**Logically Consistent Book - Google Top Interview Questions**

### Problem Statement :

You are given a two-dimensional list of integers lists. Each element contains [start, end, type], meaning that from pages [start, end] inclusive, there's either an even number of words (type = 0) or an odd number of words (type = 1). Return whether lists is logically consistent. Constraints n ≤ 100,000 where n is the length of lists Example 1 Input lists = [ [1, 5, 1], [6, 10, 0], [1, 10, 0] ] Output False Explanation If there are an odd number of words from pages [1, 5] and an even number of words from pages [6, 10], that must mean there's an odd number from pages [1, 10]. So this is a contradiction. Example 2 Input lists = [ [0, 2, 0], [2, 4, 0], [0, 4, 0] ] Output True Explanation If there are an even number of words from pages [0, 2] and an even number of words from pages [2, 4], that means there can be an even number from pages [0, 4]. So there's no contradiction. Example 3 Input lists = [ [0, 2, 1], [3, 4, 1], [0, 4, 0] ] Output True Explanation If there are an odd number of words from pages [0, 2] and an odd number of words from pages [3, 4], that must mean there's an even number from pages [0, 4]. So there's no contradiction.

### Solution :

` ````
Solution in C++ :
unordered_map<int, vector<pair<int, int>>> edges;
bool solve(vector<vector<int>>& lists) {
unordered_map<int, int> parity;
edges.clear();
for (auto& edge : lists) {
edges[edge[0] - 1].emplace_back(edge[1], edge[2]);
edges[edge[1]].emplace_back(edge[0] - 1, edge[2]);
}
for (auto edge : edges) {
int src = edge.first;
if (parity.count(src)) continue;
parity[src] = 0;
queue<int> q;
q.push(src);
while (q.size()) {
int curr = q.front();
q.pop();
for (auto edge : edges[curr]) {
int nparity = parity[curr] ^ edge.second;
if (parity.count(edge.first) && parity[edge.first] != nparity) return false;
if (!parity.count(edge.first)) {
parity[edge.first] = nparity;
q.push(edge.first);
}
}
}
}
return true;
}
```

` ````
Solution in Java :
import java.util.*;
class Solution {
public boolean solve(int[][] nums) {
Comparator c = new Comparator<int[]>() {
@Override
public int compare(int[] a, int[] b) {
if (a[0] != b[0])
return a[0] - b[0];
else
return a[1] - b[1];
}
};
PriorityQueue<int[]> pq = new PriorityQueue<int[]>(c);
for (int[] range : nums) pq.add(range);
while (pq.size() >= 2) {
int[] r1 = pq.poll();
int[] r2 = pq.peek();
if (r1[0] == r2[0]) {
if (r1[1] == r2[1]) {
if (r1[2] != r2[2])
return false;
} else {
pq.add(new int[] {r1[1] + 1, r2[1], Math.abs(r1[2] - r2[2])});
}
}
}
return true;
}
}
```

` ````
Solution in Python :
class Solution:
def solve(self, lists):
graph = defaultdict(list)
for i, j, p in lists:
graph[i].append([j + 1, p])
graph[j + 1].append([i, p])
state = {}
def dfs(node, color):
state[node] = color
for nei, w in graph[node]:
if nei not in state:
if not dfs(nei, color ^ w):
return False
elif state[nei] != color ^ w:
return False
return True
for node in graph:
if node not in state and dfs(node, 0) is False:
return False
return True
```

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