LeetCode #962 — MEDIUM

Maximum Width Ramp

Move from brute-force thinking to an efficient approach using array strategy.

The Problem

Problem Statement

A ramp in an integer array nums is a pair (i, j) for which i < j and nums[i] <= nums[j]. The width of such a ramp is j - i.

Given an integer array nums, return the maximum width of a ramp in nums. If there is no ramp in nums, return 0.

Example 1:

Input: nums = [6,0,8,2,1,5]
Output: 4
Explanation: The maximum width ramp is achieved at (i, j) = (1, 5): nums[1] = 0 and nums[5] = 5.

Example 2:

Input: nums = [9,8,1,0,1,9,4,0,4,1]
Output: 7
Explanation: The maximum width ramp is achieved at (i, j) = (2, 9): nums[2] = 1 and nums[9] = 1.

Constraints:

2 <= nums.length <= 5 * 10⁴
0 <= nums[i] <= 5 * 10⁴

Step 01

Brute Force Baseline

Problem summary: A ramp in an integer array nums is a pair (i, j) for which i < j and nums[i] <= nums[j]. The width of such a ramp is j - i. Given an integer array nums, return the maximum width of a ramp in nums. If there is no ramp in nums, return 0.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Two Pointers · Stack

Example 1

[6,0,8,2,1,5]

Example 2

[9,8,1,0,1,9,4,0,4,1]

Step 02

Core Insight

What unlocks the optimal approach

No official hints in dataset. Start from constraints and look for a monotonic or reusable state.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #962: Maximum Width Ramp
class Solution {
    public int maxWidthRamp(int[] nums) {
        int n = nums.length;
        Deque<Integer> stk = new ArrayDeque<>();
        for (int i = 0; i < n; ++i) {
            if (stk.isEmpty() || nums[stk.peek()] > nums[i]) {
                stk.push(i);
            }
        }
        int ans = 0;
        for (int i = n - 1; i >= 0; --i) {
            while (!stk.isEmpty() && nums[stk.peek()] <= nums[i]) {
                ans = Math.max(ans, i - stk.pop());
            }
            if (stk.isEmpty()) {
                break;
            }
        }
        return ans;
    }
}

// Accepted solution for LeetCode #962: Maximum Width Ramp
func maxWidthRamp(nums []int) int {
	n := len(nums)
	stk := []int{}
	for i, v := range nums {
		if len(stk) == 0 || nums[stk[len(stk)-1]] > v {
			stk = append(stk, i)
		}
	}
	ans := 0
	for i := n - 1; i >= 0; i-- {
		for len(stk) > 0 && nums[stk[len(stk)-1]] <= nums[i] {
			ans = max(ans, i-stk[len(stk)-1])
			stk = stk[:len(stk)-1]
		}
		if len(stk) == 0 {
			break
		}
	}
	return ans
}

# Accepted solution for LeetCode #962: Maximum Width Ramp
class Solution:
    def maxWidthRamp(self, nums: List[int]) -> int:
        stk = []
        for i, v in enumerate(nums):
            if not stk or nums[stk[-1]] > v:
                stk.append(i)
        ans = 0
        for i in range(len(nums) - 1, -1, -1):
            while stk and nums[stk[-1]] <= nums[i]:
                ans = max(ans, i - stk.pop())
            if not stk:
                break
        return ans

// Accepted solution for LeetCode #962: Maximum Width Ramp
struct Solution;

impl Solution {
    fn max_width_ramp(a: Vec<i32>) -> i32 {
        let mut stack: Vec<usize> = vec![];
        let n = a.len();
        for i in 0..n {
            if let Some(&j) = stack.last() {
                if a[i] < a[j] {
                    stack.push(i);
                }
            } else {
                stack.push(i);
            }
        }
        let mut res = 0;
        for i in (0..n).rev() {
            while let Some(&j) = stack.last() {
                if a[j] <= a[i] {
                    res = res.max(i - j);
                    stack.pop();
                } else {
                    break;
                }
            }
        }
        res as i32
    }
}

#[test]
fn test() {
    let a = vec![6, 0, 8, 2, 1, 5];
    let res = 4;
    assert_eq!(Solution::max_width_ramp(a), res);
    let a = vec![9, 8, 1, 0, 1, 9, 4, 0, 4, 1];
    let res = 7;
    assert_eq!(Solution::max_width_ramp(a), res);
}

// Accepted solution for LeetCode #962: Maximum Width Ramp
function maxWidthRamp(nums: number[]): number {
    let [ans, n] = [0, nums.length];
    const stk: number[] = [];

    for (let i = 0; i < n - 1; i++) {
        if (stk.length === 0 || nums[stk.at(-1)!] > nums[i]) {
            stk.push(i);
        }
    }

    for (let i = n - 1; i >= 0; i--) {
        while (stk.length && nums[stk.at(-1)!] <= nums[i]) {
            ans = Math.max(ans, i - stk.pop()!);
        }
        if (stk.length === 0) break;
    }

    return ans;
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(n)

Space

O(n)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair of elements. The outer loop picks one element, the inner loop scans the rest. For n elements that is n × (n−1)/2 comparisons = O(n²). No extra memory — just two loop variables.

TWO POINTERS

O(n) time

O(1) space

Each pointer traverses the array at most once. With two pointers moving inward (or both moving right), the total number of steps is bounded by n. Each comparison is O(1), giving O(n) overall. No auxiliary data structures are needed — just two index variables.

Shortcut: Two converging pointers on sorted data → O(n) time, O(1) space.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.

Moving both pointers on every comparison

Wrong move: Advancing both pointers shrinks the search space too aggressively and skips candidates.

Usually fails on: A valid pair can be skipped when only one side should move.

Fix: Move exactly one pointer per decision branch based on invariant.

Breaking monotonic invariant

Wrong move: Pushing without popping stale elements invalidates next-greater/next-smaller logic.

Usually fails on: Indices point to blocked elements and outputs shift.

Fix: Pop while invariant is violated before pushing current element.