Today's LeetCode challenge taught me an important lesson about problem-solving: sometimes understanding why a solution works is more valuable than just knowing how to code it. Like many developers, I initially jumped into thinking about implementation - loops, arrays, storing values. However, the real breakthrough came not from asking "how do I code this?" but from asking "why would this work?"
The Challenge
Given an array nums, find the majority element (the element that appears more than n(size of array)/2 times). For example:
javascriptCopyInput: nums = [2,2,1,1,1,2,2]
Output: 2
My Initial Approach
My first instinct was to create a separate array to store repeated elements. I thought about using nested loops to compare elements:
Outer loop to track current element
Inner loop starting one index ahead to find matches
This would work, but it felt complex and inefficient. That's when I started thinking about sorting.
The Breakthrough
The key insight came when breaking down what "majority element" really means:
In an array of length 7, n/2 is 3.5
Majority means appearing more than 3.5 times
After sorting: [1,1,1,2,2,2,2]
Then came the "ohhhh snap" moment. With a sorted array:
First half: 3 positions
Middle position: 1 position
Second half: 3 positions
Since the majority element appears more than half the time (4+ times in our example), it MUST cross the middle position. It's like having a stick longer than half the array - no matter where you place it, it has to cross the center!
The Solution: Simple and to the Point
This understanding led to a surprisingly simple solution:
javascriptCopyvar majorityElement = function(nums) {
nums.sort((a,b) => a - b);
return nums[Math.floor(nums.length/2)];
};
Just sort and return the middle element. That's it! No counting, no tracking, no complex logic.
Why It Works
Let's prove it:
After sorting, identical elements are grouped together
The majority element appears more than n/2 times
Even if all these appearances are:
At the start: [M,M,M,M,x,x,x]
At the end: [x,x,x,M,M,M,M]
Around middle: [x,M,M,M,M,x,x] It must include the middle position!
Learning Impact
This problem taught me several valuable lessons:
Question your first instinct - sometimes there's a simpler way
Understanding "why" leads to simple solutions
Visual/mathematical reasoning can reveal patterns
Breaking down the problem conditions (">n/2 times") can lead to insights
Most importantly, I learned that when you truly understand why a solution works, the code almost writes itself. It's not about memorizing patterns - it's about developing the intuition to see them.