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# Minimum number of Water to Land conversion to make two islands connected in a Grid

• Difficulty Level : Medium
• Last Updated : 01 Sep, 2021

Given a 2D grid arr[][] of ‘W’ and ‘L’ where ‘W’ denotes water and ‘L’ denotes land, the task is to find the minimum number of water components ‘W’ that must be changed to land component ‘L’ so that two islands becomes connected.

An island is the set of connected ‘L’s.

Note: There can be only two disjoint islands.

Examples:

Input: arr[][] = {{‘W’, ‘L’}, {‘L’, ‘W’}};
Output:
Explanation:
For the given set of islands if we change arr[1][1] to ‘W’ then, set of all island are connected.
Therefore, the minimum number of ‘W’ must be changed to ‘L’ is 1.

Input: arr[][] = {{‘W’, ‘L’, ‘W’}, {‘W’, ‘W’, ‘W’}, {‘W’, ‘W’, ‘L’}}
Output:

Approach: This problem can be solved using Floodfill algorithm. Below are the steps:

1. Use Floodfill algorithm for the first set of the connected islands and make all the islands as visited and store the coordinates in a hash (say hash1).
2. Use Floodfill algorithm for the second set of the connected islands and make all the islands as visited and store the coordinates in a second hash(say hash2).
3. The minimum difference between coordinates stored in both the hash is the required result.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ``using` `namespace` `std;` `// Determine the distance between two``// coordinates``int` `dist(pair<``int``, ``int``>& p1,``         ``pair<``int``, ``int``>& p2)``{` `    ``return` `abs``(p1.first - p2.first)``           ``+ ``abs``(p2.second - p1.second) - 1;``}` `// Function to implement floodfill algorithm``void` `floodfill(set >& hash,``               ``int` `i, ``int` `j,``               ``vector >& A)``{` `    ``// Base Case``    ``if` `(i < 0 || i >= A.size() || j < 0``        ``|| j >= A[0].size() || A[i][j] != ``'L'``) {``        ``return``;``    ``}` `    ``// Mark the current node visited``    ``A[i][j] = ``'V'``;` `    ``// Store the coordinates of in the``    ``// hash set``    ``hash.insert(make_pair(i, j));` `    ``// Recursively iterate for the next``    ``// four directions``    ``floodfill(hash, i - 1, j, A);``    ``floodfill(hash, i + 1, j, A);``    ``floodfill(hash, i, j - 1, A);``    ``floodfill(hash, i, j + 1, A);``}` `// Function to find the minimum 'W' to flipped``void` `findMinimumW(vector >& A)``{` `    ``// Base Case``    ``if` `(A.size() == 0)``        ``return``;` `    ``// Two sets to store the coordinates of``    ``// connected island``    ``set > hash1, hash2;` `    ``// Traversing the given grid[][]``    ``for` `(``int` `i = 0; i < A.size(); i++) {` `        ``for` `(``int` `j = 0; j < A[0].size(); j++) {` `            ``// If an island is found``            ``if` `(A[i][j] == ``'L'``) {` `                ``// Floodfill Algorithm for``                ``// the first island``                ``if` `(hash1.empty()) {``                    ``floodfill(hash1, i, j, A);``                ``}` `                ``// Floodfill Algorithm for``                ``// the second island``                ``if` `(hash2.empty()``                    ``&& !hash1.count({ i, j })) {``                    ``floodfill(hash2, i, j, A);``                ``}``            ``}``        ``}``    ``}` `    ``// To store the minimum count of 'W'``    ``int` `ans = INT_MAX;` `    ``// Traverse both pairs of hashes``    ``for` `(``auto` `i : hash1) {``        ``for` `(``auto` `j : hash2) {``            ``ans = min(ans, dist(i, j));``        ``}``    ``}` `    ``// Print the final answer``    ``cout << ans << endl;``}` `// Driver Code``int` `main()``{` `    ``// Given grid of land and water``    ``vector > arr;``    ``arr = { { ``'W'``, ``'L'` `}, { ``'L'``, ``'W'` `} };` `    ``// Function Call``    ``findMinimumW(arr);``    ``return` `0;``}`

## Python3

 `# Python3 program for the above approach``import` `sys` `# Determine the distance between two``# coordinates``def` `dist(p1, p2):``    ` `    ``return` `(``abs``(p1[``0``] ``-` `p2[``0``]) ``+``            ``abs``(p2[``1``] ``-` `p1[``1``]) ``-` `1``)` `# Function to implement floodfill algorithm``def` `floodfill(``hash``, i, j, A):``    ` `    ``# Base Case``    ``if` `(i < ``0` `or` `i >``=` `len``(A) ``or` `j < ``0` `or``        ``j >``=` `len``(A[``0``]) ``or` `A[i][j] !``=` `'L'``):``        ``return` `hash``, A``        ` `    ``# Mark the current node visited``    ``A[i][j] ``=` `'V'`` ` `    ``# Store the coordinates of in the``    ``# hash set``    ``hash``.add((i, j))``    ` `    ``# Recursively iterate for the next``    ``# four directions``    ``hash``, A ``=` `floodfill(``hash``, i ``-` `1``, j, A)``    ``hash``, A ``=` `floodfill(``hash``, i ``+` `1``, j, A)``    ``hash``, A ``=` `floodfill(``hash``, i, j ``-` `1``, A)``    ``hash``, A ``=` `floodfill(``hash``, i, j ``+` `1``, A)``    ``return` `hash``, A` `# Function to find the minimum 'W' to flipped``def` `findMinimumW(A):``    ` `    ``# Base Case``    ``if` `(``len``(A) ``=``=` `0``):``        ``return` `set``(), A``        ` `    ``# Two sets to store the coordinates of``    ``# connected island``    ``hash1 ``=` `set``()``    ``hash2 ``=` `set``()``    ` `    ``# Traversing the given grid[][]``    ``for` `i ``in` `range``(``len``(A)):``        ``for` `j ``in` `range``(``len``(A[``0``])):``            ` `            ``# If an island is found``            ``if` `(A[i][j] ``=``=` `'L'``):``                ` `                ``# Floodfill Algorithm for``                ``# the first island``                ``if` `(``len``(hash1) ``=``=` `0``):``                    ``hash1, A ``=` `floodfill(hash1, i, j, A)``                    ` `                ``# Floodfill Algorithm for``                ``# the second island``                ``if` `(``len``(hash2) ``=``=` `0` `and``                   ``(i, j) ``not` `in` `hash1):``                    ``hash2, A ``=` `floodfill(hash2, i, j, A)``                    ` `    ``# To store the minimum count of 'W'``    ``ans ``=` `sys.maxsize`` ` `    ``# Traverse both pairs of hashes``    ``for` `i ``in` `hash1:``        ``for` `j ``in` `hash2:``            ``ans ``=` `min``(ans, dist(i, j))``            ` `    ``# Print the final answer``    ``print``(ans)``    ` `# Driver Code``if` `__name__``=``=``'__main__'``:`` ` `    ``# Given grid of land and water``    ``arr ``=` `[]``    ``arr ``=` `[ [ ``'W'``, ``'L'` `], [ ``'L'``, ``'W'` `] ]`` ` `    ``# Function Call``    ``findMinimumW(arr)` `# This code is contributed by pratham76`
Output:
`1`

Time Complexity: O(N2 * log(N2))
Auxiliary Space: O(N2)

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