444. Sequence Reconstruction

Check whether the original sequence org can be uniquely reconstructed from the sequences in seqs. The org sequence is a permutation of the integers from 1 to n, with 1 ≤ n ≤ 104. Reconstruction means building a shortest common supersequence of the sequences in seqs (i.e., a shortest sequence so that all sequences in seqs are subsequences of it). Determine whether there is only one sequence that can be reconstructed from seqs and it is the org sequence.
Example 1:
Input:
org: [1,2,3], seqs: [[1,2],[1,3]]

Output:
false

Explanation:
[1,2,3] is not the only one sequence that can be reconstructed, because [1,3,2] is also a valid sequence that can be reconstructed.

Example 2:
Input:
org: [1,2,3], seqs: [[1,2]]

Output:
false

Explanation:
The reconstructed sequence can only be [1,2].

Example 3:
Input:
org: [1,2,3], seqs: [[1,2],[1,3],[2,3]]

Output:
true

Explanation:
The sequences [1,2], [1,3], and [2,3] can uniquely reconstruct the original sequence [1,2,3].

Example 4:
Input:
org: [4,1,5,2,6,3], seqs: [[5,2,6,3],[4,1,5,2]]

Output:
true

UPDATE (2017/1/8):?The seqs parameter had been changed to a list of list of strings (instead of a 2d array of strings). Please reload the code definition to get the latest changes.


// correct

This question can be simplified to three conditions:

1. TopSort order exists
2. Whether the TopSort order is the only one (Uniqueness of Topological sort, Hamilton path, see https://en.wikipedia.org/wiki/Topological_sorting#Uniqueness).如果不是，那么说明有些pair只有偏序关系，没有全序关系，这样不能完全确定元素之间的顺序
3. the only top sort order constructed should be equal to the org.

index == org.length (check condition 3) && index == map.size() (check all the vertex in the graph has been visited, so the top sort order exists, check condition 1)

How to check only one order? queue.size() should always be one, then only one element at a time has indegree to be 0, so you only have one choice (check condition 2)




public class Solution {
    public boolean sequenceReconstruction(int[] org, int[][] seqs) {
        Map<Integer, Set<Integer>> map = new HashMap<>();
        Map<Integer, Integer> indegree = new HashMap<>();
        
        for(int[] seq: seqs) {
            if(seq.length == 1) {
                if(!map.containsKey(seq[0])) {
                    map.put(seq[0], new HashSet<>());
                    indegree.put(seq[0], 0);
                }
            } else {
                for(int i = 0; i < seq.length - 1; i++) {
                    if(!map.containsKey(seq[i])) {
                        map.put(seq[i], new HashSet<>());
                        indegree.put(seq[i], 0);
                    }

                    if(!map.containsKey(seq[i + 1])) {
                        map.put(seq[i + 1], new HashSet<>());
                        indegree.put(seq[i + 1], 0);
                    }

                    if(map.get(seq[i]).add(seq[i + 1])) {
                        indegree.put(seq[i + 1], indegree.get(seq[i + 1]) + 1);
                    }
                }
            }
        }

        Queue<Integer> queue = new LinkedList<>();
        for(Map.Entry<Integer, Integer> entry: indegree.entrySet()) {
            if(entry.getValue() == 0) queue.offer(entry.getKey());
        }

        int index = 0;
        while(!queue.isEmpty()) {
            int size = queue.size();
            if(size > 1) return false;
            int curr = queue.poll();
            if(index == org.length || curr != org[index++]) return false;
            for(int next: map.get(curr)) {
                indegree.put(next, indegree.get(next) - 1);
                if(indegree.get(next) == 0) queue.offer(next);
            }
        }
        return index == org.length && index == map.size();
    }
}







// error 

class Solution {
    public boolean sequenceReconstruction(int[] org, List<List<Integer>> seqs) {
        // check two things . one is to check if the sequecne is unique, by checking the queue size = 1 
        // another thing to check if to check the size of the sequence is the same as the org size 
        // build indegree map, and the graph . 
        int n = org.length;
        Map<Integer, Set<Integer>> map = new HashMap<>();
        
        Map<Integer, Integer> indegree = new HashMap<>();
        for(List<Integer> seq : seqs){
            if(seq == null || seq.size() == 0) continue;
            if(seq.size() == 1) map.put(seq.get(0), new HashSet<>());
            for(int i = 0; i < seq.size() - 1; i++){
                int before = seq.get(i);
                int after = seq.get(i + 1);
                if(!map.containsKey(before)){
                    map.put(before, new HashSet<>());
                    indegree.put(before, 0);
                }
                if(!map.containsKey(after)){
                    map.put(after, new HashSet<>());
                    indegree.put(after, 0);
                }
                
                if(map.get(before).add(after)){
                    indegree.put(after, indegree.get(after) + 1);
                }
            }
        }
        
//         for (Map.Entry<String, String> entry : map.entrySet())
// {
//     System.out.println(entry.getKey() + "/" + entry.getValue());
// }
        
