# Build original array from the given sub-sequences

Given an integer **N** and valid subsequences of an array of integers where every element is distinct and from the range **[0, N – 1]**, the task is to find the original array.

**Examples:**

Input:N = 6, v[] = {

{1, 2, 3},

{1, 2},

{3, 4},

{5, 2},

{0, 5, 4}}

Output:0 1 5 2 3 4

Input:N = 10, v[] = {

{9, 1, 2, 8, 3},

{6, 1, 2},

{9, 6, 3, 4},

{5, 2, 7},

{0, 9, 5, 4}}

Output:0 9 6 5 1 2 8 7 3 4

**Approach:** Build a graph from given subsequences. Select each sub-sequence one by one and add an edge between two adjacent elements in the sub-sequence. After building the graph, perform topological sorting on the graph.

Refer topological sorting for understanding topological sort. This topological ordering is the required array.

Below is the implementation of the above approach:

## C++

`// C++ implementation of the approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to add edge to graph ` `void` `addEdge(vector<` `int` `> adj[], ` `int` `u, ` `int` `v) ` `{ ` ` ` `adj[u].push_back(v); ` `} ` ` ` `// Function to calculate indegrees of all the vertices ` `void` `getindeg(vector<` `int` `> adj[], ` `int` `V, vector<` `int` `>& indeg) ` `{ ` ` ` `// If there is an edge from i to x ` ` ` `// then increment indegree of x ` ` ` `for` `(` `int` `i = 0; i < V; i++) { ` ` ` `for` `(` `auto` `x : adj[i]) { ` ` ` `indeg[x]++; ` ` ` `} ` ` ` `} ` `} ` ` ` `// Function to perform topological sort ` `vector<` `int` `> topo(vector<` `int` `> adj[], ` `int` `V, vector<` `int` `>& indeg) ` `{ ` ` ` `queue<` `int` `> q; ` ` ` ` ` `// Push every node to the queue ` ` ` `// which has no incoming edge ` ` ` `for` `(` `int` `i = 0; i < V; i++) { ` ` ` `if` `(indeg[i] == 0) ` ` ` `q.push(i); ` ` ` `} ` ` ` `vector<` `int` `> res; ` ` ` `while` `(!q.empty()) { ` ` ` `int` `u = q.front(); ` ` ` `q.pop(); ` ` ` `res.push_back(u); ` ` ` ` ` `// Since edge u is removed, update the indegrees ` ` ` `// of all the nodes which had an incoming edge from u ` ` ` `for` `(` `auto` `x : adj[u]) { ` ` ` `indeg[x]--; ` ` ` `if` `(indeg[x] == 0) ` ` ` `q.push(x); ` ` ` `} ` ` ` `} ` ` ` `return` `res; ` `} ` ` ` `// Function to generate the array ` `// from the given sub-sequences ` `vector<` `int` `> makearray(vector<vector<` `int` `> > v, ` `int` `V) ` `{ ` ` ` ` ` `// Create the graph from the input sub-sequences ` ` ` `vector<` `int` `> adj[V]; ` ` ` `for` `(` `int` `i = 0; i < v.size(); i++) { ` ` ` `for` `(` `int` `j = 0; j < v[i].size() - 1; j++) { ` ` ` ` ` `// Add edge between every two consecutive ` ` ` `// elements of the given sub-sequences ` ` ` `addEdge(adj, v[i][j], v[i][j + 1]); ` ` ` `} ` ` ` `} ` ` ` ` ` `// Get the indegrees for all the vertices ` ` ` `vector<` `int` `> indeg(V, 0); ` ` ` `getindeg(adj, V, indeg); ` ` ` ` ` `// Get the topological order of the created graph ` ` ` `vector<` `int` `> res = topo(adj, V, indeg); ` ` ` `return` `res; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `// Size of the required array ` ` ` `int` `n = 10; ` ` ` ` ` `// Given sub-sequences of the array ` ` ` `vector<vector<` `int` `> > subseqs{ { 9, 1, 2, 8, 3 }, ` ` ` `{ 6, 1, 2 }, ` ` ` `{ 9, 6, 3, 4 }, ` ` ` `{ 5, 2, 7 }, ` ` ` `{ 0, 9, 5, 4 } }; ` ` ` ` ` `// Get the resultant array as vector ` ` ` `vector<` `int` `> res = makearray(subseqs, n); ` ` ` ` ` `// Printing the array ` ` ` `for` `(` `auto` `x : res) { ` ` ` `cout << x << ` `" "` `; ` ` ` `} ` ` ` ` ` `return` `0; ` `} ` |

