From 3a2ff8307436036d6b0263af8184a127377a8377 Mon Sep 17 00:00:00 2001
From: "Fernando J. Iglesias Garcia" <fernando.iglesiasg@gmail.com>
Date: Tue, 27 Aug 2024 14:18:10 +0200
Subject: [PATCH] Shortest path maximizing probability

---
 leetcode/1514.cpp | 63 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 63 insertions(+)
 create mode 100644 leetcode/1514.cpp

diff --git a/leetcode/1514.cpp b/leetcode/1514.cpp
new file mode 100644
index 0000000..f4a47d3
--- /dev/null
+++ b/leetcode/1514.cpp
@@ -0,0 +1,63 @@
+#include <cmath>
+#include <queue>
+#include <unordered_map>
+#include <utility>
+#include <vector>
+
+#include <gtest/gtest.h>
+
+using std::vector;
+using std::unordered_map;
+
+double max_probability([[maybe_unused]] int n, const vector<vector<int>>& edges, const vector<double>& probs, int start_node, int end_node) {
+  std::priority_queue<std::pair<double, int>, vector<std::pair<double, int>>, std::greater<std::pair<double, int>>> pq;
+
+  unordered_map<int, double> dist;
+  dist[start_node] = .0;
+  pq.emplace(0., start_node);
+
+  double ans = .0;
+
+  unordered_map<int, unordered_map<int, double>> edges_map;
+  for (size_t i = 0; i < edges.size(); i++) {
+    edges_map[edges[i][0]].emplace(edges[i][1], -std::log(probs[i]));
+    edges_map[edges[i][1]].emplace(edges[i][0], -std::log(probs[i]));
+  }
+
+  while(!pq.empty()) {
+    auto const top{pq.top()};
+    pq.pop();
+    for (auto const& [dst, cost] : edges_map[top.second]) {
+        if (dst == end_node) ans = std::max(ans, std::exp(-top.first-cost));
+        if (!dist.contains(dst) or dist[dst] > top.first + cost) {
+            dist[dst] = top.first + cost;
+            pq.emplace(top.first + cost, dst);
+        }
+    }
+  }
+
+  return ans;
+}
+
+TEST(path_with_maximum_probability, a) {
+    const vector<vector<int>> edges{{0, 1}, {1, 2}, {0, 2}};
+    const vector<double> probs{.5, .5, .2};
+    EXPECT_EQ(max_probability(3, edges, probs, 0, 2), .25);
+}
+
+TEST(path_with_maximum_probability, b) {
+    const vector<vector<int>> edges{{0, 1}, {1, 2}, {0, 2}};
+    const vector<double> probs{.5, .5, .3};
+    EXPECT_EQ(max_probability(3, edges, probs, 0, 2), .3);
+}
+
+TEST(path_with_maximum_probability, c) {
+    const vector<vector<int>> edges{{0, 1}};
+    const vector<double> probs{.5};
+    EXPECT_EQ(max_probability(3, edges, probs, 0, 2), .0);
+}
+
+int main(int argc, char** argv) {
+    testing::InitGoogleTest(&argc, argv);
+    return RUN_ALL_TESTS();
+}