Create 1733-minimum-number-of-people-to-teach.java

Author: sanajitjana

Medium/1733-minimum-number-of-people-to-teach.java

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+/**
+ * Problem: Minimum Number of People to Teach
+ * Link: https://leetcode.com/problems/minimum-number-of-people-to-teach/
+ *
+ * You are given n languages numbered from 1 to n, and for each user, a list of languages they know.
+ * Some pairs of users are friends but might not share a common language.
+ * You can teach one language to some users so that all friends can communicate.
+ * Return the minimum number of users you need to teach.
+ *
+ * Approach:
+ * 1. Build a mapping from each user to the set of languages they know.
+ * 2. Find all problematic friendship pairs (where no shared language exists).
+ * 3. Collect all unique users involved in problematic pairs.
+ * 4. For every language from 1 to n:
+ *      - Count how many users in the problematic set do NOT know that language.
+ *      - Keep track of the minimum such count.
+ * 5. Return the minimum number of people to teach.
+ *
+ * Time Complexity: O(n × u), where:
+ *      - n = number of languages (usually small, ≤ 500)
+ *      - u = number of unique problematic users (≤ 500)
+ *
+ * Space Complexity: O(u + p):
+ *      - u: Unique problematic users (≤ 500)
+ *      - p: Problematic friendship pairs (≤ 10⁴)
+ */
+
+class Solution {
+    public int minimumTeachings(int n, int[][] languages, int[][] friendships) {
+        // Map user to their known languages
+        HashMap<Integer, Set<Integer>> userLanguage = new HashMap<>();
+        for (int i = 0; i < languages.length; i++) {
+            HashSet<Integer> set = new HashSet<>();
+            for (int lang : languages[i]) {
+                set.add(lang);
+            }
+            userLanguage.put(i + 1, set);  // User IDs are 1-based
+        }
+
+        // Find problematic friendships
+        HashSet<Integer> uniqueProblematicUsers = new HashSet<>();
+
+        for (int[] pair : friendships) {
+            Set<Integer> firstUserLangs = userLanguage.get(pair[0]);
+            Set<Integer> secondUserLangs = userLanguage.get(pair[1]);
+
+            boolean hasCommonLang = firstUserLangs.stream().anyMatch(secondUserLangs::contains);
+
+            if (!hasCommonLang) {
+                uniqueProblematicUsers.add(pair[0]);
+                uniqueProblematicUsers.add(pair[1]);
+            }
+        }
+
+        // Try every language and compute minimum teaching effort
+        int minToTeach = Integer.MAX_VALUE;
+
+        for (int lang = 1; lang <= n; lang++) {
+            int teachCount = 0;
+            for (int user : uniqueProblematicUsers) {
+                Set<Integer> knownLanguages = userLanguage.get(user);
+                if (!knownLanguages.contains(lang)) {
+                    teachCount++;
+                }
+            }
+            minToTeach = Math.min(minToTeach, teachCount);
+        }
+
+        return minToTeach;
+    }
+}