Easy to understand O(nlogn) solution using Union-Find.

  • 2

    This solution assumes you have implemented a QuickUnion union-find DS class, with logn complexity for Union operation.

    • Initially, enter all n indices into union-find, each with their own id.
    • Then create pairs of (height, index) for each histogram, put them into a vector, and sort the vector on height of histograms. We will use this vector as a stack (popping from highest height histograms).
    • while stack not empty
      • hist = element at the top, pop it
      • if this hist's left and/or right neighbor have height GREATER than this hist, then union with their sets. (This lets me know how many neighbors are to my left and right that have height >= mine. This is because of the order we pop from the stack, from largest to smallest).
      • Find the size of my cluster, from Union-Find DS.
      • candidate for max area is (sz of cluster)*(my height)
      • if this candidate is greater than previously recorded max area, update max area.

    And that's it, just return max area at the end. Here is the code:

    class Solution {
        class Hist {
            int ht;
            int index;
            Hist(int h, int i) : ht(h), index(i) {}
        int largestRectangleArea(vector<int>& height) {
            if (height.size() == 0) return 0;
            vector<Hist> histograms;
            for (int i=0; i<height.size(); i++) {
                histograms.push_back(Hist(height[i], i));
            std::sort(histograms.begin(), histograms.end(), [] (const Hist& lhs, const Hist& rhs) -> bool {
                return (lhs.ht < rhs.ht);
            int max=0;
            QuickUnion uf(histograms.size());
            while (!histograms.empty()) {
                Hist hist = histograms.back(); histograms.pop_back();
                if (hist.index != 0 && hist.ht <= height[hist.index-1]) { //left neighbor
                    uf.Union(hist.index, hist.index-1);
                if (hist.index != height.size()-1 && hist.ht <= height[hist.index+1]) { //right neighbor
                    uf.Union(hist.index, hist.index+1);
                int clusterSz = uf.SizeSet(hist.index);
                if (max < (clusterSz * hist.ht)) {
                    max = clusterSz * hist.ht;
            return max;

  • 0

    It would also be nice to post your QuickUnion class as there are many varying implementations of QuickUnion (eg. path compression)

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