# 171. Excel Sheet Column Number

## Some tips about ASCII and mathematics

### Problem statement

Given a string `columnTitle`

that represents the column title as appears in an Excel sheet, return its corresponding column number.

For example:

```
A -> 1
B -> 2
C -> 3
...
Z -> 26
AA -> 27
AB -> 28
...
```

#### Example 1

```
Input: columnTitle = "A"
Output: 1
```

#### Example 2

```
Input: columnTitle = "AB"
Output: 28
```

#### Example 3

```
Input: columnTitle = "ZY"
Output: 701
```

#### Constraints

`1 <= columnTitle.length <= 7`

.`columnTitle`

consists only of uppercase English letters.`columnTitle`

is in the range`["A", "FXSHRXW"]`

.

### Solution: Finding The Pattern

Let us write down some other `columnTitle`

strings and its value.

```
"A" = 1
"Z" = 26
"AA" = 27
"AZ" = 52
"ZZ" = 702
"AAA" = 703
```

Then try to find the pattern

```
"A" = 1 = 1
"Z" = 26 = 26
"AA" = 27 = 26 + 1
"AZ" = 52 = 26 + 26
"ZZ" = 702 = 26*26 + 26
"AAA" = 703 = 26*26 + 26 + 1
```

If you map `'A' = 1, ..., 'Z' = 26`

, the values can be rewritten as

```
"A" = 1 = 'A'
"Z" = 26 = 'Z'
"AA" = 27 = 26*'A' + 'A'
"AZ" = 52 = 26*'A' + 'Z'
"ZZ" = 702 = 26*'Z' + 'Z'
"AAA" = 703 = 26*26*'A' + 26*'A' + 'A'
```

In general the formula for a string `columnTitle = abcd`

is

```
abcd = 26^3*a + 26^2*b + 26*c + d,
```

where `a, b, c, d`

are some uppercase English letters `A, ..., Z`

.

Longer `columnTitle`

s will have bigger leading exponents of `26`

.

#### Code

```
#include <iostream>
using namespace std;
int titleToNumber(string columnTitle) {
int column = 0;
for (char c : columnTitle) {
// The ASCII value of 'A' is 65.
column = 26*column + (c - 64);
}
return column;
}
int main() {
cout << titleToNumber("A") << endl;
cout << titleToNumber("AB") << endl;
cout << titleToNumber("ZY") << endl;
}
```

```
Output:
1
28
701
```

#### Complexity

Runtime:

`O(N)`

, where`N = columnTitle.length`

.Extra space:

`O(1)`

.

#### Implementation notes

There are many ways to compute the series

`26^3*a + 26^2*b + 26*c + d.`

If you write it as

`26*(26*(26*(0 + a) + b) + c) + d,`

you get the loop in the code above.

To map

`'A' = 1, ..., 'Z' = 26`

, you can use their ASCII values (`'A' = 65, ..., 'Z' = 90`

) minus`64`

.The parentheses around

`(c - 64)`

is needed. Otherwise the value of`columnTitle = "FXSHRXW"`

makes`26*column + c`

exceed the limit of`int`

before it substracts`64`

.

### References

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