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:
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