The Mental Model
A monotonic stack is a stack that maintains its elements in a strictly increasing or decreasing order. It is the "Silver Bullet" for problems where an element's value depends on its closest greater/smaller neighbors.
1. The "Next Greater Element" Template
public int[] nextGreaterElement(int[] nums) {
int n = nums.length;
int[] res = new int[n];
Stack<Integer> stack = new Stack<>(); // Stores indices
for (int i = 0; i < n; i++) {
// While stack is not empty and current element is greater than top
while (!stack.isEmpty() && nums[i] > nums[stack.peek()]) {
int prevIndex = stack.pop();
res[prevIndex] = nums[i]; // Found the next greater!
}
stack.push(i);
}
// Remaining indices in stack have no next greater
while (!stack.isEmpty()) {
res[stack.pop()] = -1;
}
return res;
}
2. Key Variations
| Requirement | Property | Action |
|---|---|---|
| Next Greater | Monotonic Decreasing | Pop when curr > top |
| Next Smaller | Monotonic Increasing | Pop when curr < top |
| Prev Greater | Scan Right to Left | Same logic as Next Greater |
3. Interview Discussion: The "Aha!" Moment
How do you know it's a Monotonic Stack problem? Look for words like "Nearest," "Closest," or "Next Greater/Smaller." If you find yourself thinking "I need to look back at previous elements to see which ones I just beat," the Monotonic Stack is your best friend.