

- Trending Categories
Data Structure
Networking
RDBMS
Operating System
Java
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
C++ Program to Find the Number of Ways to Write a Number as the Sum of Numbers Smaller than Itself
In this program we will count the number of ways one number can be represented by sum of numbers smaller than itself. This program will count the partition of given numbers. We take a number n as input, then starting from a number break it by removing 1 at a time. If the new partition is generated, increase the counter.
Algorithm
partitionCount(n)
Input : The number n
Output : The number of partitions
Begin Create array p of size n k := 0 count := -1 put n as the first element of array p Repeat the following steps, do increase count by 1 rem := 0 while k >= 0 and p[k] = 1, do rem := rem + p[k] decrease k by 1 done if k < 0, then return count p[k] := p[k] – 1 rem := rem + 1 while rem >= p[k], do p[k+1] := p[k] rem := rem - p[k] increase k by 1 done p[k+1] := rem increase k by 1 done End
Example Code
#include<iostream> using namespace std; int partitionCount(int n){ //used to count all possible partitions int p[n], k = 0, count = -1; p[k] = n; //add n as the first element of array while(true) { //repeat untill all elements are turned to 1 count++; int rem = 0; while (k >= 0 && p[k] == 1){ // Move the pointer to the correct index where p[k] > 1. rem += p[k]; k--; } if (k < 0) // If k < 0 then the all the element are broken down to 1. return count; //otherwise decrease the value by 1, and increase rem p[k]--; rem++; while (rem > p[k]) { // repeat until the number of 1's are greater than the value at k index. p[k+1] = p[k]; rem -= p[k]; // Decrease the rem_val value. k++; } p[k+1] = rem; // Assign remaining value to the index next to k. k++; } } main() { int n, c; cout<<"Enter number for partition counting: "; cin>>n; if (n <= 0) { //n must be greater than or equal to 1 cout<<"Invalid value of n"; exit(1); } c = partitionCount(n); cout<<"The number of partitions: "<<c; }
Output
Enter number for partition counting: 7 The number of partitions: 14
- Related Questions & Answers
- Numbers smaller than the current number JavaScript
- Count ways to express a number as sum of consecutive numbers in C++
- Write a Golang program to find the sum of digits for a given number
- Program to find number of ways we can get a number which is sum of nth power of unique numbers in Python
- Count ways to express a number as sum of powers in C++
- C Program to Find the minimum sum of factors of a number?
- Program to find number of ways where square of number is equal to product of two numbers in Python
- Counting How Many Numbers Are Smaller Than the Current Number in JavaScript
- C# program to find the sum of digits of a number using Recursion
- C program for a number to be expressed as a sum of two prime numbers.
- Represent a number as a Sum of Maximum Possible Number of Prime Numbers in C++
- What are Delannoy Numbers? Write a program in C++ to find the Delannoy number
- Find the Number of Ways to Pair People using C++
- Program to find number of ways to split a string in Python
- Write a Golang program to find the factorial of a given number (Using Recursion)
Advertisements