Add LC Solution to 997 problem

dsa-solutions/lc-solutions/997 - Find the Town Judge.md

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+---
+id: find-the-town-judge
+title: Find the Town Judge
+sidebar_label: Find the Town Judge
+tags: [Graph, Array, C++, Python, Java]
+description: Identify the town judge based on trust relationships in a town.
+---
+
+## Problem Statement
+
+### Problem Description
+
+In a town, there are `n` people labeled from `1` to `n`. There is a rumor that one of these people is secretly the town judge.
+
+If the town judge exists, then:
+
+1. The town judge trusts nobody.
+2. Everybody (except for the town judge) trusts the town judge.
+3. There is exactly one person that satisfies properties 1 and 2.
+
+You are given an array `trust` where `trust[i] = [a_i, b_i]` representing that the person labeled `a_i` trusts the person labeled `b_i`. If a trust relationship does not exist in `trust` array, then such a trust relationship does not exist.
+
+Return the label of the town judge if the town judge exists and can be identified, or return `-1` otherwise.
+
+### Example
+
+**Example 1:**
+```
+Input: n = 2, trust = [[1,2]]
+Output: 2
+```
+**Example 2:**
+```
+Input: n = 3, trust = [[1,3],[2,3]]
+Output: 3
+```
+
+### Constraints
+
+- $1 \leq n \leq 1000$
+- $0 \leq \text{trust.length} \leq 10^4$
+- `trust[i].length == 2`
+- All the pairs of trust are unique.
+- $a_i \ne b_i$
+- $1 \leq a_i, b_i \leq n$
+
+## Solution
+
+### Intuition
+
+To identify the town judge, we can use an array to keep track of the trust scores for each person. The trust score is increased by 1 for each person who trusts them and decreased by 1 for each person they trust.
+
+The town judge should have a trust score of `n-1` because they are trusted by everyone except themselves and they trust nobody.
+
+### Time Complexity and Space Complexity Analysis
+
+- **Time Complexity**: $O(n + \text{trust.length})$, where $n$ is the number of people and $\text{trust.length}$ is the number of trust relationships.
+- **Space Complexity**: $O(n)$, for the trust score array.
+
+### Code
+
+#### C++
+
+```cpp
+class Solution {
+public:
+    int findJudge(int n, vector<vector<int>>& trust) {
+        vector<int> trustScores(n + 1, 0);
+
+        for (const auto& t : trust) {
+            trustScores[t[0]]--;
+            trustScores[t[1]]++;
+        }
+
+        for (int i = 1; i <= n; ++i) {
+            if (trustScores[i] == n - 1) {
+                return i;
+            }
+        }
+
+        return -1;
+    }
+};
+```
+
+#### Python
+```python
+class Solution:
+    def findJudge(self, n: int, trust: List[List[int]]) -> int:
+        trust_scores = [0] * (n + 1)
+
+        for a, b in trust:
+            trust_scores[a] -= 1
+            trust_scores[b] += 1
+
+        for i in range(1, n + 1):
+            if trust_scores[i] == n - 1:
+                return i
+
+        return -1
+```
+
+#### Java
+```java
+class Solution {
+    public int findJudge(int n, int[][] trust) {
+        int[] trustScores = new int[n + 1];
+
+        for (int[] t : trust) {
+            trustScores[t[0]]--;
+            trustScores[t[1]]++;
+        }
+
+        for (int i = 1; i <= n; i++) {
+            if (trustScores[i] == n - 1) {
+                return i;
+            }
+        }
+
+        return -1;
+    }
+}
+```