84. Largest Rectangle in Histogram

84. Largest Rectangle in Histogram


https://www.youtube.com/watch?v=KkJrGxuQtYo&t=129s



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].
 
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?The largest rectangle is shown in the shaded area, which has area = 10 unit.



Input: [2,1,5,6,2,3]
Output: 10

Solution 1 : time o(n^ 2) 

    // loop thru from left to right
        // if the height is increasing, keep i++;
        // and once the height is decreasing, we look back at the 
        // columns and calculate every area 
        // formula is length * min(heights)
        // use a var called res to update the res 
        // after done with that, i++
        // if the height is decreasing again, we do the same as above 
     
            // check if the next one is increasing, or decreasing
            // if increasing , keep going
            // if dereasing or hit the end, reflect and calculate prev areas
            




class Solution {
    public int largestRectangleArea(int[] heights) {
      if(heights == null || heights.length == 0) return 0;
      
      int res = 0;
      for(int i = 0; i < heights.length; i++){
        // if hit the end or the next height is decreasing
        if(i == heights.length - 1 || heights[i] > heights[i + 1]){
          int minHeight = heights[i];
          for(int j = i; j >= 0; j--){
            minHeight = Math.min(minHeight, heights[j]);
            int area = (i - j + 1) * minHeight;
            res = Math.max(res, area);
          }
        }
      }
      return res;
    }
}



Solution 2 : using stack , time o(n)