// This function returns overall
// maximum path sum in 'res' And
// returns max path sum going through root.
int findMaxUtil(Node1 node, Res res)
{
// Base Case
if (node == null)
{
return(0);
}
// l and r store maximum path
// sum going through left and
// right child of root respectively
int l = findMaxUtil(node.left, res);
int r = findMaxUtil(node.right, res);
// Max path for parent call of root.
// This path must include
// at-most one child of root
int max_single = Math.Max(Math.Max(l, r) +
node.data, node.data);
// Max Top represents the sum
// when the Node under
// consideration is the root
// of the maxsum path and no
// ancestors of root are there
// in max sum path
int max_top = Math.Max(max_single,
l + r + node.data);
// Store the Maximum Result.
res.val = Math.Max(res.val, max_top);
return(max_single);
}
// Returns maximum path
// sum in tree with given root
int findMaxSum(Node1 node)
{
// Initialize result
// int res2 = int.MinValue;
Res res = new Res();
res.val = int.MinValue;
// Compute and return result
findMaxUtil(node, res);
return(res.val);
}
public int dfs(int[,] graph)
{
int m = graph.GetLength(0);
int n = graph.GetLength(1);
bool[,] visited = new bool[m, n];
int paths = 0;
Stack <Node1> s = new Stack <Node1>();
s.Push(new Node1(0, 0));
while (s.Count != 0)
{
Node1 node = s.Pop();
if (node.i == m - 1 && node.j == n - 1)
{
paths++;
s.Push(new Node1(0, 0));
continue;
}
if (!visited[node.i, node.j])
{
if (node.i != 0 && node.j != 0)
{
visited[node.i, node.j] = true;
}
if (node.i + 1 < m && graph[node.i + 1, node.j] == 0)
{
s.Push(new Node1(node.i + 1, node.j));
}
if (node.j + 1 < n && graph[node.i, node.j + 1] == 0)
{
s.Push(new Node1(node.i, node.j + 1));
}
}
}
return(paths);
}
/*
* Write a Program to Find the Maximum Depth or Height of a Tree
*
*
* Given a binary tree, find height of it. Height of empty tree is 0 and height of below tree is 2.
* 1
* / \
* / \
* 2 3
* /\
* / \
* 4 5
* Recursively calculate height of left and right subtrees of a node and assign height to the node as max of the heights of two children plus 1. See below pseudo code and program for details.
* Algorithm:
*
*
* maxDepth()
* 1. If tree is empty then return 0
* 2. Else
* (a) Get the max depth of left subtree recursively i.e.,
* call maxDepth( tree->left-subtree)
* (a) Get the max depth of right subtree recursively i.e.,
* call maxDepth( tree->right-subtree)
* (c) Get the max of max depths of left and right
* subtrees and add 1 to it for the current node.
* max_depth = max(max dept of left subtree,
* max depth of right subtree)
+ 1
+ (d) Return max_depth
+ See the below diagram for more clarity about execution of the recursive function maxDepth() for above example tree.
+
+
+ maxDepth('1') = max(maxDepth('2'), maxDepth('3')) + 1
+ = 1 + 1
+ / \
+ / \
+ / \
+ / \
+ / \
+ maxDepth('2') = 1 maxDepth('3') = 0
+ = max(maxDepth('4'), maxDepth('5')) + 1
+ = 1 + 0 = 1
+ / \
+ / \
+ / \
+ / \
+ / \
+ maxDepth('4') = 0 maxDepth('5') = 0
+
*/
int maxDepth(Node1 node)
{
if (node == null)
{
return(-1);
}
else
{
/* compute the depth of each subtree */
int lDepth = maxDepth(node.left);
int rDepth = maxDepth(node.right);
/* use the larger one */
if (lDepth > rDepth)
{
return(lDepth + 1);
}
else
{
return(rDepth + 1);
}
}
}
public Node1(int item)
{
data = item;
left = right = null;
}