        
        
        Queue<Integer> queue = new LinkedList<>();
        for(Map.Entry<Integer, Integer> entry : indegree.entrySet()){
            if(entry.getValue() == 0) queue.offer(entry.getKey());
        }
        
        List<Integer> res = new ArrayList<>();
       
        while(!queue.isEmpty()){
            int size = queue.size();
            if(size > 1) return false;
            for(int i = 0; i < size; i++){
                int cur = queue.poll();
                
                res.add(cur);
                if(map.containsKey(cur)){
                    for(int nei : map.get(cur)){
                        int degree = indegree.get(nei);
                        if(degree == 1) queue.offer(nei);
                        indegree.put(nei, degree - 1);
                    }
                    
                }
                
            }
        }
        
        
        if(res.size() != org.length) return false;
        if(res.size() != map.size()) return false;
        // check org and res 
        for(int i = 0; i < org.length; i++){
            if(res.get(i) != org[i])
                return false;
        }
        return true;
        
        
    }
}



// Runtime Error Message:
// Exception in thread "main" java.lang.NullPointerException
//     at Solution.sequenceReconstruction(Solution.java:25)
//     at __DriverSolution__.__helper__(__Driver__.java:4)
//     at __Driver__.main(__Driver__.java:50)
// Last executed input:
// [5,4,8,9,1,6,3,2,7,10]
// [[],[5],[],[10],[8,9,1,6,3,2,7],[4,8],[1,6,3,2,7,10],[3,2,7,10],[7,10],[6,3,2]]





//  Runtime Error Message:
// Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: 233665123
//     at Solution.sequenceReconstruction(Solution.java:23)
//     at __DriverSolution__.__helper__(__Driver__.java:4)
//     at __Driver__.main(__Driver__.java:50)
// Last executed input:
// [5,4,8,9,1,6,3,2,7,10]
// [[233665123,2145174067],[783368690,1102520059,2044897763,1967513926,1365180540,1540383426,304089172],[1059961393,2089018456,628175011,1656478042,1131176229],[1101513929,1801979802,1315634022,635723058,1369133069],[],[184803526],[1025202362],[859484421,1914544919,608413784],[1734575198,1973594324,149798315],[35005211,521595368,294702567,1726956429,336465782,861021530]]









public class Solution {
    public boolean sequenceReconstruction(int[] org, int[][] seqs) {
        Map<Integer, Set<Integer>> map = new HashMap<>();
        Map<Integer, Integer> indegree = new HashMap<>();
        
        for(int[] seq: seqs) {
            if(seq.length == 1) {
                if(!map.containsKey(seq[0])) {
                    map.put(seq[0], new HashSet<>());
                    indegree.put(seq[0], 0);
                }
            } else {
                for(int i = 0; i < seq.length - 1; i++) {
                    if(!map.containsKey(seq[i])) {
                        map.put(seq[i], new HashSet<>());
                        indegree.put(seq[i], 0);
                    }

                    if(!map.containsKey(seq[i + 1])) {
                        map.put(seq[i + 1], new HashSet<>());
                        indegree.put(seq[i + 1], 0);
                    }

                    if(map.get(seq[i]).add(seq[i + 1])) {
                        indegree.put(seq[i + 1], indegree.get(seq[i + 1]) + 1);
                    }
                }
            }
        }

        Queue<Integer> queue = new LinkedList<>();
        for(Map.Entry<Integer, Integer> entry: indegree.entrySet()) {
            if(entry.getValue() == 0) queue.offer(entry.getKey());
        }

        int index = 0;
        while(!queue.isEmpty()) {
            int size = queue.size();
            if(size > 1) return false;
            int curr = queue.poll();
            if(index == org.length || curr != org[index++]) return false;
            for(int next: map.get(curr)) {
                indegree.put(next, indegree.get(next) - 1);
                if(indegree.get(next) == 0) queue.offer(next);
            }
        }
        return index == org.length && index == map.size();
    }
}



// Input:
// org: [4,1,5,2,6,3], seqs: [[5,2,6,3],[4,1,5,2]]

// 4: 1
// 1: 5 
// 5: 2 
// 2: 6 
// 6: 3 
    
    
    
    
    
    
    
    
    
// Input:
// org: [1,2,3], seqs: [[1,2]]

// Output:
// false

// Explanation:
// The reconstructed sequence can only be [1,2].
// Example 3:

// Input:
// org: [1,2,3], seqs: [[1,2],[1,3],[2,3]]

// Output:
// true

// Explanation:
// The sequences [1,2], [1,3], and [2,3] can uniquely reconstruct the original sequence [1,2,3].
// Example 4:

// Input:
// org: [4,1,5,2,6,3], seqs: [[5,2,6,3],[4,1,5,2]]

// 4: 1
// 1: 5 
// 5: 2 
// 2: 6 
// 6: 3 
    

// Output:
// true