算法题-柱状图中最大的矩形【JS实现】

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。

输入: [2,1,5,6,2,3]
输出: 10

暴力法：

/**
 * @param {number[]} heights
 * @return {number}
 */
var largestRectangleArea = function (heights) {
    
    
  if (!heights || !heights.length) return 0;
  let maxArea = 0;
  for (let i = 0; i < heights.length; i++) {
    
    
    let minHeight = Infinity;
    for (let j = i; j < heights.length; j++) {
    
    
      minHeight = Math.min(minHeight, heights[j]);
      maxArea = Math.max(maxArea, (j - i + 1) * minHeight);
    }
  }

  return maxArea;
};

var largestRectangleArea = function (heights) {
    
    
  if (!heights || !heights.length) return 0;

  let maxArea = 0;
  for (let i = 0; i < heights.length; i++) {
    
    
    let left = i,
      right = i;
    while (left - 1 > -1 && heights[left - 1] >= heights[i]) {
    
    
      --left;
    }
    while (right + 1 < heights.length && heights[right + 1] >= heights[i]) {
    
    
      ++right;
    }
    maxArea = Math.max(maxArea, heights[i] * (right - left + 1));
  }

  return maxArea;
};

栈

var largestRectangleArea = function (heights) {
    
    
  let maxArea = 0;
  let stack = [-1];
  for (let i = 0; i < heights.length; i++) {
    
    
    while (stack.length > 1 && heights[stack[stack.length - 1]] >= heights[i]) {
    
    
      maxArea = Math.max(
        maxArea,
        heights[stack.pop()] * (i - stack[stack.length - 1] - 1)
      );
    }
    stack.push(i);
  }
  while (stack.length > 1) {
    
    
    maxArea = Math.max(
      maxArea,
      heights[stack.pop()] * (heights.length - stack[stack.length - 1] - 1)
    );
  }
  return maxArea;
};

var largestRectangleArea = function (heights) {
    
    
  heights.push(0);
  const stack = [];
  let maxArea = 0;

  for (let i = 0; i < heights.length; i++) {
    
    
    while (stack.length > 1 && heights[stack[stack.length - 1]] > heights[i]) {
    
    
      maxArea = Math.max(heights[stack.pop()] * (i - 1 - stack[stack.length - 1]), maxArea);
    }
    if (stack.length && heights[stack[stack.length - 1]] > heights[i]) {
    
    
      maxArea = Math.max(heights[stack.pop()] * i, maxArea);
    }
    stack.push(i);
  }
  return maxArea;
};

/**
 * @param {number[]} heights
 * @return {number}
 */
const largestRectangleArea = function (heights) {
    
    
    let maxArea = 0;
    const stack = [];
    heights = [0].concat(heights).concat([0]);
    for (let i = 0; i < heights.length; i++) {
    
    
        while (stack && heights[stack[stack.length - 1]] > heights[i]) {
    
    
            const j = stack.pop();
            maxArea = Math.max((i - stack[stack.length - 1] - 1) * heights[j], maxArea);
        }
        stack.push(i);
    }
    return maxArea;
};