
- Python Basic Tutorial
- Python - Home
- Python - Overview
- Python - Environment Setup
- Python - Basic Syntax
- Python - Comments
- Python - Variables
- Python - Data Types
- Python - Operators
- Python - Decision Making
- Python - Loops
- Python - Numbers
- Python - Strings
- Python - Lists
- Python - Tuples
- Python - Dictionary
- Python - Date & Time
- Python - Functions
- Python - Modules
- Python - Files I/O
- Python - Exceptions
Program find number of subsets of colorful vertices that meets given conditions in Python
Suppose we have an array colors, representing colors for one regular n-gon. Here each vertex of this n-gon was randomly colored with one of n different colors present in the given array. We have to find the number of special subsets of polygon vertices, such that these subsets meet these conditions −
- The size of subset must be at least two.
- If we remove vertices which are present in the subset, from the polygon (the adjacent edges of those vertices will also get removed), then the remaining vertices and edges form some continuous paths.
- None of those paths should contain two vertices of the same color.
We have to count number of such subsets are present. If the answer is too large, then return result mod 10^9 + 7.
So, if the input is like colors = [1,2,3,4], then the output will be 11.
To solve this, we will follow these steps −
- count := an empty map where all values will be an empty list.
- n := size of colors
- for i in range 0 to size of colors - 1, do
- insert i at the end of count[colors[i]]
- answer := 0
- for i in range 2 to n, do
- answer := answer + nCr(n, i)
- for each i in list of all keys of count, do
- l0 := count[i]
- n0 := size of l0
- if n0 > 1, then
- for i in range 0 to n0-2, do
- for j in range i+1 to n0 - 1, do
- d1 := l0[j] -l0[i]
- d2 := l0[i] -l0[j] + n
- if d1 <= n-3 or d2<= n-3, then
- answer := answer - 1
- for j in range i+1 to n0 - 1, do
- for i in range 0 to n0-2, do
- return answer
Example
Let us see the following implementation to get better understanding −
from collections import defaultdict from math import factorial def nCr(n, i): if n==1: return 1 return factorial(n)//factorial(i)//factorial(n-i) def solve(colors): count = defaultdict(list) n = len(colors) for i in range(len(colors)): count[colors[i]].append(i) answer = 0 for i in range(2, n+1): answer += nCr(n, i) for i in count.keys(): l0 = count[i] n0 = len(l0) if n0 > 1: for i in range(n0-1): for j in range(i+1, n0): d1 = l0[j] -l0[i] d2 = l0[i] -l0[j] + n if d1 <= n-3 or d2<= n-3: answer -=1 return answer colors = [1,2,3,4] print(solve(colors))
Input
[1,2,3,4]
Output
11
- Related Articles
- Program to find number of strictly increasing colorful candle sequences are there in Python
- Program to check number of requests that will be processed with given conditions in python
- Program to find number of tasks can be finished with given conditions in Python
- Program to find number of elements in all permutation which are following given conditions in Python
- Python program to get all subsets of given size of a set
- Python program to get all subsets of a given size of a set
- Python Program To Find all the Subsets of a String
- Program to find minimum number of vertices to reach all nodes using Python
- Program to find number of subsequences that satisfy the given sum condition using Python
- Program to find number of bit 1 in the given number in Python
- Find all distinct subsets of a given set in C++
- Program to count subsets that sum up to k in python
- Program to check whether given password meets criteria or not in Python
- Program to find the sum of all digits of given number in Python
- Program to count number of unique paths that includes given edges in Python

Advertisements