Destroy Sequential Targets

Destroy Sequential Targets

What is this problem about?

In the Destroy Sequential Targets coding problem, you are given an array of integers nums representing targets and an integer space. You can choose one target to start with and then destroy any other target $x$ if $x = target + k imes space$ for some non-negative integer $k$. You want to find the starting target that allows you to destroy the maximum number of total targets. If there's a tie, choose the smallest target value.

Why is this asked in interviews?

Intuit asks this to test your ability to transform numeric properties into categorical groups. The condition $x = target + k imes space$ is equivalent to saying that $x$ and $target$ have the same remainder when divided by space ($x \pmod{space} == target \pmod{space}$). It evaluations your proficiency with the hash table design pattern and your understanding of modular arithmetic.

Algorithmic pattern used

This problem uses Modular Arithmetic and Frequency Counting.

1. For every number in nums, calculate remainder = num % space.
2. Use a Hash Map to count the frequency of each remainder.
3. Find the remainder with the highest frequency.
4. Among all numbers that produce that remainder, find the smallest one.

Example explanation

nums = [1, 3, 5, 2, 4, 6], space = 2.

1. Remainders:
   • 1%2=1, 3%2=1, 5%2=1. Frequency(1) = 3.
   • 2%2=0, 4%2=0, 6%2=0. Frequency(0) = 3.
2. Both remainders 0 and 1 have frequency 3.
3. Smallest number with remainder 1 is 1.
4. Smallest number with remainder 0 is 2.
5. Comparison: 1 is smaller than 2. Result: 1.

Common mistakes candidates make

• Brute Force: Trying to simulate the "destruction" starting from every single number in the array ($O(N^2)$).
• Smallest Number vs Smallest Remainder: Forgetting that the goal is to return the smallest original target value, not the smallest remainder value.
• Negative Numbers: If the input can have negative numbers, ensure your modulo operation handles them correctly (e.g., (num % space + space) % space).

Interview preparation tip

Problems involving "arithmetic sequences" or "multiples of a gap" almost always boil down to grouping numbers by their remainder modulo the gap. This is a common trick in number theory and competitive programming.