Excel Column Number | InterviewBit | Solution Explained

Excel Column Number is a math problem on InterviewBit. I explain the solution using a simple approach. Problem Link.

This solution is the inverse of: Excel Column Title | InterviewBit | Solution Explained

0. Excel Column Number: Problem Discussion

0.0. IO Format

  • input:
    • a string of characters
  • output:
    • an integer, which is the equivalent of the input string
  • constraints:
    • characters given are capital English letters
    • solution must be better than O(N) time and space each

0.1. Examples

The problem statement is weird, so let’s take a look at some examples.

  • A -> 1
  • B -> 2
  • Z -> 26
  • AA -> 27
  • AZ -> 52

And so on.

1. Excel Column Number: Observations & Logic

1.0. Intuitions

Right away it is clear that we are dealing with characters that have different significances on each position.

For example, AB -> 28 since A = 1, but is at the position 1 – so we actually do 26 * 1 for A. Then, since B is at the position 0, we just add +2. This gives us the answer as 261 * 1 + 260 * 2.

If you notice, this is equivalent of saying 26i * val(X) where X is the character.

1.1. Formal Logic

  • reverse the string: AB -> BA
  • keep a track of the index: i = 0 -> 1 -> 2 -> ...
  • find the value of a character: val = ord(c) - ord('A') + 1
  • then finally add to total: 26i + val

2. Excel Column Number: Implementation

2.0. Code

class Solution:
def titleToNumber(self, A):
    ans = 0
    for i, c in enumerate(reversed(A)):
        ans += (26**i) * (ord(c)-ord('A') + 1)
    return ans

2.1. Complexity Analysis

  • Time: O(N), to iterate over all the elements in the string, where N is the length of the input string.
  • Space: O(N), since reversing the string in python creates a new copy of it, and thus takes O(N) space.
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    Comments

    1. Please write the proof.

    2. This solution need an amendment for 2 digit number.

    3. Please write a Proof for this

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