- C++ Basics
- C++ Home
- C++ Overview
- C++ Environment Setup
- C++ Basic Syntax
- C++ Comments
- C++ Data Types
- C++ Variable Types
- C++ Variable Scope
- C++ Constants/Literals
- C++ Modifier Types
- C++ Storage Classes
- C++ Operators
- C++ Loop Types
- C++ Decision Making
- C++ Functions
- C++ Numbers
- C++ Arrays
- C++ Strings
- C++ Pointers
- C++ References
- C++ Date & Time
- C++ Basic Input/Output
- C++ Data Structures

- C++ Object Oriented
- C++ Classes & Objects
- C++ Inheritance
- C++ Overloading
- C++ Polymorphism
- C++ Abstraction
- C++ Encapsulation
- C++ Interfaces

# Find the number of stair steps using C++

In this problem, we are given a number N denoting the number of bricks provided to create the stair. Our task is to *f**ind the number of stair steps*.

Using the given bricks, we need to create a stair step. Each step takes one more brick that the last step. And the first step is two bricks high. We need to find the number of such steps that can be made from bricks.

**Let’s take an example to understand the problem,**

**Input**

N = 40

**Output**

3

## Explanation

Step = 1 ; bricks required = 2; total bricks used = 2 ; bricks remaining = 38

Step = 2 ; bricks required = 3; total bricks used = 5 ; bricks remaining = 35

Step = 3 ; bricks required = 4; total bricks used = 9 ; bricks remaining = 31

Step = 4 ; bricks required = 5; total bricks used = 14 ; bricks remaining = 26

Step = 5 ; bricks required = 6; total bricks used = 20 ; bricks remaining = 20

Step = 6 ; bricks required = 7; total bricks used = 27 ; bricks remaining = 13

Step = 7 ; bricks required = 8; total bricks used = 35 ; bricks remaining = 5

No further steps can be created as 8th steps require 9 bricks and only 5 are present.

## Solution Approach

A simple solution to the problem is by using a loop, starting from 2 till the number of bricks used surpasses N and then return the last step’s count.

This solution is good but the time complexity is of the order N. And a better approach can be made to find the solution using the sum formula and binary search.

We have X which is the total count of bricks to be used which is always created than (n*(n+1)) /2 as we have the sum of all bricks required. In this case, we have a solution from either of two values which is found from mid and mid - 1.

## Example

Program to illustrate the working of our solution

#include <iostream> using namespace std; int findStairCount(int T){ int low = 1; int high = T/2; while (low <= high) { int mid = (low + high) / 2; if ((mid * (mid + 1)) == T) return mid; if (mid > 0 && (mid * (mid + 1)) > T && (mid * (mid - 1)) <= T) return mid - 1; if ((mid * (mid + 1)) > T) high = mid - 1; else low = mid + 1; } return -1; } int main(){ int N = 60; int stepCount = findStairCount(2*N); if (stepCount != -1) stepCount--; cout<<"The number of stair steps that can be made is "<<stepCount; return 0; }

## Output

The number of stair steps that can be made is 9

- Related Articles
- How to find the minimum number of steps needed by knight to reach the destination using C#?
- Find the minimum number of steps to reach M from N in C++
- Program to find number of optimal steps needed to reach destination by baby and giant steps in Python
- Program to find minimum number of steps required to catch the opponent in C++
- Count ways to reach the n’th stair
- Program to find number of steps to solve 8-puzzle in python
- Program to create one triangle stair by using stars in Python
- Program to find number of minimum steps to reach last index in Python
- Find the number of zeroes using C++
- Count ways to reach the nth stair using step 1, 2 or 3 in C++
- What are the steps of key generation using RSA algorithm?
- Find the Number of Stopping Stations using C++
- Program to find number of steps required to change one word to another in Python
- C++ program to find minimum number of steps needed to move from start to end
- Find the slope of the given number using C++