467. Unique Substrings in Wraparound String

Description

We define the string base to be the infinite wraparound string of "abcdefghijklmnopqrstuvwxyz", so base will look like this:

• "...zabcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyzabcd....".

Given a string s, return the number of unique non-empty substrings of s are present in base.

 

Example 1:

Input: s = "a"
Output: 1
Explanation: Only the substring "a" of s is in base.

Example 2:

Input: s = "cac"
Output: 2
Explanation: There are two substrings ("a", "c") of s in base.

Example 3:

Input: s = "zab"
Output: 6
Explanation: There are six substrings ("z", "a", "b", "za", "ab", and "zab") of s in base.

 

Constraints:

• 1 <= s.length <= 105
• s consists of lowercase English letters.

Solutions

Solution 1: Dynamic Programming

We can define an array $f$ of length $26$, where $f[i]$ represents the length of the longest consecutive substring ending with the $i$th character. The answer is the sum of all elements in $f$.

We define a variable $k$ to represent the length of the longest consecutive substring ending with the current character. We iterate through the string $s$. For each character $c$, if the difference between $c$ and the previous character $s[i - 1]$ is $1$, then we increment $k$ by $1$, otherwise, we reset $k$ to $1$. Then we update $f[c]$ to be the larger value of $f[c]$ and $k$.

Finally, we return the sum of all elements in $f$.

The time complexity is $O(n)$, where $n$ is the length of the string $s$. The space complexity is $O(|\Sigma|)$, where $\Sigma$ is the character set, in this case, the set of lowercase letters.

Python3JavaC++GoTypeScriptRust

class Solution:
    def findSubstringInWraproundString(self, s: str) -> int:
        f = defaultdict(int)
        k = 0
        for i, c in enumerate(s):
            if i and (ord(c) - ord(s[i - 1])) % 26 == 1:
                k += 1
            else:
                k = 1
            f[c] = max(f[c], k)
        return sum(f.values())

class Solution {
    public int findSubstringInWraproundString(String s) {
        int[] f = new int[26];
        int n = s.length();
        for (int i = 0, k = 0; i < n; ++i) {
            if (i > 0 && (s.charAt(i) - s.charAt(i - 1) + 26) % 26 == 1) {
                ++k;
            } else {
                k = 1;
            }
            f[s.charAt(i) - 'a'] = Math.max(f[s.charAt(i) - 'a'], k);
        }
        return Arrays.stream(f).sum();
    }
}

class Solution {
public:
    int findSubstringInWraproundString(string s) {
        int f[26]{};
        int n = s.length();
        for (int i = 0, k = 0; i < n; ++i) {
            if (i && (s[i] - s[i - 1] + 26) % 26 == 1) {
                ++k;
            } else {
                k = 1;
            }
            f[s[i] - 'a'] = max(f[s[i] - 'a'], k);
        }
        return accumulate(begin(f), end(f), 0);
    }
};

func findSubstringInWraproundString(s string) (ans int) {
    f := [26]int{}
    k := 0
    for i := range s {
        if i > 0 && (s[i]-s[i-1]+26)%26 == 1 {
            k++
        } else {
            k = 1
        }
        f[s[i]-'a'] = max(f[s[i]-'a'], k)
    }
    for _, x := range f {
        ans += x
    }
    return
}

function findSubstringInWraproundString(s: string): number {
    const idx = (c: string): number => c.charCodeAt(0) - 97;
    const f: number[] = Array(26).fill(0);
    const n = s.length;
    for (let i = 0, k = 0; i < n; ++i) {
        const j = idx(s[i]);
        if (i && (j - idx(s[i - 1]) + 26) % 26 === 1) {
            ++k;
        } else {
            k = 1;
        }
        f[j] = Math.max(f[j], k);
    }
    return f.reduce((acc, cur) => acc + cur, 0);
}

impl Solution {
    pub fn find_substring_in_wrapround_string(s: String) -> i32 {
        let idx = |c: u8| -> usize { (c - b'a') as usize };
        let mut f = vec![0; 26];
        let n = s.len();
        let s = s.as_bytes();
        let mut k = 0;
        for i in 0..n {
            let j = idx(s[i]);
            if i > 0 && ((j as i32) - (idx(s[i - 1]) as i32) + 26) % 26 == 1 {
                k += 1;
            } else {
                k = 1;
            }
            f[j] = f[j].max(k);
        }

        f.iter().sum()
    }
}

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