Given binary string str, the task is to find the minimum number of flips required to keep all 1s together in the given binary string, i.e. there must not be any 0 between 1s in the string.
Input: str = “0011111100”
Explanation: We dont need to flip any bits because all the ones are grouped together and there is no zero between any two ones.
Input: str = “11100111000101”
Explanation: We can flip the 4th and 5th bit to make them 1 and flip 12th and 14th bit to make them 0. So the resulting string is “11111111000000” with 4 possible flips.
Approach: To solve the problem mentioned above we will implement the dynamic programming approach where we will have the following states:
- The first state is dp[i] which signifies the number of flips required to make all zeroes up to the ith bit.
- Second state dp[i] which signifies the number of flips required to make the current bit 1 such that the conditions given in the question are satisfied.
So the required answer will be minimum flips for making the current bit 1 + minimum flips for making all bits after the current bit 0 for all values of i. But if all the bits in the given string are 0 then we don’t have to change anything, so we can check the minimum between our answer and the number of flips required to make the string with all zeroes. So we can compute the answer by iterating over all the characters in the string where,
answer = min ( answer, dp[i] + dp[n-1] – dp[i])
dp[i] = Minimum number of flips to set current bit to 1
dp[n-1] – dp[i] = Minimum number of flips required to make all bits after i as 0
Below is the implementation of the above approach:
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Minimum flips required in a binary string such that all K-size substring contains 1
- Minimum flips required to form given binary string where every flip changes all bits to its right as well
- Minimum jumps required to group all 1s together in a given Binary string
- Minimum Count of Bit flips required to make a Binary String Palindromic
- Minimize flips required to make all shortest paths from top-left to bottom-right of a binary matrix equal to S
- Minimum flips required to convert given string into concatenation of equal substrings of length K
- Minimum flips required to maximize a number with k set bits
- Minimum flips required to generate continuous substrings of 0’s and 1’s
- Minimum number of flips with rotation to make binary string alternating
- Minimum operations required to convert a binary string to all 0s or all 1s
- Minimum flips in a Binary array such that XOR of consecutive subarrays of size K have different parity
- Minimum Group Flips to Make Binary Array Elements Same
- Minimize count of flips required such that no substring of 0s have length exceeding K
- Count minimum right flips to set all values in an array
- Minimum flips to make all 1s in left and 0s in right | Set 1 (Using Bitmask)
- Minimum flips to make all 1s in left and 0s in right | Set 2
- Find Bit whose minimum sequence flips makes all bits same
- Number of flips to make binary string alternate | Set 1
- Number of ways to make binary string of length N such that 0s always occur together in groups of size K
- Min flips of continuous characters to make all characters same in a string
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.
Improved By : mohit kumar 29