By Long Luo

This article is the solution 2 Approaches: Base Conversion from High to Low and from Low to High of Problem 171. Excel Sheet Column Number.

Intuition

Basiclly, It’s base conversion.

We are familiar base \(10\). How do we calculate a number?

From high to low, starting with \(ans\) as \(0\), update \(ans\) with the current digit value each time, the update rule is \(ans = ans \times 10 + val\).

If there is a decimal number, encoded as \(\textit{ABC}\) not the arabic number, what’s it?

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ans = 0
ans = ans * 10 + 1  => A
ans = ans * 10 + 2  => B
ans = ans * 10 + 3  => C

The answer is: \(123\).

from High to Low

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public int titleToNumber(String columnTitle) {
    int n = columnTitle.length();
    int ans = 0;
    int base = 1;
    for (int i = n - 1; i >= 0; i--) {
        int temp = 0;
        if (columnTitle.charAt(i) == 'Z') {
            temp = 26;
        } else {
            temp = columnTitle.charAt(i) - 'A' + 1;
        }
        ans = ans + base * temp;
        base *= 26;
    }

    return ans;
}

from High to Low

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public int titleToNumber_base26(String columnTitle) {
    int len = columnTitle.length();
    int ans = 0;
    for (int i = 0; i < len; i++) {
        int num = columnTitle.charAt(i) - 'A' + 1;
        ans = ans * 26 + num;
    }

    return ans;
}

Analysis

• Time Complexity: \(O(N)\), \(N\) is the length of the string \(\textit{columnTitle}\).
• Space Complexity: \(O(1)\).

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