Construct a binary string following the given constraints

Given three integers A, B and X. The task is to construct a binary string str which has exactly A number of 0’s and B number of 1’s provided there has to be at least X indices such that str[i] != str[i+1]. Inputs are such that there’s always a valid solution.

Examples:

Input: A = 2, B = 2, X = 1
Output: 1100
There are two 0’s and two 1’s and one (=X) index such that s[i] != s[i+1] (i.e. i = 1)

Input: A = 4, B = 3, X = 2
Output: 0111000



Approach:

  • Divide x by 2 and store it in a variable d.
  • Check if d is even and d / 2 != a, if the condition is true then print 0 and decrement d and a by 1.
  • Loop from 1 to d and print 10 and in the end update a = a – d and b = b – d.
  • Finally print the remaining 0’s and 1’s depending on the values of a and b.

Below is the implementation of the above approach:

C++

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// C++ implementation of the appraoch
#include <iostream>
using namespace std;
  
// Function to print a binary string which has
// 'a' number of 0's, 'b' number of 1's and there are
// at least 'x' indices such that s[i] != s[i+1]
int constructBinString(int a, int b, int x)
{
    int d, i;
  
    // Divide index value by 2 and store
    // it into d
    d = x / 2;
  
    // If index value x is even and
    // x/2 is not equal to a
    if (x % 2 == 0 && x / 2 != a) {
        d--;
        cout << 0;
        a--;
    }
  
    // Loop for d for each d print 10
    for (i = 0; i < d; i++)
        cout << "10";
  
    // subtract d from a and b
    a = a - d;
    b = b - d;
  
    // Loop for b to print remaining 1's
    for (i = 0; i < b; i++) {
        cout << "1";
    }
  
    // Loop for a to print remaining 0's
    for (i = 0; i < a; i++) {
        cout << "0";
    }
}
  
// Driver code
int main()
{
    int a = 4, b = 3, x = 2;
    constructBinString(a, b, x);
    return 0;
}

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PHP

Output:

0111000


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