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Commit c06e63f

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solves #1168: optimize water distribution in village
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-126
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3 files changed

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-126
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β€ŽREADME.mdβ€Ž

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514514
| 1154 | [Day of The Year](https://leetcode.com/problems/day-of-the-year) | [![Java](assets/java.png)](src/DayOfTheYear.java) | |
515515
| 1160 | [Find Words That Can Be Formed By Characters](https://leetcode.com/problems/find-words-that-can-be-formed-by-characters) | | |
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| 1165 | [Single Row Keyboard](https://leetcode.com/problems/single-row-keyboard) | [![Java](assets/java.png)](src/FindWordsThatCanBeFormedByCharacters.java) | |
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| 1168 | [Optimize Water Distribution in a Village](https://leetcode.com/problems/optimize-water-distribution-in-a-village) | [![Java](assets/java.png)](src/OptimizeWaterDistributionInAVillage.java) | |
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| 1170 | [Compare Strings By Frequency of the Smallest Character](https://leetcode.com/problems/compare-strings-by-frequency-of-the-smallest-character) | | |
518519
| 1175 | [Prime Arrangements](https://leetcode.com/problems/prime-arrangements) | [![Java](assets/java.png)](src/PrimeArrangements.java) | |
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| 1176 | πŸ”’ [Diet Plan Performance](https://leetcode.com/problems/diet-plan-performance) | | |

β€Žsrc/HelloWorld.javaβ€Ž

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import java.util.ArrayList;
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import java.util.Arrays;
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import java.util.HashMap;
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import java.util.HashSet;
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import java.util.LinkedList;
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import java.util.List;
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import java.util.Map;
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import java.util.Queue;
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import java.util.Set;
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/*
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kahns algorithm
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t: O(V + E)
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S: O(E)
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*/
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public class HelloWorld {
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private static class QuickUnionFind {
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private final int[] array;
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public QuickUnionFind(int size) {
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array = new int[size];
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for (int i = 0 ; i < array.length ; i++) {
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array[i] = i;
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}
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}
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public void union(int x, int y) {
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final int rootX = find(x), rootY = find(y);
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if (rootY == rootX) {
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return;
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}
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for (int i = 0 ; i < array.length ; i++) {
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if (array[i] == rootY) {
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array[i] = rootX;
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}
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}
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}
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public int find(int num) {
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return array[num];
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}
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public boolean areConnected(int x, int y) {
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return find(x) == find(y);
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}
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}
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private static final class QuickUnionDisjointSet {
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private final int[] array;
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public QuickUnionDisjointSet(int size) {
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array = new int[size];
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for (int i = 0 ; i < array.length ; i++) {
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array[i] = i;
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}
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}
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public int find(int num) {
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while (array[num] != num) {
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num = array[num];
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}
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return num;
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}
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public boolean areConnected(int x, int y) {
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return find(x) == find(y);
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}
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public void union(int x, int y) {
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final int rootX = find(x), rootY = find(y);
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if (rootX == rootY) {
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return;
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}
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array[rootY] = rootX;
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}
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}
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private static final class DisjointSetRank {
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private final int[] array;
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private final int[] rank;
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public DisjointSetRank(int size) {
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array = new int[size];
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rank = new int[size];
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for (int i = 0 ; i < array.length ; i++) {
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rank[i] = 1;
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array[i] = i;
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}
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}
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// T: O(logN)
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// S: O(1)
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public int find(int num) {
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if (num == array[num]) {
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return num;
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}
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final int root = find(array[num]);
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array[num] = root;
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return root;
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}
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// T: O(logN)
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// S: O(1)
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public void union(int x, int y) {
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final int rootX = find(x), rootY = find(y);
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if (rootX == rootY) {
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return;
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}
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if (rank[rootX] > rank[rootY]) {
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array[rootY] = rootX;
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} else if (rank[rootX] < rank[rootY]) {
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array[rootX] = rootY;
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} else {
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array[rootY] = rootX;
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rank[rootX]++;
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}
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}
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// T: O(logN)
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// S: O(1)
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public boolean areConnected(int x, int y) {
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return find(x) == find(y);
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}
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}
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}
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}
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// https://leetcode.com/problems/optimize-water-distribution-in-a-village
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// N = n, E = |pipes|
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// T: O(N + (N + E) log(N + E) + E al(N)) = O((N + E) log(N + E)) al = inverse Ackermann function
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// S: O(N + E)
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import java.util.ArrayList;
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import java.util.Arrays;
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import java.util.Comparator;
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import java.util.List;
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public class OptimizeWaterDistributionInAVillage {
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private static final class DisjointSet {
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private final int[] roots, rank;
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public DisjointSet(int size) {
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roots = new int[size];
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rank = new int[size];
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for (int i = 0 ; i < size ; i++) {
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roots[i] = i;
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rank[i] = 1;
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}
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}
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public int find(int num) {
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if (num == roots[num]) {
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return num;
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}
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return roots[num] = find(roots[num]);
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}
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public boolean isConnected(int x, int y) {
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return find(x) == find(y);
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}
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public void union(int x, int y) {
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final int rootX = find(x), rootY = find(y);
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if (rootX == rootY) {
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return;
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}
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if (rank[rootX] > rank[rootY]) {
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roots[rootY] = rootX;
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} else if (rank[rootX] < rank[rootY]) {
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roots[rootX] = rootY;
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} else {
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roots[rootY] = rootX;
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rank[rootX]++;
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}
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}
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}
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// Kruskal's algorithm to find MST in unordered weighted graph
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public int minCostToSupplyWater(int n, int[] wells, int[][] pipes) {
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final List<int[]> edges = new ArrayList<>(pipes.length + n + 1);
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final DisjointSet disjointSet = new DisjointSet(n + 1);
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// add extra vertex and extra edges
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for (int i = 0 ; i < n ; i++) {
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edges.add(new int[] {0, i + 1, wells[i]});
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}
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// add preexisting edges
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edges.addAll(Arrays.asList(pipes));
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// sort edges according to weight
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edges.sort(Comparator.comparingInt(a -> a[2]));
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int totalCost = 0;
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for (int[] edge : edges) {
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final int house1 = edge[0], house2 = edge[1], cost = edge[2];
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if (!disjointSet.isConnected(house1, house2)) {
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disjointSet.union(house1, house2);
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totalCost += cost;
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n--;
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if (n == 0) {
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break;
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}
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}
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}
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return totalCost;
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}
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}

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