Given a Binary Tree, the task is to find the count of diagonal paths to the leaf of a binary tree such that values of all the nodes on the same diagonal are equal.

**Examples:**

Input:5 / \ 6 5 \ \ 6 5

Output:2Explanation:

Diagonal 6 – 6 and 5 – 5 contains equal value.

Therefore, the required output is 2.

Input:5 / \ 6 5 \ \ 5 5

Output:1

**Approach: **The main idea is to traverse the tree diagonally using a Map. Follow the steps below to solve this problem:

- Traverse the given binary tree in a diagonal order and store the starting node of each diagonal as the
**key**and for each**key**, store all the values in that diagonal in a Hashset. - After the traversal, find the number of
**keys**having size of the set equal to**1**and print it as the answer.

Below is the implementation of the above approach.

## C++14

`// C++ program of the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `struct` `TreeNode` `{` ` ` `int` `val = 0;` ` ` `TreeNode *left, *right;` ` ` ` ` `TreeNode(` `int` `x)` ` ` `{` ` ` `val = x;` ` ` `left = NULL;` ` ` `right = NULL;` ` ` `}` `};` `// Function to perform diagonal` `// traversal on the given binary tree` `void` `fillMap(TreeNode *root, ` `int` `left,` ` ` `map<` `int` `, set<` `int` `>> &diag)` `{` ` ` ` ` `// If tree is empty` ` ` `if` `(!root)` ` ` `return` `;` ` ` `// If current diagonal is not visited` ` ` `if` `(diag[left].size() == 0)` ` ` `{` ` ` ` ` `// Update diag[left]` ` ` `diag[left].insert(root->val);` ` ` `}` ` ` ` ` `// Otherwise, map current node` ` ` `// with its diagonal` ` ` `else` ` ` `diag[left].insert(root->val);` ` ` `// Recursively, traverse left subtree` ` ` `fillMap(root->left, left + 1, diag);` ` ` `// Recursively, traverse right subtree` ` ` `fillMap(root->right, left, diag);` `}` `// Function to count diagonal` `// paths having same-valued nodes` `int` `sameDiag(TreeNode *root)` `{` ` ` ` ` `// Maps the values of all` ` ` `// nodes with its diagonal` ` ` `map<` `int` `, set<` `int` `>> diag;` ` ` `// Stores indexing of diagonal` ` ` `int` `left = 0;` ` ` `// Function call to perform` ` ` `// diagonal traversal` ` ` `fillMap(root, left, diag);` ` ` `// Stores count of diagonals such` ` ` `// that all the nodes on the same` ` ` `// diagonal are equal` ` ` `int` `count = 0;` ` ` `// Traverse each diagonal` ` ` `for` `(` `auto` `d : diag)` ` ` `{` ` ` ` ` `// If all nodes on the current` ` ` `// diagonal are equal` ` ` `if` `(diag[d.first].size() == 1)` ` ` ` ` `// Update count` ` ` `count += 1;` ` ` `}` ` ` `return` `count;` `}` `// Driver Code` `int` `main()` `{` ` ` ` ` `// Given tree` ` ` `TreeNode *root = ` `new` `TreeNode(5);` ` ` `root->left = ` `new` `TreeNode(6);` ` ` `root->right = ` `new` `TreeNode(5);` ` ` `root->left->right = ` `new` `TreeNode(6);` ` ` `root->right->right = ` `new` `TreeNode(5);` ` ` ` ` `// Function call` ` ` `cout << sameDiag(root);` `}` `// This code is contributed by mohit kumar 29` |

