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 $\mathit{\text{ABC}}$ 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 $\mathit{\text{columnTitle}}$.
• Space Complexity: $O(1)$.

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