Sri Hari: Batch-5/Neetcode-ALL/Develop-articles (#3836)

* Batch-5/Neetcode-ALL/Added-articles

* Batch-5/Neetcode-ALL/Added-articles

* Batch-5/Neetcode-ALL/Added-articles

* Batch-5/Neetcode-ALL/Added-articles

* Batch-5/Neetcode-ALL/Added-articles

Author: Srihari2222

articles/as-far-from-land-as-possible.md

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+## 1. Depth First Search
+
+::tabs-start
+
+```python
+class Solution:
+    def minimumFuelCost(self, roads: list[list[int]], seats: int) -> int:
+        adj = defaultdict(list)
+        for src, dst in roads:
+            adj[src].append(dst)
+            adj[dst].append(src)
+
+        res = 0
+        def dfs(node, parent):
+            nonlocal res
+            passengers = 0
+            for child in adj[node]:
+                if child != parent:
+                    p = dfs(child, node)
+                    passengers += p
+                    res += ceil(p / seats)
+            return passengers + 1
+
+        dfs(0, -1)
+        return res
+```
+
+```java
+public class Solution {
+    private List<Integer>[] adj;
+    private long res = 0;
+
+    public long minimumFuelCost(int[][] roads, int seats) {
+        int n = roads.length + 1;
+        adj = new ArrayList[n];
+
+        for (int i = 0; i < n; i++) {
+            adj[i] = new ArrayList<>();
+        }
+
+        for (int[] road : roads) {
+            adj[road[0]].add(road[1]);
+            adj[road[1]].add(road[0]);
+        }
+
+        dfs(0, -1, seats);
+        return res;
+    }
+
+    private int dfs(int node, int parent, int seats) {
+        int passengers = 0;
+        for (int child : adj[node]) {
+            if (child != parent) {
+                int p = dfs(child, node, seats);
+                passengers += p;
+                res += Math.ceil((double) p / seats);
+            }
+        }
+        return passengers + 1;
+    }
+}
+```
+
+```cpp
+class Solution {
+private:
+    vector<vector<int>> adj;
+    long long res = 0;
+
+public:
+    long long minimumFuelCost(vector<vector<int>>& roads, int seats) {
+        int n = roads.size() + 1;
+        adj.resize(n);
+
+        for (auto& road : roads) {
+            adj[road[0]].push_back(road[1]);
+            adj[road[1]].push_back(road[0]);
+        }
+
+        dfs(0, -1, seats);
+        return res;
+    }
+
+private:
+    int dfs(int node, int parent, int seats) {
+        int passengers = 0;
+        for (int child : adj[node]) {
+            if (child != parent) {
+                int p = dfs(child, node, seats);
+                passengers += p;
+                res += ceil((double) p / seats);
+            }
+        }
+        return passengers + 1;
+    }
+};
+```
+
+```javascript
+class Solution {
+    /**
+     * @param {number[][]} roads
+     * @param {number} seats
+     * @return {number}
+     */
+    minimumFuelCost(roads, seats) {
+        const n = roads.length + 1;
+        const adj = Array.from({ length: n }, () => []);
+        let res = 0;
+
+        for (const [src, dst] of roads) {
+            adj[src].push(dst);
+            adj[dst].push(src);
+        }
+
+        const dfs = (node, parent) => {
+            let passengers = 0;
+            for (const child of adj[node]) {
+                if (child !== parent) {
+                    let p = dfs(child, node);
+                    passengers += p;
+                    res += Math.ceil(p / seats);
+                }
+            }
+            return passengers + 1;
+        };
+
+        dfs(0, -1);
+        return res;
+    }
+}
+```
+
+::tabs-end
+
+### Time & Space Complexity
+
+* Time complexity: $O(n)$
+* Space complexity: $O(n)$
+
+---
+
+## 2. Topological Sort (Kahn's Algorithm)
+
+::tabs-start
+
+```python
+class Solution:
+    def minimumFuelCost(self, roads: list[list[int]], seats: int) -> int:
+        n = len(roads) + 1
+        adj = [[] for _ in range(n)]
+        indegree = [0] * n
+        passengers = [1] * n
