LeetCode in Swift: Largest Rectangle in Histogram

Problem Statement

Given n non-negative integers representing the histogram’s bar height where the width of each bar is 1, find the area of largest rectangle in the histogram.

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Above is a histogram where width of each bar is 1, given height = [2,1,5,6,2,3].

Image may be NSFW.
Clik here to view.

The largest rectangle is shown in the shaded area, which has area = 10 unit.

For example,
Given height = [2,1,5,6,2,3],
return 10.

Original LeetCode problem page

My Solution in Swift

I used a stack to make the solution run in linear time O(n)

func largestRectangleArea(heights: [Int]) -> Int {
    var widths = [Int](count: heights.count, repeatedValue: 1)
    var stack: [Int] = []
    var largestRectangleArea = 0
    // calc left half of width for each reference histogram bar
    for var i = 0; i < heights.count; ++i {
        while let sIdx = stack.last {
            if heights[sIdx] < heights[i] {
                break
            }
            stack.removeLast()
        }
        if let sIdx = stack.last {
            widths[i] += i - sIdx - 1
        } else {
            widths[i] += i
        }
        stack.append(i)
    }
    stack.removeAll(keepCapacity: true)
    // calc right half of width for each reference histogram bar while find out
    // the largest rectangle
    for var i = heights.count - 1; i >= 0; --i {
        while let sIdx = stack.last {
            if heights[sIdx] < heights[i] {
                break
            }
            stack.removeLast()
        }
        if let sIdx = stack.last {
            widths[i] += sIdx - i - 1
        } else {
            widths[i] += heights.count - 1 - i
        }
        stack.append(i)

        largestRectangleArea = max(widths[i] * heights[i], largestRectangleArea)
    }
    return largestRectangleArea
}

Try It Yourself

1: each links to a blog post of mine that is dedicated to the problem
2: total execution time of a solution on my MacBook Pro (Late 2013, 2.6 GHz Intel Core i7, 16 GB 1600 MHz DDR3). Each solution is compiled with following command:

$ swiftc -O -sdk `xcrun --show-sdk-path --sdk macosx` json.swift main.swift -o mySolution

The total execution time is the average of 10 runs.
3: these test cases are semi-automatically :P retrieved from LeetCode Online Judge system and are kept in JSON format
4: each Xcode project includes everything (my Swift solution to a problem, its JSON test cases and a driver code to test the solution on those test cases)

More Problems Solved in Swift

My full list of LeetCode problems attempted using Swift