Find longest sequence of 1’s in binary representation with one flip

4.3

Give an integer n. We can flip exactly one bit. Write code to find the length of the longest sequence of 1 s you could create.

Examples:

Input : 1775         
Output : 8 
Binary representation of 1775 is 11011101111.
After flipping the highlighted bit, we get 
consecutive 8 bits. 11011111111.

Input : 12         
Output : 3 

Input : 15
Output : 5

Input : 71
Output: 4

Binary representation of 71 is 1000111.
After flipping the highlighted bit, we get 
consecutive 4 bits. 1001111.

A simple solution is to store binary representation of given number in a binary array. Once we have elements in binary array, we can apply methods discussed here.

An efficient solution is to walk through the bits in binary representation of given number. We keep track of current 1’s sequence length and the previous 1’s sequence length. When we see a zero, update previous Length:

  1. If the next bit is a 1, previous Length should be set to current Length.
  2. If the next bit is a 0, then we can’t merge these sequences together. So, set previous Length to 0.

We update max length by comparing following two:

  1. Current value of max-length
  2. Current-Length + Previous-Length .
  • result = return max-length+1 (// add 1 for flip bit count )
  • .

    Below is C++ implementation of above idea.

    // C++ program to find maximum consecutive
    // 1's in binary representation of a number
    // after flipping one bit.
    #include<bits/stdc++.h>
    using namespace std;
    
    int flipBit(unsigned a)
    {
        /* If all bits are l, binary representation
           of 'a' has all 1s */
        if (~a == 0)
            return 8*sizeof(int);
    
        int currLen = 0, prevLen = 0, maxLen = 0;
        while (a!= 0)
        {
            // If Current bit is a 1 then increament currLen++
            if ((a & 1) == 1)
                currLen++;
    
            // If Current bit is a 0 then check next bit of a
            else if ((a & 1) == 0)
            {
                /* Update prevLen to 0 (if next bit is 0)
                or currLen (if next bit is 1). */
                prevLen = (a & 2) == 0? 0 : currLen;
    
                // If two consecutively bits are 0
                // then currLen also will be 0.
                currLen = 0;
            }
    
            // Update maxLen if required
            maxLen = max(prevLen + currLen, maxLen);
    
            // Remove last bit (Right shift)
            a >>= 1;
        }
    
        // We can always have a sequence of
        // at least one 1, this is fliped bit
        return maxLen+1;
    }
    
    // Driver code
    int main()
    {
        // input 1
        cout << flipBit(13);
        cout << endl;
    
        // input 2
        cout << flipBit(1775);
        cout << endl;
    
        // input 3
        cout << flipBit(15);
        return 0;
    }
    

    Output :

    4
    8
    5
    

    This article is contributed by Mr. Somesh Awasthi. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

    Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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