# Implementing Water Supply Problem using Breadth First Search

Given **N** cities which are connected using **N-1** roads. Between Cities **[i, i+1]**, there exists an edge for all **i** from 1 to N-1.

The task is to set up a connection for water supply. Set the water supply in one city and water gets transported from it to other cities using road transport. Certain cities are blocked which means that water cannot pass through that particular city. Determine the maximum number of cities to which water can be supplied.

**Input format:**

- The first line contains an integer >strong>N denoting the number of cities.
- The next N-1 lines contain two space-separated integers
**u v**denoting a road between

city u and v. - The next line contains N space-separated integers where it is 1 if the
**ith**city is

blocked, else it is 0.

**Examples:**

Input :

4

1 2

2 3

3 4

0 1 1 0

Output :

2

Explanation :If city 1 is chosen, then water is supplied from

city 1 to 2. If city 4 is chosen, water is supplied from city 4 to 3

hence maximum of 2 cities can be supplied with water.

Input :

7

1 2

2 3

3 4

4 5

5 6

6 7

0 1 1 0 0 0 0

Output :

5

Explanation :If city 1 is chosen than water is supplied from

city 1 to 2 or if city 4 is chosen water is supplied from city 4 to

3, 5, 6 and 7 hence maximum of 5 cities are supplied with water.

**Approach:**

In this post a BFS based solution is discussed.

We run a breadth-first search on each city and check for two things: The city is not blocked and the city is not visited. If both these conditions return true then we run a breadth-first search from that city and count the number of cities up to which water can be supplied.

This solution can also be achieved using a depth-first search.

Below is the implementation of the above approach:

## C++

`// C++ program to solve water ` `// supply problem using BFS ` ` ` `#include <iostream> ` `#include <vector> ` `#include <queue> ` `using` `namespace` `std; ` ` ` `// Function to perform BFS ` `int` `bfsUtil(` `int` `v[], ` `bool` `vis[], vector<` `int` `> adj[], ` ` ` `int` `src) ` `{ ` ` ` `// Mark current source visited ` ` ` `vis[src] = ` `true` `; ` ` ` ` ` `queue<` `int` `> q; ` `//Queue for BFS ` ` ` `q.push(src); ` `// Push src to queue ` ` ` ` ` `int` `count = 0; ` ` ` `while` `(!q.empty()) { ` ` ` ` ` `int` `p = q.front(); ` ` ` ` ` `for` `(` `int` `i = 0; i < adj[p].size(); i++) { ` ` ` ` ` `// When the adjacent city not visited and ` ` ` `// not blocked, push city in the queue. ` ` ` `if` `(!vis[adj[p][i]] && v[adj[p][i]] == 0) { ` ` ` `count++; ` ` ` `vis[adj[p][i]] = ` `true` `; ` ` ` `q.push(adj[p][i]); ` ` ` `} ` ` ` ` ` `// when the adjacent city is not visited ` ` ` `// but blocked so the blocked city is ` ` ` `// not pushed in queue ` ` ` `else` `if` `(!vis[adj[p][i]] && v[adj[p][i]] == 1) { ` ` ` `count++; ` ` ` `} ` ` ` `} ` ` ` `q.pop(); ` ` ` `} ` ` ` ` ` `return` `count + 1; ` `} ` ` ` `// Utility function to perform BFS ` `int` `bfs(` `int` `N, ` `int` `v[], vector<` `int` `> adj[]) ` `{ ` ` ` `bool` `vis[N + 1]; ` ` ` `int` `max = 1, res; ` ` ` ` ` `// marking visited array false ` ` ` `for` `(` `int` `i = 1; i <= N; i++) ` ` ` `vis[i] = ` `false` `; ` ` ` ` ` `// Check for each and every city ` ` ` `for` `(` `int` `i = 1; i <= N; i++) { ` ` ` `// Checks that city is not blocked ` ` ` `// and not visited. ` ` ` `if` `(v[i] == 0 && !vis[i]) { ` ` ` `res = bfsUtil(v, vis, adj, i); ` ` ` `if` `(res > max) { ` ` ` `max = res; ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` ` ` `return` `max; ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `int` `N = 4; ` `// Denotes the number of cities ` ` ` `vector<` `int` `> adj[N + 1]; ` ` ` `int` `v[N + 1]; ` ` ` ` ` `// Adjacency list denoting road ` ` ` `// between city u and v ` ` ` `adj[1].push_back(2); ` ` ` `adj[2].push_back(1); ` ` ` `adj[2].push_back(3); ` ` ` `adj[3].push_back(2); ` ` ` `adj[3].push_back(4); ` ` ` `adj[4].push_back(3); ` ` ` ` ` `// array for storing whether ith ` ` ` `// city is blocked or not ` ` ` `v[1] = 0; ` ` ` `v[2] = 1; ` ` ` `v[3] = 1; ` ` ` `v[4] = 0; ` ` ` ` ` `cout<<bfs(N, v, adj); ` ` ` ` ` `return` `0; ` `} ` |

