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
1
s in the binary representation ofk
. This step ensures you understand the minimum distinct elements required. - If
num > n
orn > k
, output-1
since it’s impossible to form the string.
Frequency Array:
- Create a
freq
array wherefreq[i]
represents the number of times the character corresponding to value2^i
should be used. - Populate the
freq
array by iterating through the bits ofk
and settingfreq[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 reachesn
.
String Construction:
- Construct the result string using the characters based on their frequencies, ensuring lexicographical order.
Complexity:
- Time Complexity:
O(n + log(k))
, wheren
is the maximum number of characters needed in the result, andlog(k)
is the number of bits ink
. - For typical integer limits (e.g.,
k
up to 32 or 64 bits), thelog(k)
factor is constant, so the time complexity is dominated byO(n)
. - Space Complexity:
O(n)
for the string result, plusO(1)
for the auxiliaryfreq
array because of constant value.