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

    • Maximum falling path sum

    Given a grid of height h and width w, you are asked to calculate the maximum sum one might obtain by moving from top to bottom, where on each step it’s only allowed to move to the below adjacent 3 cells. In other words, being at position (r, c), you can move to positions: (r + 1, c - 1), (r + 1, c), and (r + 1, c + 1). That’s why we call it a falling sum - as we fall from the top to the very bottom of the grid. Find the maximum sum of the path.
    ㅤ
    o
    ㅤ
    ㅤ
    ↙️
    ⬇️
    ↘️
    ㅤ
    ㅤ
    ㅤ
    ㅤ
    ㅤ
    ㅤ
    ㅤ
    ㅤ
    ㅤ

    Input

    The first line of the input contains two integers h and w (1 ≤ h, w ≤ 100).
    The next h lines contain w numbers (-100 ≤ ≤ 100) representing the values of the grid at row r and column c.

    Output

    The program should print the maximum possible sum obtained among all the possible falling paths.

    Examples

    Input
    Output
    3 3 2 1 3 6 5 4 7 8 9
    17
     

    Constraints

    Time limit: 1 seconds

    Memory limit: 512 MB

    Output limit: 1 MB

    To check your solution you need to sign in
    Sign in to continue