] == '0')
            c0++;
    }
  
    // If the frequency of '1' is 0
    if (c0 == n) {
  
        // Print n as the result
        cout << n;
        return;
    }
  
    // Concatenate the string
    // with itself
    string s = str + str;
  
    // Stores the required result
    int mx = 0;
  
    // Generate all rotations of the string
    for (int i = 0; i < n; ++i) {
  
        // Store the number of consecutive 0s
        // at the start and end of the string
        int cs = 0;
        int ce = 0;
  
        // Count 0s present at the start
        for (int j = i; j < i + n; ++j) {
            if (s[j] == '0')
                cs++;
            else
                break;
        }
  
        // Count 0s present at the end
        for (int j = i + n - 1; j >= i; --j) {
            if (s[j] == '0')
                ce++;
            else
                break;
        }
  
        // Calculate the sum
        int val = cs + ce;
  
        // Update the overall
        // maximum sum
        mx = max(val, mx);
    }
  
    // Print the result
    cout << mx;
}
  
// Driver Code
int main()
{
    // Given string
    string s = "1001";
  
    // Store the size of the string
    int n = s.size();
  
    findMaximumZeros(s, n);
  
    return 0;
}
Output: 
2

 

Time Complexity: O(N2)
Auxiliary Space: O(N)

Efficient Approach: The idea is to find the maximum number of consecutive 0s in the given string. Also, find the sum of consecutive 0s at the start and the end of the string, and then print the maximum out of them. 
Follow the steps below to solve the problem:

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 the maximum sum of
// consecutive 0s present at the start
// and end of any rotation of the string str
void findMaximumZeros(string str, int n)
{
    // Stores the count of 0s
    int c0 = 0;
    for (int i = 0; i < n; ++i) {
        if (str[i] == '0')
            c0++;
    }
  
    // If the frequency of '1' is 0
    if (c0 == n) {
  
        // Print n as the result
        cout << n;
        return;
    }
  
    // Stores the required sum
    int mx = 0;
  
    // Find the maximum consecutive
    // length of 0s present in the string
    int cnt = 0;
  
    for (int i = 0; i < n; i++) {
        if (str[i] == '0')
            cnt++;
        else {
            mx = max(mx, cnt);
            cnt = 0;
        }
    }
  
    // Update the overall maximum sum
    mx = max(mx, cnt);
  
    // Find the number of 0s present at
    // the start and end of the string
    int start = 0, end = n - 1;
    cnt = 0;
  
    // Update the count of 0s at the start
    while (str[start] != '1' && start < n) {
        cnt++;
        start++;
    }
  
    // Update the count of 0s at the end
    while (str[end] != '1' && end >= 0) {
        cnt++;
        end--;
    }
  
    // Update the maximum sum
    mx = max(mx, cnt);
  
    // Print the result
    cout << mx;
}
  
// Driver Code
int main()
{
    // Given string
    string s = "1001";
  
    // Store the size of the string
    int n = s.size();
  
    findMaximumZeros(s, n);
  
    return 0;
}
Output: 
2

 

Time Complexity: O(N)
Auxiliary Space: O(1)

Please refer complete article on Maximum number of 0s placed consecutively at the start and end in any rotation of a Binary String for more details!


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