Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Program to find sum of differences between max and min elements from randomly selected k balls from n balls in Python
Suppose we have n balls which are numbered by an array nums, whose size is n and nums[i] represents the number of ball i. Now we have another value k. In each turn we pick k balls from n different balls and find the difference of maximum and minimum values of k balls and store the difference in a table. Then put these k balls again into that pot and pick again until we have selected all possible selections. Finally find the sum of all differences from the table. If the answer is too large, then return result mod 10^9+7.
So, if the input is like n = 4 k = 3 nums = [5, 7, 9, 11], then the output will be 20 because combinations are −
- [5,7,9], difference 9-5 = 4
- [5,7,11], difference 11-5 = 6
- [5,9,11], difference 11-5 = 6
- [7,9,11], difference 11-7 = 4
so 4+6+6+4 = 20.
To solve this, we will follow these steps −
- m := 10^9 + 7
- inv := a new list with elements [0, 1]
- for i in range 2 to n, do
- insert (m - floor of (m / i) * inv[m mod i] mod m) at the end of inv
- comb_count := 1
- res := 0
- for pick in range k - 1 to n - 1, do
- res := res +(nums[pick] - nums[n - 1 - pick]) * comb_count mod m
- res := res mod m
- comb_count := comb_count *(pick + 1) mod m * inv[pick + 2 - k] mod m
- return res
Example
Let us see the following implementation to get better understanding −
def solve(n, k, nums): m = 10**9 + 7 inv = [0, 1] for i in range(2, n + 1): inv.append(m - m // i * inv[m % i] % m) comb_count = 1 res = 0 for pick in range(k - 1, n): res += (nums[pick] - nums[n - 1 - pick]) * comb_count % m res %= m comb_count = comb_count * (pick + 1) % m * inv[pick + 2 - k] % m return res n = 4 k = 3 nums = [5, 7, 9, 11] print(solve(n, k, nums))
Input
4, 3, [5, 7, 9, 11]
Output
20
69 Views
