Given a string S, we need to write a program to check if it is possible to construct the given string S by performing any of the below operations any number of times. In each step, we can:
- Add any character at the end of the string.
- or, append the string to the string itself.
The above steps can be applied any number of times. We need to write a program to print the minimum steps required to form the string.
Input : aaaaaaaa Output : 4 Explanation: move 1: add 'a' to form "a" move 2: add 'a' to form "aa" move 3: append "aa" to form "aaaa" move 4: append "aaaa" to form "aaaaaaaa" Input: aaaaaa Output: 4 Explanation: move 1: add 'a' to form "a" move 2: add 'a' to form "aa" move 3: add 'a' to form "aaa" move 4: append "aaa" to form "aaaaaa" Input: abcabca Output: 5
The idea to solve this problem is to use Dynamic Programming to count the minimum number of moves. Create an array named dp of size n, where n is the length of the input string. dp[i] stores the minimum number of moves that are required to make substring (0…i). According to the question there are two moves that are possible:
- dp[i] = min(dp[i], dp[i-1] + 1) which signifies addition of characters.
- dp[i*2+1] = min(dp[i]+1, dp[i*2+1]), appending of string is done if s[0…i]==s[i+1..i*2+1]
- Lexicographically smallest string formed by appending a character from the first K characters of a given string
- Lexicographically smallest string formed by appending a character from first K characters of a string | Set 2
- Find the character made by adding all the characters of the given string
- Check if characters of one string can be swapped to form other
- Check if characters of a given string can be rearranged to form a palindrome
- Check if the characters in a string form a Palindrome in O(1) extra space
- Replace minimal number of characters to make all characters pair wise distinct
- Minimum length of the sub-string whose characters can be used to form a palindrome of length K
- Find the count of palindromic sub-string of a string in its sorted form
- Create a new string by alternately combining the characters of two halves of the string in reverse
- Minimum deletions from string to reduce it to string with at most 2 unique characters
- Find the smallest window in a string containing all characters of another string
- Reorder the given string to form a K-concatenated string
- String matching where one string contains wildcard characters
- Check whether second string can be formed from characters of first string
The answer will be stored in dp[n-1] as we need to form the string(0..n-1) index-wise.
Below is the implementation of above idea:
Time Complexity : O(n2), where n is the length of input string.
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