+        res = 0
+
+        for src, dst in roads:
+            adj[src].append(dst)
+            adj[dst].append(src)
+            indegree[src] += 1
+            indegree[dst] += 1
+
+        q = deque()
+        for i in range(1, n):
+            if indegree[i] == 1:
+                q.append(i)
+
+        while q:
+            node = q.popleft()
+            res += math.ceil(passengers[node] / seats)
+            for parent in adj[node]:
+                indegree[parent] -= 1
+                if indegree[parent] == 1 and parent != 0:
+                    q.append(parent)
+                passengers[parent] += passengers[node]
+
+        return res
+```
+
+```java
+public class Solution {
+    public long minimumFuelCost(int[][] roads, int seats) {
+        int n = roads.length + 1;
+        List<Integer>[] adj = new ArrayList[n];
+        int[] indegree = new int[n];
+        int[] passengers = new int[n];
+        Arrays.fill(passengers, 1);
+        long res = 0;
+
+        for (int i = 0; i < n; i++) adj[i] = new ArrayList<>();
+
+        for (int[] road : roads) {
+            int src = road[0], dst = road[1];
+            adj[src].add(dst);
+            adj[dst].add(src);
+            indegree[src]++;
+            indegree[dst]++;
+        }
+
+        Queue<Integer> q = new LinkedList<>();
+        for (int i = 1; i < n; i++) {
+            if (indegree[i] == 1) q.offer(i);
+        }
+
+        while (!q.isEmpty()) {
+            int node = q.poll();
+            res += (int) Math.ceil((double) passengers[node] / seats);
+            for (int parent : adj[node]) {
+                if (--indegree[parent] == 1 && parent != 0) q.offer(parent);
+                passengers[parent] += passengers[node];
+            }
+        }
+
+        return res;
+    }
+}
+```
+
+```cpp
+class Solution {
+public:
+    long long minimumFuelCost(vector<vector<int>>& roads, int seats) {
+        int n = roads.size() + 1;
+        vector<vector<int>> adj(n);
+        vector<int> indegree(n, 0), passengers(n, 1);
+        long long res = 0;
+
+        for (auto& road : roads) {
+            int src = road[0], dst = road[1];
+            adj[src].push_back(dst);
+            adj[dst].push_back(src);
+            indegree[src]++;
+            indegree[dst]++;
+        }
+
+        queue<int> q;
+        for (int i = 1; i < n; i++) {
+            if (indegree[i] == 1) q.push(i);
+        }
+
+        while (!q.empty()) {
+            int node = q.front();q.pop();
+            res += ceil((double) passengers[node] / seats);
+            for (int parent : adj[node]) {
+                if (--indegree[parent] == 1 && parent != 0) q.push(parent);
+                passengers[parent] += passengers[node];
+            }
+        }
+
+        return res;
+    }
+};
+```
+
+```javascript
+class Solution {
+    /**
+     * @param {number[][]} roads
+     * @param {number} seats
+     * @return {number}
+     */
+    minimumFuelCost(roads, seats) {
+        const n = roads.length + 1;
+        const adj = Array.from({ length: n }, () => []);
+        const indegree = new Array(n).fill(0);
+        const passengers = new Array(n).fill(1);
+        let res = 0;
+
+        for (const [src, dst] of roads) {
+            adj[src].push(dst);
+            adj[dst].push(src);
+            indegree[src] += 1;
+            indegree[dst] += 1;
+        }
+
+        const q = new Queue();
+        for (let i = 1; i < n; i++) {
+            if (indegree[i] === 1) q.push(i);
+        }
+
+        while (!q.isEmpty()) {
+            const node = q.pop();
+            res += Math.ceil(passengers[node] / seats);
+            for (const parent of adj[node]) {
+                if (--indegree[parent] === 1 && parent !== 0) q.push(parent);
+                passengers[parent] += passengers[node];
+            }
+        }
+
+        return res;
+    }
+}
+```
+
+::tabs-end
+
+### Time & Space Complexity
+
+* Time complexity: $O(n)$
+* Space complexity: $O(n)$