You are given a list of edges in a graph with weight. Find all the paths between start node and end node with min weights in the path.
The edges like (node1, node2, weight)
class Solution { int minPathSum = Integer.MAX_VALUE; public List<List<Integer>> allShortestPaths(int[][] edges, int start, int end) { Map<Integer, Map<Integer, Integer>> graph = buildGraph(edges); List<List<Integer>> results = new LinkedList<>(); Set<Integer> visited = new HashSet<>(); dfs(start, end, visited, graph, new LinkedList<>(), results, 0); return results; } private void dfs(int current, int end, Set<Integer> visited, Map<Integer, Map<Integer, Integer>> graph, List<Integer> path, List<List<Integer>> results, int pathSum) { path.add(current); if (current == end) { if (minPathSum > pathSum) { results.clear(); results.add(new LinkedList<>(path)); minPathSum = pathSum; } else if (pathSum == minPathSum) { results.add(new LinkedList<>(path)); } path.remove(path.size() - 1); return; } visited.add(current); for (Map.Entry<Integer, Integer> entry : graph.getOrDefault(current, new HashMap<>()).entrySet()) { if (!visited.contains(entry.getKey())) { dfs(entry.getKey(), end, visited, graph, path, results, pathSum + entry.getValue()); } } path.remove(path.size() - 1); visited.remove(current); } private Map<Integer, Map<Integer, Integer>> buildGraph(int[][] edges) { Map<Integer, Map<Integer, Integer>> graph = new HashMap<>(); for (int[] edge : edges) { graph.putIfAbsent(edge[0], new HashMap<>()); graph.putIfAbsent(edge[1], new HashMap<>()); graph.get(edge[0]).put(edge[1], edge[2]); graph.get(edge[1]).put(edge[0], edge[2]); } return graph; } }
If we want to get only one path, we can use the following approach
1 public List<Integer> shortestPaths(int[][] edges, int start, int end) { 2 Map<Integer, Integer> currentValue = new HashMap<>(); 3 currentValue.put(start, 0); 4 Map<Integer, Integer> parentMap = new HashMap<>(); 5 6 Map<Integer, Map<Integer, Integer>> graph = buildGraph(edges); 7 Queue<int[]> minQueue = new PriorityQueue<>((arr1, arr2) -> arr1[0] - arr2[0]); 8 minQueue.offer(new int[] {0, start}); 9 while (!minQueue.isEmpty()) { 10 int[] current = minQueue.poll(); 11 if (current[1] == end) { 12 return getPath(parentMap, end); 13 } 14 15 for (Map.Entry<Integer, Integer> neighbor : graph.getOrDefault(current[1], new HashMap<>()).entrySet()) { 16 int neighborValue = currentValue.getOrDefault(neighbor.getKey(), Integer.MAX_VALUE); 17 if (current[0] + neighbor.getValue() < neighborValue) { 18 currentValue.put(neighbor.getKey(), current[0] + neighbor.getValue()); 19 parentMap.put(neighbor.getKey(), current[1]); 20 minQueue.offer(new int[] {current[0] + neighbor.getValue(), neighbor.getKey()}); 21 } 22 } 23 } 24 return new LinkedList<>(); 25 } 26 27 private List<Integer> getPath(Map<Integer, Integer> parentMap, int end) { 28 List<Integer> list = new LinkedList<>(); 29 list.add(0, end); 30 while (parentMap.containsKey(end)) { 31 end = parentMap.get(end); 32 list.add(0, end); 33 } 34 return list; 35 }