## Java

`// Java program for above approach` `import` `java.util.*;` `import` `java.lang.*;` `class` `GFG` `{` ` ` `// Structure of a Node` ` ` `static` `class` `TreeNode` ` ` `{` ` ` `int` `val;` ` ` `TreeNode left, right;` ` ` `TreeNode(` `int` `key)` ` ` `{` ` ` `val = key;` ` ` `left = ` `null` `;` ` ` `right = ` `null` `;` ` ` `}` ` ` `};` ` ` `// Function to perform diagonal` ` ` `// traversal on the given binary tree` ` ` `static` `void` `fillMap(TreeNode root, ` `int` `left,` ` ` `Map<Integer,Set<Integer>> diag)` ` ` `{` ` ` `// If tree is empty` ` ` `if` `(root == ` `null` `)` ` ` `return` `;` ` ` `// If current diagonal is not visited` ` ` `if` `(diag.get(left) == ` `null` `)` ` ` `{` ` ` `// Update diag[left]` ` ` `diag.put(left, ` `new` `HashSet<Integer>());` ` ` `diag.get(left).add(root.val);` ` ` `}` ` ` `// Otherwise, map current node` ` ` `// with its diagonal` ` ` `else` ` ` `diag.get(left).add(root.val);` ` ` `// Recursively, traverse left subtree` ` ` `fillMap(root.left, left + ` `1` `, diag);` ` ` `// Recursively, traverse right subtree` ` ` `fillMap(root.right, left, diag);` ` ` `}` ` ` `// Function to count diagonal` ` ` `// paths having same-valued nodes` ` ` `static` `int` `sameDiag(TreeNode root)` ` ` `{` ` ` `// Maps the values of all` ` ` `// nodes with its diagonal` ` ` `Map<Integer, Set<Integer>> diag = ` `new` `HashMap<>();` ` ` `// Stores indexing of diagonal` ` ` `int` `left = ` `0` `;` ` ` `// Function call to perform` ` ` `// diagonal traversal` ` ` `fillMap(root, left, diag);` ` ` `// Stores count of diagonals such` ` ` `// that all the nodes on the same` ` ` `// diagonal are equal` ` ` `int` `count = ` `0` `;` ` ` `// Traverse each diagonal` ` ` `for` `(Map.Entry<Integer,Set<Integer>> d:diag.entrySet())` ` ` `{` ` ` `// If all nodes on the current` ` ` `// diagonal are equal` ` ` `if` `(d.getValue().size() == ` `1` `)` ` ` `// Update count` ` ` `count += ` `1` `;` ` ` `}` ` ` `return` `count;` ` ` `}` ` ` `// Driver function` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `TreeNode root = ` `new` `TreeNode(` `5` `);` ` ` `root.left = ` `new` `TreeNode(` `6` `);` ` ` `root.right = ` `new` `TreeNode(` `5` `);` ` ` `root.left.right = ` `new` `TreeNode(` `6` `);` ` ` `root.right.right = ` `new` `TreeNode(` `5` `);` ` ` `System.out.println(sameDiag(root));` ` ` `}` `}` `// This code is contributed by offbeat` |

## Python3

`# Python3 program of the above approach` `# Structure of a Node` `class` `TreeNode:` ` ` `def` `__init__(` `self` `, val ` `=` `0` `, left ` `=` `None` `, right ` `=` `None` `):` ` ` `self` `.val ` `=` `val` ` ` `self` `.left ` `=` `left` ` ` `self` `.right ` `=` `right` `# Function to count diagonal` `# paths having same-valued nodes` `def` `sameDiag(root):` ` ` `# Maps the values of all` ` ` `# nodes with its diagonal` ` ` `diag ` `=` `{}` ` ` `# Stores indexing of diagonal` ` ` `left ` `=` `0` ` ` `# Function to perform diagonal` ` ` `# traversal on the given binary tree` ` ` `def` `fillMap(root, left):` ` ` `# If tree is empty` ` ` `if` `not` `root:` ` ` `return` ` ` `# If current diagonal is not visited` ` ` `if` `left ` `not` `in` `diag:` ` ` `# Update diag[left]` ` ` `diag[left] ` `=` `set` `([root.val])` ` ` `# Otherwise, map current node` ` ` `# with its diagonal` ` ` `else` `:` ` ` `diag[left].add(root.val)` ` ` `# Recursively, traverse left subtree` ` ` `fillMap(root.left, left ` `+` `1` `)` ` ` `# Recursively, traverse right subtree` ` ` `fillMap(root.right, left)` ` ` `# Function call to perform` ` ` `# diagonal traversal` ` ` `fillMap(root, left)` ` ` `# Stores count of diagonals such` ` ` `# that all the nodes on the same` ` ` `# diagonal are equal` ` ` `count ` `=` `0` ` ` `# Traverse each diagonal` ` ` `for` `d ` `in` `diag:` ` ` `# If all nodes on the current` ` ` `# diagonal are equal` ` ` `if` `len` `(` `list` `(diag[d])) ` `=` `=` `1` `:` ` ` `# Update count` ` ` `count ` `+` `=` `1` ` ` `return` `count` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` ` ` `# Given tree` ` ` `root ` `=` `TreeNode(` `5` `)` ` ` `root.left ` `=` `TreeNode(` `6` `)` ` ` `root.right ` `=` `TreeNode(` `5` `)` ` ` `root.left.right ` `=` `TreeNode(` `6` `)` ` ` `root.right.right ` `=` `TreeNode(` `5` `)` ` ` `# Function call` ` ` `print` `(sameDiag(root))` |

**Output:**

2

**Time Complexity:** O(N)**Auxiliary Space:** O(N)

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