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# Length of longest connected 1’s in a Binary Grid

• Difficulty Level : Hard
• Last Updated : 04 May, 2021

Given a grid of size N*M consists of 0 and 1 only, the task is to find the length of longest connected 1s in the given grid. We can only move to left, right, up or down from any current cell of the grid.

Examples:

Input: N = 3, M = 3, grid[][] = { {0, 0, 0}, {0, 1, 0}, {0, 0, 0} }
Output:
Explanation:
The longest possible route is 1 as there cant be any movement from (1, 1) position of the matrix.

Input: N = 6, M = 7, grid[][] = { {0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 1, 0, 0, 0}, {0, 1, 0, 1, 0, 0, 0}, {0, 1, 0, 1, 0, 1, 0}, {0, 1, 1, 1, 1, 1, 0}, {0, 0, 0, 0, 0, 0, 0}}
Output:
Explanation:
The longest possible route is 9 starting from (1, 1) -> (2, 1) -> (3, 1) -> (4, 1) -> (4, 2) -> (4, 3) -> (4, 4) -> (4, 5) -> (3, 5).

Approach: The idea is to do DFS Traversal on grid where the value of current cell is 1 and recursively call for all the four direction of the current cell where value is 1 and updated the maximum length of connected 1.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ``#define row 6``#define col 7``using` `namespace` `std;` `int` `vis[row + 1][col + 1], id;``int` `diameter = 0, length = 0;` `// Keeps a track of directions``// that is up, down, left, right``int` `dx[] = { -1, 1, 0, 0 };``int` `dy[] = { 0, 0, -1, 1 };` `// Function to perform the dfs traversal``void` `dfs(``int` `a, ``int` `b, ``int` `lis[][col],``         ``int``& x, ``int``& y)``{` `    ``// Mark the current node as visited``    ``vis[a][b] = id;` `    ``// Increment length from this node``    ``length++;` `    ``// Update the diameter length``    ``if` `(length > diameter) {``        ``x = a;``        ``y = b;``        ``diameter = length;``    ``}``    ``for` `(``int` `j = 0; j < 4; j++) {` `        ``// Move to next cell in x-direction``        ``int` `cx = a + dx[j];` `        ``// Move to next cell in y-direction``        ``int` `cy = b + dy[j];` `        ``// Check if cell is invalid``        ``// then continue``        ``if` `(cx < 0 || cy < 0 || cx >= row``            ``|| cy >= col || lis[cx][cy] == 0``            ``|| vis[cx][cy]) {``            ``continue``;``        ``}` `        ``// Perform DFS on new cell``        ``dfs(cx, cy, lis, x, y);``    ``}` `    ``vis[a][b] = 0;` `    ``// Decrement the length``    ``length--;``}` `// Function to find the maximum length of``// connected 1s in the given grid``void` `findMaximumLength(``int` `lis[][col])``{` `    ``int` `x, y;` `    ``// Increment the id``    ``id++;``    ``length = 0;``    ``diameter = 0;` `    ``// Traverse the grid[]``    ``for` `(``int` `i = 0; i < row; i++) {` `        ``for` `(``int` `j = 0; j < col; j++) {` `            ``if` `(lis[i][j] != 0) {` `                ``// Find start point of``                ``// start dfs call``                ``dfs(i, j, lis, x, y);``                ``i = row;``                ``break``;``            ``}``        ``}``    ``}` `    ``id++;``    ``length = 0;``    ``diameter = 0;` `    ``// DFS Traversal from cell (x, y)``    ``dfs(x, y, lis, x, y);` `    ``// Print the maximum length``    ``cout << diameter;``}` `// Driver Code``int` `main()``{``    ``// Given grid[][]``    ``int` `grid[][col] = { { 0, 0, 0, 0, 0, 0, 0 },``                        ``{ 0, 1, 0, 1, 0, 0, 0 },``                        ``{ 0, 1, 0, 1, 0, 0, 0 },``                        ``{ 0, 1, 0, 1, 0, 1, 0 },``                        ``{ 0, 1, 1, 1, 1, 1, 0 },``                        ``{ 0, 0, 0, 1, 0, 0, 0 } };` `    ``// Function Call``    ``findMaximumLength(grid);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.util.*;` `class` `GFG{``    ` `static` `final` `int` `row = ``6``;``static` `final` `int` `col = ``7``;``static` `int` `[][]vis = ``new` `int``[row + ``1``][col + ``1``];``static` `int` `id;``static` `int` `diameter = ``0``, length = ``0``;``static` `int` `x = ``0``, y = ``0``;` `// Keeps a track of directions``// that is up, down, left, right``static` `int` `dx[] = { -``1``, ``1``, ``0``, ``0` `};``static` `int` `dy[] = { ``0``, ``0``, -``1``, ``1` `};` `// Function to perform the dfs traversal``static` `void` `dfs(``int` `a, ``int` `b, ``int` `lis[][])``{``    ` `    ``// Mark the current node as visited``    ``vis[a][b] = id;` `    ``// Increment length from this node``    ``length++;` `    ``// Update the diameter length``    ``if` `(length > diameter)``    ``{``        ``x = a;``        ``y = b;``        ``diameter = length;``    ``}` `    ``for``(``int` `j = ``0``; j < ``4``; j++)``    ``{``        ` `       ``// Move to next cell in x-direction``       ``int` `cx = a + dx[j];``       ` `       ``// Move to next cell in y-direction``       ``int` `cy = b + dy[j];``       ` `       ``// Check if cell is invalid``       ``// then continue``       ``if` `(cx < ``0` `|| cy < ``0` `||``           ``cx >= row || cy >= col ||``           ``lis[cx][cy] == ``0` `|| vis[cx][cy] > ``0``)``       ``{``           ``continue``;``       ``}``       ` `       ``// Perform DFS on new cell``       ``dfs(cx, cy, lis);``    ``}``    ` `    ``vis[a][b] = ``0``;` `    ``// Decrement the length``    ``length--;``}` `// Function to find the maximum length of``// connected 1s in the given grid``static` `void` `findMaximumLength(``int` `lis[][])``{``    ` `    ``// Increment the id``    ``id++;``    ``length = ``0``;``    ``diameter = ``0``;` `    ``// Traverse the grid[]``    ``for``(``int` `i = ``0``; i < row; i++)``    ``{``       ``for``(``int` `j = ``0``; j < col; j++)``       ``{``          ``if` `(lis[i][j] != ``0``)``          ``{``              ` `              ``// Find start point of``              ``// start dfs call``              ``dfs(i, j, lis);``              ``i = row;``              ``break``;``          ``}``       ``}``    ``}` `    ``id++;``    ``length = ``0``;``    ``diameter = ``0``;` `    ``// DFS Traversal from cell (x, y)``    ``dfs(x, y, lis);` `    ``// Print the maximum length``    ``System.out.print(diameter);``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ` `    ``// Given grid[][]``    ``int` `grid[][] = { { ``0``, ``0``, ``0``, ``0``, ``0``, ``0``, ``0` `},``                     ``{ ``0``, ``1``, ``0``, ``1``, ``0``, ``0``, ``0` `},``                     ``{ ``0``, ``1``, ``0``, ``1``, ``0``, ``0``, ``0` `},``                     ``{ ``0``, ``1``, ``0``, ``1``, ``0``, ``1``, ``0` `},``                     ``{ ``0``, ``1``, ``1``, ``1``, ``1``, ``1``, ``0` `},``                     ``{ ``0``, ``0``, ``0``, ``1``, ``0``, ``0``, ``0` `} };` `    ``// Function Call``    ``findMaximumLength(grid);``}``}` `// This code is contributed by amal kumar choubey`

