How to find Time complexity of Graph coloring using backtracking?
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I have to find out the time complexity of graph coloring problem using backtracking. I have found somewhere it is O(n*m^n) where n=no vertex and m= number of color.
Suppose my code is given below how to find time complexity?
bool isSafe (int v, bool graph[V][V], int color, int c)
for (int i = 0; i < V; i++)
if (graph[v][i] && c == color[i])
return false;
return true;
bool graphColoringUtil(bool graph[V][V], int m, int color, int v)
if (v == V)
return true;
for (int c = 1; c <= m; c++)
if (isSafe(v, graph, color, c))
color[v] = c;
if (graphColoringUtil (graph, m, color, v+1) == true)
return true;
color[v] = 0;
return false;
bool graphColoring(bool graph[V][V], int m)
int *color = new int[V];
for (int i = 0; i < V; i++)
color[i] = 0;
if (graphColoringUtil(graph, m, color, 0) == false)
printf("Solution does not existn");
return false;
printSolution(color);
return true;
void printSolution(int color)
printf("Solution Exists:"
" Following are the assigned colors n");
for (int i = 0; i < V; i++)
printf(" %d ", color[i]);
printf("n");
algorithm graph colors backtracking
asked Apr 17 at 20:55
Rahul Krishna
136
add a comment |
up vote
1
down vote
favorite
I have to find out the time complexity of graph coloring problem using backtracking. I have found somewhere it is O(n*m^n) where n=no vertex and m= number of color.
Suppose my code is given below how to find time complexity?
bool isSafe (int v, bool graph[V][V], int color, int c)
for (int i = 0; i < V; i++)
if (graph[v][i] && c == color[i])
return false;
return true;
bool graphColoringUtil(bool graph[V][V], int m, int color, int v)
if (v == V)
return true;
for (int c = 1; c <= m; c++)
if (isSafe(v, graph, color, c))
color[v] = c;
if (graphColoringUtil (graph, m, color, v+1) == true)
return true;
color[v] = 0;
return false;
bool graphColoring(bool graph[V][V], int m)
int *color = new int[V];
for (int i = 0; i < V; i++)
color[i] = 0;
if (graphColoringUtil(graph, m, color, 0) == false)
printf("Solution does not existn");
return false;
printSolution(color);
return true;
void printSolution(int color)
printf("Solution Exists:"
" Following are the assigned colors n");
for (int i = 0; i < V; i++)
printf(" %d ", color[i]);
printf("n");
algorithm graph colors backtracking
asked Apr 17 at 20:55
Rahul Krishna
136
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I have to find out the time complexity of graph coloring problem using backtracking. I have found somewhere it is O(n*m^n) where n=no vertex and m= number of color.
Suppose my code is given below how to find time complexity?
bool isSafe (int v, bool graph[V][V], int color, int c)
for (int i = 0; i < V; i++)
if (graph[v][i] && c == color[i])
return false;
return true;
bool graphColoringUtil(bool graph[V][V], int m, int color, int v)
if (v == V)
return true;
for (int c = 1; c <= m; c++)
if (isSafe(v, graph, color, c))
color[v] = c;
if (graphColoringUtil (graph, m, color, v+1) == true)
return true;
color[v] = 0;
return false;
bool graphColoring(bool graph[V][V], int m)
int *color = new int[V];
for (int i = 0; i < V; i++)
color[i] = 0;
if (graphColoringUtil(graph, m, color, 0) == false)
printf("Solution does not existn");
return false;
printSolution(color);
return true;
void printSolution(int color)
printf("Solution Exists:"
" Following are the assigned colors n");
for (int i = 0; i < V; i++)
printf(" %d ", color[i]);
printf("n");
algorithm graph colors backtracking
asked Apr 17 at 20:55
Rahul Krishna
136
I have to find out the time complexity of graph coloring problem using backtracking. I have found somewhere it is O(n*m^n) where n=no vertex and m= number of color.
Suppose my code is given below how to find time complexity?
bool isSafe (int v, bool graph[V][V], int color, int c)
for (int i = 0; i < V; i++)
if (graph[v][i] && c == color[i])
return false;
return true;
bool graphColoringUtil(bool graph[V][V], int m, int color, int v)
if (v == V)
return true;
for (int c = 1; c <= m; c++)
if (isSafe(v, graph, color, c))
color[v] = c;
if (graphColoringUtil (graph, m, color, v+1) == true)
return true;
color[v] = 0;
return false;
bool graphColoring(bool graph[V][V], int m)
int *color = new int[V];
for (int i = 0; i < V; i++)
color[i] = 0;
if (graphColoringUtil(graph, m, color, 0) == false)
printf("Solution does not existn");
return false;
printSolution(color);
return true;
void printSolution(int color)
printf("Solution Exists:"
" Following are the assigned colors n");
for (int i = 0; i < V; i++)
printf(" %d ", color[i]);
printf("n");
algorithm graph colors backtracking
algorithm graph colors backtracking
asked Apr 17 at 20:55
Rahul Krishna
136
asked Apr 17 at 20:55
Rahul Krishna
136
asked Apr 17 at 20:55
Rahul Krishna
136
asked Apr 17 at 20:55
Rahul Krishna
136
asked Apr 17 at 20:55
Rahul Krishna
136
136
add a comment |
add a comment |
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