Given an integer N, the task is to count the number of binary strings possible of length N such that they don’t contain “111” as a substring. The answer could be large so print answer modulo 109 + 7.
Input: N = 3
All possible substring are “000”, “001”,
“010”, “011”, “100”, “101” and “110”.
“111” is not a valid string.
Input N = 16
Approach: Dynamic programming can be used to solve this problem. Create a dp array where dp[i][j] will store the count of possible substrings such that 1 appears j times consecutively upto the ith index. Now, the recurrence relations will be:
dp[i] = dp[i – 1] + dp[i – 1] + dp[i – 1]
dp[i] = dp[i – 1]
dp[i] = dp[i – 1]
And the base cases will be dp = 1, dp = 1 and dp = 0. Now, the required count of strings will be dp[N] + dp[N] + dp[N].
Below is the implementation of the above approach:
- Length of the largest substring which have character with frequency greater than or equal to half of the substring
- Count number of binary strings of length N having only 0's and 1's
- Number of non-decreasing sub-arrays of length greater than or equal to K
- Count the number of subsequences of length k having equal LCM and HCF
- Find the number of binary strings of length N with at least 3 consecutive 1s
- Number of Binary Strings of length N with K adjacent Set Bits
- Length of the longest substring with equal 1s and 0s
- Count number of binary strings without consecutive 1's
- Count of strings that become equal to one of the two strings after one removal
- Count of sub-strings of length n possible from the given string
- All possible binary numbers of length n with equal sum in both halves
- Count ways to increase LCS length of two strings by one
- Generate all binary strings of length n with sub-string "01" appearing exactly twice
- Maximum count of sub-strings of length K consisting of same characters
- Check whether all the rotations of a given number is greater than or equal to the given number or not
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.