## Python3

 `# Python3 program for the above approach``row ``=` `6``col ``=` `7`` ` `vis ``=` `[[``0` `for` `i ``in` `range``(col ``+` `1``)]``          ``for` `j ``in` `range``(row ``+` `1``)]``id` `=` `0``diameter ``=` `0``length ``=` `0`` ` `# Keeps a track of directions``# that is up, down, left, right``dx ``=` `[ ``-``1``, ``1``, ``0``, ``0` `]``dy ``=` `[ ``0``, ``0``, ``-``1``, ``1` `]`` ` `# Function to perform the dfs traversal``def` `dfs(a, b, lis, x, y):``    ` `    ``global` `id``, length, diameter``    ` `    ``# Mark the current node as visited``    ``vis[a][b] ``=` `id`` ` `    ``# Increment length from this node``    ``length ``+``=` `1`` ` `    ``# Update the diameter length``    ``if` `(length > diameter):``        ``x ``=` `a``        ``y ``=` `b``        ``diameter ``=` `length``    ` `    ``for` `j ``in` `range``(``4``):`` ` `        ``# Move to next cell in x-direction``        ``cx ``=` `a ``+` `dx[j]`` ` `        ``# Move to next cell in y-direction``        ``cy ``=` `b ``+` `dy[j]`` ` `        ``# Check if cell is invalid``        ``# then continue``        ``if` `(cx < ``0` `or` `cy < ``0` `or``            ``cx >``=` `row ``or` `cy >``=` `col ``or``            ``lis[cx][cy] ``=``=` `0` `or` `vis[cx][cy]):``            ``continue``    ` `        ``# Perform DFS on new cell``        ``dfs(cx, cy, lis, x, y)``    ` `    ``vis[a][b] ``=` `0`` ` `    ``# Decrement the length``    ``length ``-``=` `1``    ` `    ``return` `x, y` `# Function to find the maximum length of``# connected 1s in the given grid``def` `findMaximumLength(lis):``    ` `    ``global` `id``, length, diameter``    ` `    ``x ``=` `0``    ``y ``=` `0`` ` `    ``# Increment the id``    ``id` `+``=` `1``    ` `    ``length ``=` `0``    ``diameter ``=` `0`` ` `    ``# Traverse the grid[]``    ``for` `i ``in` `range``(row):``        ``for` `j ``in` `range``(col):``            ``if` `(lis[i][j] !``=` `0``):`` ` `                ``# Find start point of``                ``# start dfs call``                ``x, y ``=` `dfs(i, j, lis, x, y)``                ``i ``=` `row``                ``break`` ` `    ``id` `+``=` `1``    ``length ``=` `0``    ``diameter ``=` `0`` ` `    ``# DFS Traversal from cell (x, y)``    ``x, y ``=` `dfs(x, y, lis, x, y)`` ` `    ``# Print the maximum length``    ``print``(diameter)` `# Driver Code``if` `__name__``=``=``"__main__"``:``    ` `    ``# Given grid[][]``    ``grid ``=` `[ [ ``0``, ``0``, ``0``, ``0``, ``0``, ``0``, ``0` `],``             ``[ ``0``, ``1``, ``0``, ``1``, ``0``, ``0``, ``0` `],``             ``[ ``0``, ``1``, ``0``, ``1``, ``0``, ``0``, ``0` `],``             ``[ ``0``, ``1``, ``0``, ``1``, ``0``, ``1``, ``0` `],``             ``[ ``0``, ``1``, ``1``, ``1``, ``1``, ``1``, ``0` `],``             ``[ ``0``, ``0``, ``0``, ``1``, ``0``, ``0``, ``0` `] ]`` ` `    ``# Function Call``    ``findMaximumLength(grid)`` ` `# This code is contributed by rutvik_56`

