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题目：
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.
Above is a histogram where width of each bar is 1, given height = [2,1,5,6,2,3].
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.
思路：
1）对每个直方维护它能拓展到左右两边最远的边界。
package area; public class LargestRectangleInHistogram { public int largestRectangleArea(int[] height) { int n = height.length; int max = 0; int[] left = new int[n]; int[] right = new int[n]; for (int pos = 0; pos < n; ++pos) { left[pos] = right[pos] = pos; int i = pos - 1; for (; i >= 0; --i) { if (height[i] < height[pos]) { left[pos] = i + 1; break; } } if (i == -1) left[pos] = 0; for (i = pos + 1; i < n; ++i) { if (height[i] < height[pos]) { right[pos] = i - 1; break; } } if (i == n) right[pos] = n - 1; int area = height[pos] * (right[pos] - left[pos] + 1); if (area > max) max = area; } return max; } public static void main(String[] args) { // TODO Auto-generated method stub int[] height = { 1,1,1,1 }; LargestRectangleInHistogram l = new LargestRectangleInHistogram(); System.out.println(l.largestRectangleArea(height)); } }
2）维护一个栈，对比当前元素，如果大于当前元素，则pop，否则push当前元素的index
package area; import java.util.Stack; public class LargestRectangleInHistogram { public int largestRectangleArea(int[] height) { Stack<Integer> stack = new Stack<Integer>(); int max = 0; int n = height.length; int[] newHeight = new int[n + 1]; for (int i = 0; i < n; ++i) newHeight[i] = height[i]; newHeight[n] = 0; int i = 0; while (i < n + 1) { if (stack.isEmpty() || newHeight[stack.peek()] <= newHeight[i]) { stack.push(i++); } else { int index = stack.pop(); int area = (stack.isEmpty() ? i : (i - stack.peek() - 1)) * newHeight[index]; max = (max < area ? area : max); } } return max; } public static void main(String[] args) { // TODO Auto-generated method stub int[] height = { 1,1 }; LargestRectangleInHistogram l = new LargestRectangleInHistogram(); System.out.println(l.largestRectangleArea(height)); } }
LeetCode - Largest Rectangle in Histogram
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原文地址：http://www.cnblogs.com/shuaiwhu/p/5096633.html
