# Find the color of given node in an infinite binary tree

Given an infinitely long binary tree having a pattern as below:

1 / \ 2 3 / \ / \ 4 5 6 7 / \ / \ / \ / \ ......................

Also given an array **arr** of size **N** and a number **K**. The task is to color all the subtrees of node arr[i] with colour i (1 <= i <= N) one after another. Find the colour of node **K** after colouring all subtrees.

**Note:-** Initially all nodes have color 0.

Input :arr[] = {3, 2, 1, 3}, K = 7

Output :4

Explanation :

After applying the color 1 to subtree at node 3, node 7 contains color 1.

After applying the color 2 to subtree at node 2, node 7 contains color 1.

After applying the color 3 to subtree at node 1, node 7 contains color 3.

After applying the color 4 to subtree at node 3, node 7 contains color 4.

Input :arr[] = {3, 2, 1, 3}, K = 4

Output :3

Explanation :

After applying the color 1 to subtree at node 3, node 4 contains color 0.

After applying the color 2 to subtree at node 2, node 4 contains color 2.

After applying the color 3 to subtree at node 1, node 4 contains color 3.

After applying the color 4 to subtree at node 3, node 4 contains color 3.

A **naive approach ** is for every index i (1 <= i <= N) update color all nodes in a subtree until the level of the nodes less than the level of given node K. After N such operations print the color of node K.

An **efficient approach** is to use hashing

- First, insert all the nodes with their respective colors in a map( in case, if a node has more than one color, keep one with the maximum color number).
- Find all ancestors of the given node k and output the color having a maximum number. (If the current node is
**x**, then**(x-1)/2**or**x/2**are its ancestors)

Below is the implementation of the above approach:

## CPP

`// CPP program to find color of the node ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find color of the node ` `int` `findColor(map<` `int` `, ` `int` `> mapWithColor, ` `int` `query) ` `{ ` ` ` `// Maximum is to store maximum color ` ` ` `int` `maximum = 0; ` ` ` ` ` `// Loop to check all the parent ` ` ` `// values to get maximum color ` ` ` `while` `(query >= 1) { ` ` ` ` ` `// Find the number into map and get maximum color ` ` ` `if` `(mapWithColor.find(query) != mapWithColor.end()) ` ` ` `{ ` ` ` `// Take the maximum color and ` ` ` `// assign into maximum variable ` ` ` `maximum = max(maximum, mapWithColor[query]); ` ` ` `} ` ` ` ` ` `// Find parent index ` ` ` `if` `(query % 2 == 1) ` ` ` `query = (query - 1) / 2; ` ` ` `else` ` ` `query = query / 2; ` ` ` `} ` ` ` ` ` `// Return maximum color ` ` ` `return` `maximum; ` `} ` ` ` `// Function to build hash map with color ` `map<` `int` `, ` `int` `> buildMapWithColor(` `int` `arr[], ` `int` `n) ` `{ ` ` ` `// To store color of each node ` ` ` `map<` `int` `, ` `int` `> mapWithColor; ` ` ` ` ` `// For each number add a color number ` ` ` `for` `(` `int` `i = 0; i < n; i++) { ` ` ` `// Assigning color ` ` ` `mapWithColor[arr[i]] = i + 1; ` ` ` `} ` ` ` ` ` `// Return hash map ` ` ` `return` `mapWithColor; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `arr[] = { 3, 2, 1, 3 }; ` ` ` ` ` `int` `n = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]); ` ` ` ` ` `int` `k = 7; ` ` ` ` ` `// Build mapWithColor ` ` ` `map<` `int` `, ` `int` `> mapWithColor = buildMapWithColor(arr, n); ` ` ` ` ` `// Print the maximum color ` ` ` `cout << findColor(mapWithColor, k); ` ` ` ` ` `return` `0; ` `} ` |

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## Python3

`# Python3 code program to find color of the node ` ` ` `# Function to find color of the node ` `def` `findColor(mapWithColor, query): ` ` ` ` ` `# Maximum is to store maximum color ` ` ` `maximum ` `=` `0` ` ` ` ` `# Loop to check all the parent ` ` ` `# values to get maximum color ` ` ` `while` `(query >` `=` `1` `): ` ` ` ` ` `# Find the number into map and get maximum color ` ` ` `if` `(query) ` `in` `mapWithColor.keys(): ` ` ` `# Take the maximum color and ` ` ` `# assign into maximum variable ` ` ` `maximum ` `=` `max` `(maximum, mapWithColor[query]) ` ` ` ` ` `# Find parent index ` ` ` `if` `(query ` `%` `2` `=` `=` `1` `): ` ` ` `query ` `=` `(query ` `-` `1` `) ` `/` `/` `2` ` ` `else` `: ` ` ` `query ` `=` `query ` `/` `/` `2` ` ` ` ` ` ` `# Return maximum color ` ` ` `return` `maximum ` ` ` `# Function to build hash map with color ` `def` `buildMapWithColor(arr, n): ` ` ` `# To store color of each node ` ` ` `mapWithColor` `=` `{} ` ` ` ` ` `# For each number add a color number ` ` ` `for` `i ` `in` `range` `(n): ` ` ` `# Assigning color ` ` ` `mapWithColor[arr[i]] ` `=` `i ` `+` `1` ` ` ` ` `# Return hash map ` ` ` `return` `mapWithColor ` ` ` ` ` `# Driver code ` ` ` `arr ` `=` `[` `3` `, ` `2` `, ` `1` `, ` `3` `] ` ` ` `n ` `=` `len` `(arr) ` ` ` `k ` `=` `7` ` ` `# Build mapWithColor ` `mapWithColor ` `=` `buildMapWithColor(arr, n) ` ` ` `# Prthe maximum color ` `print` `(findColor(mapWithColor, k)) ` ` ` `# This code is contributed by mohit kumar 29 ` |

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**Output:**

4

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