给定 n 个非负整数,用来表示柱状图中各个柱子的高度。每个柱子彼此相邻,且宽度为 1 。
求在该柱状图中,能够勾勒出来的矩形的最大面积。
思路:
方法1:栈 + 邵兵
public int largestRectangleArea(int[] heights) {
int len = heights.length;
if (len == 0) return 0;
if (len == 1) return heights[0];
int area = 0;
//新建一个数组,加头尾两个节点,作为两个邵兵
int[] newHeights = new int[len + 2];
//1.将数组赋值给有头尾邵兵的新数组
for (int i = 0; i < len; i++) {
newHeights[i + 1] = heights[i];
}
//数组长度和变量重置
len += 2;
heights = newHeights;
Deque<Integer> stack = new ArrayDeque<>();
stack.addLast(0);
for (int i = 1; i < len; i++) {
while (heights[stack.peekLast()] > heights[i]) {
int height = heights[stack.removeLast()];
int width =i - stack.peekLast() - 1;
area = Math.max(area, width * height);
}
stack.addLast(i);
}
return area;
}
时间复杂度:O(N)
空间复杂度:O(N)