Create shortest-path-visiting-all-nodes.cpp

Author: kamyu104

C++/shortest-path-visiting-all-nodes.cpp

@@ -0,0 +1,29 @@
+// Time:  O(n * 2^n)
+// Space: O(n * 2^n)
+
+class Solution {
+public:
+    int shortestPathLength(vector<vector<int>>& graph) {
+        static const auto& INF = numeric_limits<int>::max();
+        vector<vector<int>> dp(1 << graph.size(),
+                               vector<int>(graph.size(), INF));
+        queue<pair<int, int>> q;
+        for (int i = 0; i < graph.size(); ++i) {
+            dp[1 << i][i] = 0;
+            q.emplace(1 << i, i);
+        }
+        while (!q.empty()) {
+            int state, node;
+            tie(state, node) = q.front(); q.pop();
+            auto steps = dp[state][node];
+            for (const auto& nei : graph[node]) {
+                auto new_state = state | (1 << nei);								
+                if (dp[new_state][nei] == INF) {
+                    dp[new_state][nei] = steps + 1;
+                    q.emplace(new_state, nei);
+                }
+            }
+        }
+        return *min_element(dp.back().cbegin(), dp.back().cend());
+    }
+};