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## Python3

`# Python3 program to solve water ` `# supply problem using BFS ` ` ` `# Function to perform BFS ` `def` `bfsUtil(v, vis, adj, src): ` ` ` ` ` `# Mark current source visited ` ` ` `vis[src] ` `=` `True` ` ` ` ` `# Queue for BFS ` ` ` `q ` `=` `[] ` ` ` ` ` `# Push src to queue ` ` ` `q.append(src) ` ` ` ` ` `count ` `=` `0` ` ` `while` `(` `len` `(q) !` `=` `0` `): ` ` ` `p ` `=` `q[` `0` `] ` ` ` ` ` `for` `i ` `in` `range` `(` `len` `(adj[p])): ` ` ` ` ` `# When the adjacent city not visited and ` ` ` `# not blocked, push city in the queue. ` ` ` `if` `(vis[adj[p][i]] ` `=` `=` `False` `and` `v[adj[p][i]] ` `=` `=` `0` `): ` ` ` `count ` `+` `=` `1` ` ` `vis[adj[p][i]] ` `=` `True` ` ` `q.push(adj[p][i]) ` ` ` ` ` `# when the adjacent city is not visited ` ` ` `# but blocked so the blocked city is ` ` ` `# not pushed in queue ` ` ` `elif` `(vis[adj[p][i]] ` `=` `=` `False` `and` `v[adj[p][i]] ` `=` `=` `1` `): ` ` ` `count ` `+` `=` `1` ` ` `q.remove(q[` `0` `]) ` ` ` ` ` `return` `count ` `+` `1` ` ` `# Utility function to perform BFS ` `def` `bfs(N, v, adj): ` ` ` `vis ` `=` `[ ` `0` `for` `i ` `in` `range` `(N ` `+` `1` `)] ` ` ` `mx ` `=` `1` ` ` ` ` `# marking visited array false ` ` ` `for` `i ` `in` `range` `(` `1` `, N ` `+` `1` `, ` `1` `): ` ` ` `vis[i] ` `=` `False` ` ` ` ` `# Check for each and every city ` ` ` `for` `i ` `in` `range` `(` `1` `, N ` `+` `1` `, ` `1` `): ` ` ` ` ` `# Checks that city is not blocked ` ` ` `# and not visited. ` ` ` `if` `(v[i] ` `=` `=` `0` `and` `vis[i] ` `=` `=` `False` `): ` ` ` `res ` `=` `bfsUtil(v, vis, adj, i) ` ` ` `if` `(res > mx): ` ` ` `mx ` `=` `res ` ` ` ` ` `return` `mx ` ` ` `# Driver Code ` `if` `__name__ ` `=` `=` `'__main__'` `: ` ` ` `N ` `=` `4` ` ` ` ` `# Denotes the number of cities ` ` ` `adj ` `=` `[[] ` `for` `i ` `in` `range` `(N ` `+` `1` `)] ` ` ` `v ` `=` `[` `0` `for` `i ` `in` `range` `(N ` `+` `1` `)] ` ` ` ` ` `# Adjacency list denoting road ` ` ` `# between city u and v ` ` ` `adj[` `1` `].append(` `2` `) ` ` ` `adj[` `2` `].append(` `1` `) ` ` ` `adj[` `2` `].append(` `3` `) ` ` ` `adj[` `3` `].append(` `2` `) ` ` ` `adj[` `3` `].append(` `4` `) ` ` ` `adj[` `4` `].append(` `3` `) ` ` ` ` ` `# array for storing whether ith ` ` ` `# city is blocked or not ` ` ` `v[` `1` `] ` `=` `0` ` ` `v[` `2` `] ` `=` `1` ` ` `v[` `3` `] ` `=` `1` ` ` `v[` `4` `] ` `=` `0` ` ` ` ` `print` `(bfs(N, v, adj)) ` ` ` `# This code is contributed by Bhupendra_Singh ` |

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** Output:**

2

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