Longest path in 2-D that contains increasing sequence in JavaScript

Increasing Sequence

A sequence of numbers in which each succeeding element is either greater or equal to the preceding element is an increasing sequence.

For instance,

4, 6, 8, 9, 11, 14 is increasing sequence
3, 3, 3, 3, 3, 3, 3 is also an increasing sequence

Problem:

We are required to write a JavaScript function that takes in a 2-D array of numbers, arr, as the only argument. Our function should find and return the length of that longest path in the array that contains only increasing numbers.

For example, if the input to the function is −

const arr = [
   [4, 5, 6],
   [4, 3, 7],
   [3, 3, 2]
];

Then the output should be −

const output = 4;

Output Explanation:

Because the longest increasing sequence is 4, 5, 6, 7.

Example

The code for this will be −

const arr = [
   [4, 5, 6],
   [4, 3, 7],
   [3, 3, 2]
];
const longestIncreasingPath = (arr = []) => {
   let longest = 0;
   let dp = Array(arr.length).fill(null).map(() =>
   Array(arr[0].length).fill(1));
   const backtracking = (row, col) => {
      if (dp[row][col]!=1) return dp[row][col];
      let dRow = [1,0,-1,0];
      let dCol = [0,1,0,-1];
      for (let i = 0;i<dRow.length;i++) {
         let nR = row + dRow[i], nC = col+dCol[i];
         if (nR >= 0 && nR < arr.length && nC >= 0 && nC < arr[0].length && arr[nR][nC] > arr[row][col]) {
            dp[row][col] = Math.max(dp[row][col], 1 + backtracking(nR, nC))
         };
      };
      return dp[row][col];
   }
   for (let i=0;i<arr.length;i++) {
      for (let j=0;j<arr[0].length;j++) {
         longest = Math.max(longest, backtracking(i, j));
      };
   };
   return longest;
};
console.log(longestIncreasingPath(arr));

Code Explanation:

The Idea

• Here, we have used backtracking depth first search.

• The recursion function simply returns the longest increasing path for a given row and column

• If we already have a record of the longest increasing path for a position, then we can simply return that.

Output

And the output in the console will be −

4

AmitDiwan

Published on 19-Mar-2021 06:11:51

• Related Questions & Answers
• Longest Increasing Path in a Matrix in Python
• Longest subarray which only contains strictly increasing numbers JavaScript
• Strictly increasing sequence JavaScript
• Reshaping 2-D array in JavaScript
• Converting array into increasing sequence in JavaScript
• Find longest bitonic sequence such that increasing and decreasing parts are from two different arrays in C++
• Find longest bitonic sequence such that increasing and decreasing parts are from two different arrays in Python
• Longest Increasing Subsequence
• Program to length of longest increasing path in a given matrix in Python
• Total number of longest increasing sequences in JavaScript
• Grouping and sorting 2-D array in JavaScript
• Converting object to 2-D array in JavaScript
• Longest Increasing Subsequence in Python
• C++ Program to Find the Longest Increasing Subsequence of a Given Sequence
• Equality of two 2-D arrays - JavaScript