# 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)
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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); ` `    ``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 `

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).

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