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## Python3

`# Python3 implementation of the approach ` `from` `collections ` `import` `deque ` `adj` `=` `[[] ` `for` `i ` `in` `range` `(` `100` `)] ` ` ` `# Function to add edge to graph ` `def` `addEdge(u, v): ` ` ` `adj[u].append(v) ` ` ` `# Function to calculate indegrees of all the vertices ` `def` `getindeg(V,indeg): ` ` ` ` ` `# If there is an edge from i to x ` ` ` `# then increment indegree of x ` ` ` `for` `i ` `in` `range` `(V): ` ` ` `for` `x ` `in` `adj[i]: ` ` ` `indeg[x] ` `+` `=` `1` ` ` ` ` `# Function to perform topological sort ` `def` `topo(V,indeg): ` ` ` `q ` `=` `deque() ` ` ` ` ` `# Push every node to the queue ` ` ` `# which has no incoming edge ` ` ` `for` `i ` `in` `range` `(V): ` ` ` `if` `(indeg[i] ` `=` `=` `0` `): ` ` ` `q.appendleft(i) ` ` ` `res` `=` `[] ` ` ` `while` `(` `len` `(q) > ` `0` `): ` ` ` `u ` `=` `q.popleft() ` ` ` `res.append(u) ` ` ` ` ` `# Since edge u is removed, update the indegrees ` ` ` `# of all the nodes which had an incoming edge from u ` ` ` `for` `x ` `in` `adj[u]: ` ` ` `indeg[x]` `-` `=` `1` ` ` `if` `(indeg[x] ` `=` `=` `0` `): ` ` ` `q.appendleft(x) ` ` ` ` ` `return` `res ` ` ` ` ` `# Function to generate the array ` `# from the given sub-sequences ` `def` `makearray(v, V): ` ` ` ` ` `# Create the graph from the input sub-sequences ` ` ` `for` `i ` `in` `range` `(` `len` `(v)): ` ` ` `for` `j ` `in` `range` `(` `len` `(v[i])` `-` `1` `): ` ` ` ` ` `# Add edge between every two consecutive ` ` ` `# elements of the given sub-sequences ` ` ` `addEdge(v[i][j], v[i][j ` `+` `1` `]) ` ` ` ` ` ` ` `# Get the indegrees for all the vertices ` ` ` `indeg` `=` `[` `0` `for` `i ` `in` `range` `(V)] ` ` ` `getindeg(V, indeg) ` ` ` ` ` `# Get the topological order of the created graph ` ` ` `res ` `=` `topo(V, indeg) ` ` ` `return` `res ` ` ` `# Driver code ` ` ` `# Size of the required array ` `n ` `=` `10` ` ` `# Given sub-sequences of the array ` `subseqs` `=` `[ [ ` `9` `, ` `1` `, ` `2` `, ` `8` `, ` `3` `], ` ` ` `[ ` `6` `, ` `1` `, ` `2` `], ` ` ` `[ ` `9` `, ` `6` `, ` `3` `, ` `4` `], ` ` ` `[ ` `5` `, ` `2` `, ` `7` `], ` ` ` `[ ` `0` `, ` `9` `, ` `5` `, ` `4` `] ] ` ` ` `# Get the resultant array as vector ` `res ` `=` `makearray(subseqs, n) ` ` ` `# Printing the array ` `for` `x ` `in` `res: ` ` ` `print` `(x,end` `=` `" "` `) ` ` ` `# This code is contributed by mohit kumar 29 ` |

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**Output:**

0 9 6 5 1 2 8 7 3 4

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