Find the string of length N according to the given conditions

Given two integers N and K. Then your task is to output the string of length N such that the cumulative sum of the string is equal to K:

• Where the Cumulative sum of the string is: For each character add 2^pos into the sum. Where pos is equivalent to the position of the character in the alphabet series. For example: a = 0, b = 1, c = 2 . . . . z = 25.

Note: If no such string is possible then output -1. If there are multiple answers, then print any of them.

Examples:

Input: N = 5, K = 13
Output: dbaaa
Explanation: The value of Z for d, b and a are 3, 1 and 0. Then cumulative sum of dbaaa is: (2³) + (2¹) + (3*(2⁰)) = 8 + 2 + 3 = 13. So both conditions met, length of output string is N = 5 and cumulative sum is K = 13.

Input: N = 4, K = 3
Output: -1
Explanation: It can be verified that no such string is possible.

Approach: Implement the idea to solve the problem

The problem is based on the Greedy logic and some observation. The problem can be divided into sub-parts as:

• If (N > K)
  • No string of length N is possible in such cases. Because Minimum power of 2 is 1 so we need the cumulative sum to be at least equal to N.
• If (N == K)
  • The answer will be a string of length N with all characters equal to 'a'.
• If (N < K)
  • Define an array let say power[], which is initialized to store the powers of 2.
  • Find the highest power of 2 that is less than or equal to K and store it in a variable let say P.
  • While there are still characters left to add (N > 0), calculate the remaining value of K after subtracting the current power of 2 (remk = K - power[P]). If this remaining value is less than the number of characters left to add minus one (remk < N - 1), it decreases P by 1. Otherwise, it adds a character corresponding to the current power of 2 to the string, decreases N by 1, and updates K to the remaining value.
  • If there's still a remaining value after all characters have been added (K > 0), it means a string couldn't be formed, so -1 is returned, else return the answer string.

Steps were taken to solve the problem:

• Create an array let say Power[] of length 26.
• Run a loop and initialize 2's power into Power[] from 2⁰ to 2²⁵
• Create a StringBuilder let say Sb
• If (N > K), append "-1" to Sb
• Else if (N == K) append 'a' to Sb N times.
• Else if (N < K),
  • Find the highest power of 2 that is less than or equal to K and store it in a variable, P.
  • While (N > 0)
    • Initialize remk with (K - Power[P])
    • If(remk < (N - 1)), decrease P by 1
    • Else, append character corresponding to P to sb, decrease N by 1 and update K = remK
  • If (K > 0)
    • Append "-1" to sb
• Output Sb.

Code to implement the approach:

dbaaa

Time Complexity: O(N), where N is the length of the output string
Auxiliary Space: O(26) ~ O(1)