Given a string consisting of only 0’s and 1’s. Now you are given N non-intersecting ranges L, R ( L <= R), more specifically [L1, R1], [L2, R2], …, [LN, RN], No two of these intervals overlap — formally, for each valid i, j such that i!=j, either Ri<Lj or Rj<Li.
The task is to find a valid permutation which will hold two following conditions simultaneously:
- Sum of numbers between all N given ranges will be maximum.
- The string will be lexicographically largest. A string 1100 is lexicographically larger than string 1001.
First we put 1’s in position 2 and 3 then in 5 as
there are no 1’s left, the string formed is 01101.
In the above example we 1st put 1 in 1st and 2nd position then we have another ‘1’ left,
So, we use it to maximize the string lexicographically and we put it in the 3rd position and thus the rearrangement is complete.
- First priority is given to make the count of 1’s between all l and r to be max. We count the number of 1’s in the array and store in a variable.
- After taking input we update the range of each l and r by 1 to just mark the position to be filled with 1 first.
- Then, we take prefix sum of the array so that we get the positions where to fix the 1’s first. Then we run a loop in that prefix sum array from left. If we get any position with value greater than 1 that means we have a l-r in that index. We continue to put 1’s in those indices until the count of 1 becomes zero.
- Now after the maximization operation is finished and if there are some 1’s left then we start the lexicographic maximization. We again start a loop from left of the prefix sum array if we find an index having value 0 which indicates that there is no l-r having that index then we put a 1 in that index and thus continue until all remaining 1’s are filled.
Below is the implementation of the above approach:
- Count number of indices such that s[i] = s[i+1] : Range queries
- Find the maximum possible Binary Number from given string
- Maximum difference of zeros and ones in binary string
- Maximum contiguous 1 possible in a binary string after k rotations
- Maximum Consecutive Zeroes in Concatenated Binary String
- Maximum difference of zeros and ones in binary string | Set 2 (O(n) time)
- Maximum length of consecutive 1's in a binary string in Python using Map function
- Find indices of all occurrence of one string in other
- Find the starting indices of the substrings in string (S) which is made by concatenating all words from a list(L)
- String Range Queries to find the number of subsets equal to a given String
- Maximum Bitwise OR pair from a range
- Range maximum query using Sparse Table
- Binary array after M range toggle operations
- Longest sub string of 0's in a binary string which is repeated K times
- Find the number in a range having maximum product of the digits
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.