week 1

Author: sachuverma

Leetcode Daily Challenge/August-2021/Optimize Water Distribution in a Village.cpp

@@ -0,0 +1,88 @@
+/*
+Optimize Water Distribution in a Village
+========================================
+
+There are n houses in a village. We want to supply water for all the houses by building wells and laying pipes.
+
+For each house i, we can either build a well inside it directly with cost wells[i - 1] (note the -1 due to 0-indexing), or pipe in water from another well to it. The costs to lay pipes between houses are given by the array pipes, where each pipes[j] = [house1j, house2j, costj] represents the cost to connect house1j and house2j together using a pipe. Connections are bidirectional.
+
+Return the minimum total cost to supply water to all houses.
+
+Example 1:
+Input: n = 3, wells = [1,2,2], pipes = [[1,2,1],[2,3,1]]
+Output: 3
+Explanation: 
+The image shows the costs of connecting houses using pipes.
+The best strategy is to build a well in the first house with cost 1 and connect the other houses to it with cost 2 so the total cost is 3.
+ 
+Constraints:
+1 <= n <= 104
+wells.length == n
+0 <= wells[i] <= 105
+1 <= pipes.length <= 104
+pipes[j].length == 3
+1 <= house1j, house2j <= n
+0 <= costj <= 105
+house1j != house2j
+*/
+
+class DSU {
+public:
+    vector<int> parent, rank;
+    
+    DSU(int n) {
+        parent = vector <int> (n+1, 0);
+        rank = vector <int> (n+1, 0);
+        
+        for(int i = 0; i <= n; ++i) {
+            parent[i] = i;
+            rank[i] = 1;
+        }
+    }
+    
+    int find(int a) {
+        if(parent[a] == a) return a;
+        return parent[a] = find(parent[a]);
+    }
+    
+    void join(int a, int b) {
+        int pa = find(a), pb = find(b);
+        if(pa == pb) return;
+        
+        if(rank[pa] > rank[pb]) parent[pb] = pa;
+        else if(rank[pa] < rank[pb]) parent[pa] = pb;
+        else {
+            parent[pa] = pb;
+            rank[pb]++;
+        }
+    }
+};
+
+class Solution {
+public:
+    int minCostToSupplyWater(int n, vector<int>& wells, vector<vector<int>>& pipes) {
+        DSU obj(n);
+        vector<vector<int>> edges;
+        
+        for(auto& pipe : pipes) edges.push_back({ pipe[2], pipe[0], pipe[1] });
+        for(int i = 0; i < n; ++i) edges.push_back({ wells[i], 0, i+1 });
+        
+        sort(edges.begin(), edges.end(), [](vector<int>& a, vector<int>& b){
+           return a[0] < b[0]; 
+        });
+        
+        int edges_added = 0;
+        int ans = 0;
+        
+        for(int i = 0; i < edges.size() && edges_added < n; ++i) {
+            int cost = edges[i][0], node1 = edges[i][1], node2 = edges[i][2];
+            if(obj.find(node1) == obj.find(node2)) continue;
+            
+            obj.join(node1, node2);
+            ans += cost;
+            edges_added++;
+        }
+        
+        return ans;
+    }
+};

Leetcode Daily Challenge/August-2021/README.md

@@ -2,6 +2,7 @@
 
 | Day | Question Links                                                                                                                               |                   Solutions                    |
 | :-: | :------------------------------------------------------------------------------------------------------------------------------------------- | :--------------------------------------------: |
+|  | [Optimize Water Distribution in a Village](https://leetcode.com/explore/challenge/card/august-leetcoding-challenge-2021/613/week-1-august-1st-august-7th/3834/) | [cpp](./Optimize%20Water%20Distribution%20in%20a%20Village.cpp) |
 | 1.  | [Making A Large Island](https://leetcode.com/explore/challenge/card/august-leetcoding-challenge-2021/613/week-1-august-1st-august-7th/3835/) | [cpp](./01.%20Making%20A%20Large%20Island.cpp) |
 | 2.  | [Two Sum](https://leetcode.com/explore/challenge/card/august-leetcoding-challenge-2021/613/week-1-august-1st-august-7th/3836/)               |          [cpp](./02.%20Two%20Sum.cpp)          |
 | 3.  | [Subsets II](https://leetcode.com/explore/challenge/card/august-leetcoding-challenge-2021/613/week-1-august-1st-august-7th/3837/)            |        [cpp](./03.%20Subsets%20II.cpp)         |