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

• 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 {
public:
int ht;
int index;
Hist(int h, int i) : ht(h), index(i) {}
};

public:
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;
}
};``````

• 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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