## C#

 `// C# program for the above approach``using` `System;` `class` `GFG{``    ` `static` `readonly` `int` `row = 6;``static` `readonly` `int` `col = 7;``static` `int` `[,]vis = ``new` `int``[row + 1, col + 1];``static` `int` `id;``static` `int` `diameter = 0, length = 0;``static` `int` `x = 0, y = 0;` `// Keeps a track of directions``// that is up, down, left, right``static` `int` `[]dx = { -1, 1, 0, 0 };``static` `int` `[]dy = { 0, 0, -1, 1 };` `// Function to perform the dfs traversal``static` `void` `dfs(``int` `a, ``int` `b, ``int` `[,]lis)``{``    ` `    ``// Mark the current node as visited``    ``vis[a, b] = id;` `    ``// Increment length from this node``    ``length++;` `    ``// Update the diameter length``    ``if` `(length > diameter)``    ``{``        ``x = a;``        ``y = b;``        ``diameter = length;``    ``}` `    ``for``(``int` `j = 0; j < 4; j++)``    ``{``        ` `        ``// Move to next cell in x-direction``        ``int` `cx = a + dx[j];``        ` `        ``// Move to next cell in y-direction``        ``int` `cy = b + dy[j];``        ` `        ``// Check if cell is invalid``        ``// then continue``        ``if` `(cx < 0 || cy < 0 ||``            ``cx >= row || cy >= col ||``            ``lis[cx, cy] == 0 || vis[cx, cy] > 0)``        ``{``            ``continue``;``        ``}``        ` `        ``// Perform DFS on new cell``        ``dfs(cx, cy, lis);``    ``}``    ``vis[a, b] = 0;``    ` `    ``// Decrement the length``    ``length--;``}` `// Function to find the maximum length of``// connected 1s in the given grid``static` `void` `findMaximumLength(``int` `[,]lis)``{``    ` `    ``// Increment the id``    ``id++;``    ``length = 0;``    ``diameter = 0;` `    ``// Traverse the grid[]``    ``for``(``int` `i = 0; i < row; i++)``    ``{``        ``for``(``int` `j = 0; j < col; j++)``        ``{``            ``if` `(lis[i, j] != 0)``            ``{``                ` `                ``// Find start point of``                ``// start dfs call``                ``dfs(i, j, lis);``                ``i = row;``                ``break``;``            ``}``        ``}``    ``}``    ` `    ``id++;``    ``length = 0;``    ``diameter = 0;` `    ``// DFS Traversal from cell (x, y)``    ``dfs(x, y, lis);` `    ``// Print the maximum length``    ``Console.Write(diameter);``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ` `    ``// Given grid[,]``    ``int` `[,]grid = { { 0, 0, 0, 0, 0, 0, 0 },``                    ``{ 0, 1, 0, 1, 0, 0, 0 },``                    ``{ 0, 1, 0, 1, 0, 0, 0 },``                    ``{ 0, 1, 0, 1, 0, 1, 0 },``                    ``{ 0, 1, 1, 1, 1, 1, 0 },``                    ``{ 0, 0, 0, 1, 0, 0, 0 } };` `    ``// Function Call``    ``findMaximumLength(grid);``}``}` `// This code is contributed by amal kumar choubey`

## Javascript

 ``
Output:
`9`

Time Complexity: O(rows + cols)

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