Merge pull request #266 from neha030/dev6

Largest rectangle area under histogram added

Author: smv1999

Data Structures/Stacks/Largest_rectangle_area_under_histogram.cpp

@@ -0,0 +1,90 @@
+/*
+Given the heights of the bars of a histogram, find out the largest
+rectangular area under the histogram. Width of each bar is 1 unit.
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+// Prints largest rectangular area under histogram
+void largestAreaUnderHistogram(int height[], int n)
+{
+
+	// Stores index of the bars
+	stack<int> s;
+	int ans = 0;
+	int l = 0, r = 0;
+	for (int i = 0; i < n; i++)
+	{
+
+		// If stack is empty, push the bar
+		if (s.empty())
+		{
+			s.push(i);
+			continue;
+		}
+
+		// If height[i] is greater then push the bar
+		if (height[i] > height[s.top()])
+		{
+			s.push(i);
+		}
+		else
+		{
+			// I have encountered a height that is less than my last height
+
+			// Pop out all bars whose height is greater than height[i],
+			// Simulataneously calculate the new area
+			while (!s.empty() && height[i] < height[s.top()])
+			{
+				int toBeRemoved = s.top();
+				s.pop();
+				int area;
+				if (s.empty())
+				{
+					area = height[toBeRemoved] * i;
+				}
+				else
+				{
+					area = height[toBeRemoved] * (i - s.top() - 1);
+				}
+				//cout << toBeRemoved << " " << area << endl;
+				if (area > ans)
+				{
+					ans = area;
+					l = (!s.empty()) ? s.top() : 0;
+					r = i;
+				}
+				ans = max(ans, area);
+			}
+			s.push(i);
+		}
+	}
+	cout << "Largest area = " << ans << " between bars " << l << " and " << r;
+}
+
+int main()
+{
+
+	// Input number of bars
+	cout << "Enter number of bars: ";
+	int n;
+	cin >> n;
+	// Input heights
+	cout << "Enter height of each bar: ";
+	int height[n];
+	for (int i = 0; i < n; i++)
+		cin >> height[i];
+
+	largestAreaUnderHistogram(height, n);
+}
+
+/*
+Time Complexity: O(n)
+Space Complexity: O(n)
+
+SAMPLE INPUT AND OUTPUT 
+Enter number of bars: 7
+Enter height of each bar: 6 2 5 4 5 1 6
+Largest area = 12 between bars 1 and 5
+*/