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

  • Maximum submatrix

    Given an matrix of integers, you are asked to calculate the submatrix with the maximum sum.

    Input

    The first line of the input contains two integers - the number of rows in the matrix r and the number of columns c (1 ≀ r, c ≀ 50).
    The next r lines contain c integers separated by a space, that represent the elements in the matrix .

    Output

    The program should print a single integer - the largest submatrix sum.

    Examples

    Input
    Output
    3 5 1 2 -3 4 -6 -1 3 -100 4 0 0 1 -2 0 100
    104

    Explanation

    1
    2
    -3
    4
    -6
    -1
    3
    -100
    4
    0
    0
    1
    -2
    0
    100
    Β 

    Constraints

    Time limit: 2 seconds

    Memory limit: 512 MB

    Output limit: 1 MB

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