CAB - Editorial

editorial
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Problem Link - Cybalphabit Practice Problem in 1600 to 1800 difficulty problems

Problem Statement:

Given two integers n (number of characters) and k (integer to be represented in character values), construct a string using exactly n characters with the smallest lexicographical order such that the sum of the character values equals k. The character value of ‘a’ is 2^0, ‘b’ is 2^1, …, and ‘z’ is 2^{25}. If it’s impossible to form such a string, print -1.

Approach:

Bit Representation:

  • Calculate the number of 1s in the binary representation of k. This step ensures you understand the minimum distinct elements required.
  • If num > n or n > k, output -1 since it’s impossible to form the string.

Frequency Array:

  • Create a freq array where freq[i] represents the number of times the character corresponding to value 2^i should be used.
  • Populate the freq array by iterating through the bits of k and setting freq[25 - temp] (to represent ‘z’ down to ‘a’).

Redistribution Logic:

  • Redistribute bits to achieve exactly n characters. Start with lower bit positions and move excess bits to higher positions, doubling their value (e.g., moving two 'a’s to one ‘b’) until the count of characters reaches n.

String Construction:

  • Construct the result string using the characters based on their frequencies, ensuring lexicographical order.

Complexity:

  • Time Complexity: O(n + log(k)), where n is the maximum number of characters needed in the result, and log(k) is the number of bits in k.
  • For typical integer limits (e.g., k up to 32 or 64 bits), the log(k) factor is constant, so the time complexity is dominated by O(n).
  • Space Complexity: O(n) for the string result, plus O(1) for the auxiliary freq array because of constant value.