1794. Count Pairs of Equal Substrings With Minimum Difference π
Description
You are given two strings firstString
and secondString
that are 0-indexed and consist only of lowercase English letters. Count the number of index quadruples (i,j,a,b)
that satisfy the following conditions:
0 <= i <= j < firstString.length
0 <= a <= b < secondString.length
- The substring of
firstString
that starts at theith
character and ends at thejth
character (inclusive) is equal to the substring ofsecondString
that starts at theath
character and ends at thebth
character (inclusive). j - a
is the minimum possible value among all quadruples that satisfy the previous conditions.
Return the number of such quadruples.
Example 1:
Input: firstString = "abcd", secondString = "bccda" Output: 1 Explanation: The quadruple (0,0,4,4) is the only one that satisfies all the conditions and minimizes j - a.
Example 2:
Input: firstString = "ab", secondString = "cd" Output: 0 Explanation: There are no quadruples satisfying all the conditions.
Constraints:
1 <= firstString.length, secondString.length <= 2 * 105
- Both strings consist only of lowercase English letters.
Solutions
Solution 1: Greedy + Hash Table
The problem actually asks us to find a smallest index $i$ and a largest index $j$ such that $firstString[i]$ equals $secondString[j]$, and the value of $i - j$ is the smallest among all index pairs that meet the conditions.
Therefore, we first use a hash table $last$ to record the index of the last occurrence of each character in $secondString$. Then we traverse $firstString$. For each character $c$, if $c$ has appeared in $secondString$, we calculate $i - last[c]$. If the value of $i - last[c]$ is less than the current minimum value, we update the minimum value and set the answer to 1. If the value of $i - last[c]$ equals the current minimum value, we increment the answer by 1.
The time complexity is $O(m + n)$, and the space complexity is $O(C)$. Here, $m$ and $n$ are the lengths of $firstString$ and $secondString$ respectively, and $C$ is the size of the character set. In this problem, $C = 26$.
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