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# Construct a graph from given degrees of all vertices

This is a C++ program to generate a graph for a given fixed degree sequence. This algorithm generates a undirected graph for the given degree sequence.It does not include self-edge and multiple edges.

Examples:

```Input : degrees[] = {2, 2, 1, 1}
Output :  (0)  (1)  (2)  (3)
(0)    0    1    1    0
(1)    1    0    0    1
(2)    1    0    0    0
(3)    0    1    0    0
Explanation : We are given that there
are four vertices with degree of vertex
0 as 2, degree of vertex 1 as 2, degree
of vertex 2 as 1 and degree of vertex 3
as 1. Following is graph that follows
given conditions.
(0)----------(1)
|            |
|            |
|            |
(2)          (3) ```

Approach :

1. Take the input of the number of vertexes and their corresponding degree.
2. Declare adjacency matrix, mat[ ][ ] to store the graph.
3. To create the graph, create the first loop to connect each vertex ‘i’.
4. Second nested loop to connect the vertex ‘i’ to the every valid vertex ‘j’, next to it.
5. If the degree of vertex ‘i’ and ‘j’ are more than zero then connect them.

Based on the above explanation, below are implementations:

## C++

 `// C++ program to generate a graph for a``// given fixed degrees``#include ``using` `namespace` `std;` `// A function to print the adjacency matrix.``void` `printMat(``int` `degseq[], ``int` `n)``{``    ``// n is number of vertices``    ``int` `mat[n][n];``    ``memset``(mat, 0, ``sizeof``(mat));` `    ``for` `(``int` `i = 0; i < n; i++) {``        ``for` `(``int` `j = i + 1; j < n; j++) {` `            ``// For each pair of vertex decrement``            ``// the degree of both vertex.``            ``if` `(degseq[i] > 0 && degseq[j] > 0) {``                ``degseq[i]--;``                ``degseq[j]--;``                ``mat[i][j] = 1;``                ``mat[j][i] = 1;``            ``}``        ``}``    ``}` `    ``// Print the result in specified format``    ``cout << ``"\n"``         ``<< setw(3) << ``"     "``;``    ``for` `(``int` `i = 0; i < n; i++)``        ``cout << setw(3) << ``"("` `<< i << ``")"``;``    ``cout << ``"\n\n"``;``    ``for` `(``int` `i = 0; i < n; i++) {``        ``cout << setw(4) << ``"("` `<< i << ``")"``;``        ``for` `(``int` `j = 0; j < n; j++)``            ``cout << setw(5) << mat[i][j];``        ``cout << ``"\n"``;``    ``}``}` `// driver program to test above function``int` `main()``{``    ``int` `degseq[] = { 2, 2, 1, 1, 1 };``    ``int` `n = ``sizeof``(degseq) / ``sizeof``(degseq[0]);``    ``printMat(degseq, n);``    ``return` `0;``}`

## Java

 `// Java program to generate a graph for a``// given fixed degrees``import` `java.util.*;` `class` `GFG``{` `// A function to print the adjacency matrix.``static` `void` `printMat(``int` `degseq[], ``int` `n)``{``    ``// n is number of vertices``    ``int` `[][]mat = ``new` `int``[n][n];` `    ``for` `(``int` `i = ``0``; i < n; i++)``    ``{``        ``for` `(``int` `j = i + ``1``; j < n; j++)``        ``{` `            ``// For each pair of vertex decrement``            ``// the degree of both vertex.``            ``if` `(degseq[i] > ``0` `&& degseq[j] > ``0``)``            ``{``                ``degseq[i]--;``                ``degseq[j]--;``                ``mat[i][j] = ``1``;``                ``mat[j][i] = ``1``;``            ``}``        ``}``    ``}` `    ``// Print the result in specified format``    ``System.out.print(``"\n"` `+ setw(``3``) + ``"     "``);``    ` `    ``for` `(``int` `i = ``0``; i < n; i++)``        ``System.out.print(setw(``3``) + ``"("` `+ i + ``")"``);``    ``System.out.print(``"\n\n"``);``    ``for` `(``int` `i = ``0``; i < n; i++)``    ``{``        ``System.out.print(setw(``4``) + ``"("` `+ i + ``")"``);``        ` `        ``for` `(``int` `j = ``0``; j < n; j++)``            ``System.out.print(setw(``5``) + mat[i][j]);``        ``System.out.print(``"\n"``);``    ``}``}` `static` `String setw(``int` `n)``{``    ``String space = ``""``;``    ``while``(n-- > ``0``)``        ``space += ``" "``;``    ``return` `space;``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `degseq[] = { ``2``, ``2``, ``1``, ``1``, ``1` `};``    ``int` `n = degseq.length;``    ``printMat(degseq, n);``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 program to generate a graph``# for a given fixed degrees` `# A function to print the adjacency matrix.``def` `printMat(degseq, n):``    ` `    ``# n is number of vertices``    ``mat ``=` `[[``0``] ``*` `n ``for` `i ``in` `range``(n)]` `    ``for` `i ``in` `range``(n):``        ``for` `j ``in` `range``(i ``+` `1``, n):` `            ``# For each pair of vertex decrement``            ``# the degree of both vertex.``            ``if` `(degseq[i] > ``0` `and` `degseq[j] > ``0``):``                ``degseq[i] ``-``=` `1``                ``degseq[j] ``-``=` `1``                ``mat[i][j] ``=` `1``                ``mat[j][i] ``=` `1` `    ``# Print the result in specified form``    ``print``(``"      "``, end ``=` `" "``)``    ``for` `i ``in` `range``(n):``        ``print``(``" "``, ``"("``, i, ``")"``, end ``=` `"")``    ``print``()``    ``print``()``    ``for` `i ``in` `range``(n):``        ``print``(``" "``, ``"("``, i, ``")"``, end ``=` `"")``        ``for` `j ``in` `range``(n):``            ``print``(``"     "``, mat[i][j], end ``=` `"")``        ``print``()` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ``degseq ``=` `[``2``, ``2``, ``1``, ``1``, ``1``]``    ``n ``=` `len``(degseq)``    ``printMat(degseq, n)` `# This code is contributed by PranchalK`

## C#

 `// C# program to generate a graph for a``// given fixed degrees``using` `System;``    ` `class` `GFG``{` `// A function to print the adjacency matrix.``static` `void` `printMat(``int` `[]degseq, ``int` `n)``{``    ``// n is number of vertices``    ``int` `[,]mat = ``new` `int``[n, n];` `    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``for` `(``int` `j = i + 1; j < n; j++)``        ``{` `            ``// For each pair of vertex decrement``            ``// the degree of both vertex.``            ``if` `(degseq[i] > 0 && degseq[j] > 0)``            ``{``                ``degseq[i]--;``                ``degseq[j]--;``                ``mat[i, j] = 1;``                ``mat[j, i] = 1;``            ``}``        ``}``    ``}` `    ``// Print the result in specified format``    ``Console.Write(``"\n"` `+ setw(3) + ``"     "``);``    ` `    ``for` `(``int` `i = 0; i < n; i++)``        ``Console.Write(setw(3) + ``"("` `+ i + ``")"``);``    ``Console.Write(``"\n\n"``);``    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``Console.Write(setw(4) + ``"("` `+ i + ``")"``);``        ` `        ``for` `(``int` `j = 0; j < n; j++)``            ``Console.Write(setw(5) + mat[i, j]);``        ``Console.Write(``"\n"``);``    ``}``}` `static` `String setw(``int` `n)``{``    ``String space = ``""``;``    ``while``(n-- > 0)``        ``space += ``" "``;``    ``return` `space;``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]degseq = { 2, 2, 1, 1, 1 };``    ``int` `n = degseq.Length;``    ``printMat(degseq, n);``}``}` `// This code is contributed by Princi Singh`

## Javascript

 ``

Output

```       (0)  (1)  (2)  (3)  (4)

(0)    0    1    1    0    0
(1)    1    0    0    1    0
(2)    1    0    0    0    0
(3)    0    1    0    0    0
(4)    0    0    0    0    0```

Time Complexity: O(v*v).

Space complexity : O(n^2) because it creates a 2-dimensional array (matrix) of size n * n, where n is the number of vertices in the graph.