LeetCode: Maximum Width Ramp

Posted on June 18, 2019July 26, 2020 by braindenny

Maximum Width Ramp

Similar Problems:

Given an array A of integers, a ramp is a tuple (i, j) for which i < j and A[i] <= A[j]. The width of such a ramp is j – i.

Find the maximum width of a ramp in A. If one doesn’t exist, return 0.

Example 1:

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

Example 2:

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

Note:

2 <= A.length <= 50000
0 <= A[i] <= 50000

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

Solution:

// https://code.dennyzhang.com/maximum-width-ramp
// Basic Ideas: monotone stack + binarysearch
//
//   For each j, find i.
//     Value vs location
//
// Complexity: Time O(n*log(n)), Space O(n)
func maxWidthRamp(A []int) int {
    res := 0
    stack := []int{}
    for i, v := range A {
        if len(stack) == 0 || A[stack[len(stack)-1]] > v {
            stack = append(stack, i)
        }
        left, right := 0, len(stack)-1
        // F, F, F, T, T, T
        for left<right {
            mid := (right-left)/2+left
            if A[stack[mid]] <= v {
                right = mid
            } else {
                left = mid+1
            }
        }
        if i-stack[left] > res {
            res = i-stack[left]
        }
    }
    return res
}

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