Is Check If Digits Are Equal in String After Operations II easy or hard?

Check If Digits Are Equal in String After Operations II is classified as Hard. The challenge is recognizing that repeated pair operations form Pascal's Triangle and then handling binomial coefficients modulo a non-prime number (10) using number theory techniques.

Check If Digits Are Equal in String After Operations II Python/Java solution

Most implementations compute binomial coefficients modulo 10 while iterating through the string and accumulating two weighted sums. The same logic translates directly across Python, Java, C++, and Go because it only uses integer arithmetic and modular operations.

What is the best approach for Check If Digits Are Equal in String After Operations II?

The optimal approach uses combinatorics. Repeated pair-sum operations form Pascal's Triangle coefficients, so the final digits can be expressed as weighted sums using C(n-2, i). Compute these binomial coefficients modulo 10 using Lucas' theorem with mod 2 and mod 5, then combine the results. This reduces the complexity to O(n) time and O(1) space.

Is Check If Digits Are Equal in String After Operations II asked at Google/Amazon/Meta?

Problems combining combinatorics, modular arithmetic, and string transformations commonly appear in interviews at companies like Google, Amazon, and Meta. The pattern-recognition aspect—reducing repeated operations to a binomial expansion—is a typical advanced interview expectation.

What data structure is used in Check If Digits Are Equal in String After Operations II?

The solution does not rely on complex data structures. It mainly uses arithmetic on digits and combinatorial coefficients. The key techniques come from number theory and combinatorics rather than arrays, trees, or hash maps.

What is the time complexity of Check If Digits Are Equal in String After Operations II?

The optimal combinatorial solution runs in O(n) time with O(1) extra space because it processes each digit once while computing binomial coefficients modulo 10. A naive simulation requires O(n^2) time since each operation rebuilds a slightly shorter string.

Description Hints 3 Video 42:11

3463. Check If Digits Are Equal in String After Operations II

Q: How to solve Check If Digits Are Equal in String After Operations II in O(n)?

Observe that repeated adjacent sums follow Pascal's Triangle. After n-2 operations, the final digits equal weighted sums of the original digits using coefficients C(n-2, i). Compute each coefficient modulo 10 using Lucas' theorem for mod 2 and mod 5, combine them with the Chinese Remainder method, and accumulate the two final sums in one pass.

Hard14.3% acceptance2 companies

You are given a string s consisting of digits. Perform the following operation repeatedly until the string has exactly two digits:

For each pair of consecutive digits in s, starting from the first digit, calculate a new digit as the sum of the two digits modulo 10.
Replace s with the sequence of newly calculated digits, maintaining the order in which they are computed.

Return true if the final two digits in s are the same; otherwise, return false.

Example 1:

Input: s = "3902"

Output: true

Explanation:

Initially, s = "3902"
First operation:
- (s[0] + s[1]) % 10 = (3 + 9) % 10 = 2
- (s[1] + s[2]) % 10 = (9 + 0) % 10 = 9
- (s[2] + s[3]) % 10 = (0 + 2) % 10 = 2
- s becomes "292"
Second operation:
- (s[0] + s[1]) % 10 = (2 + 9) % 10 = 1
- (s[1] + s[2]) % 10 = (9 + 2) % 10 = 1
- s becomes "11"
Since the digits in "11" are the same, the output is true.

Example 2:

Input: s = "34789"

Output: false

Explanation:

Initially, s = "34789".
After the first operation, s = "7157".
After the second operation, s = "862".
After the third operation, s = "48".
Since '4' != '8', the output is false.

Constraints:

3 <= s.length <= 10⁵
s consists of only digits.

Asked at 2 companies

ADP

Google

Topics

Hints open one at a time

Hint 1

Can we use nCr and use Pascal's triangle values here?

Hint 2

nCr mod 10 can be uniquely determined from nCr mod 2 and nCr mod 5.

Hint 3

Use Lucas's theorem.