Algorithms and Data Structures

  • Profound Academy

    • Status
      • 1
        Implementation
      • 2
        Bitwise operations
      • 3
        Prefix Sums
      • 4
        Sliding window / Two pointers
      • 5
        Modular Arithmetic
      • 6
        Number Theory
      • 7
        Binary Search
      • 8
        Basic Sorting
      • 9
        Greedy Algorithms
      • 10
        Basic Dynamic Programming
      • 11
        Recursion
      • 12
        Linked LIst
      • 13
        Queue & Stack
      • 14
        Binary tree + BST
      • 15
        Divide & Conquer + Advanced Sorting
      • 16
        Heap
      • 17
        Hashing
      • 18
        Graph Representation
      • 19
        BFS

    • Largest Rectangular Area in a Histogram

    Given n numbers representing the heights of bars in a histogram, you are asked to calculate the largest area that can be obtained in the histogram without going out of the bars.
    All the bars in the histogram have a width of 1, while the heights are arbitrary nonnegative integers.
    notion image

    Input

    The first line of the input contains a single integer n (1 ≤ n ≤ ).
    The next line contains n space-separated integers (0 ≤ ≤ ).

    Output

    The program should print the largest area possible to obtain from the bars of the histogram.

    Examples

    Input
    Output
    8 6 2 5 4 5 1 6 1
    12
    Hint
    For each element in the histogram, you can calculate 2 numbers - the closest element that’s smaller than the current element on the left and on the right. That would be sufficient to calculate the area of the rectangle having the height of the current bar.
     

    Constraints

    Time limit: 2 seconds

    Memory limit: 512 MB

    Output limit: 1 MB

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