Minimum steps to reach N from 1 by multiplying each step by 2, 3, 4 or 5

• Last Updated : 16 Nov, 2021

Given an integer N, the task is to find the minimum number of steps to reach the number N from 1 by multiplying each step by 2, 3, 4 or 5. If it is not possible to reach N, print -1.
Examples:

Input: N = 10
Output:
Explanation:
Initial number = 1
Step 1: Multiply it by 2, Current Number = 2
Step 2: Multiply it by 5, Current Number = 10
Therefore, Minimum 2 steps required to reach 10.
Input: N = 13
Output: -1
Explanation:
There is no way reach 13 using any given operations

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Approach: The idea is to use Greedy Alogorithm to choose the operation that should be performed at each step and perform the operations in the reverse manner that is instead of going from 1 to N, find the operations required to reach N to 1. Below is the illustration of the steps:

• Apply the operations below until N is greater than 1.
• Check if N is divisible by 5, Then increase steps by 1 and reduce N to N/5
• Else, check if N is divisible by 4, Then increase steps by 1 and reduce N to N/4
• Else, check if N is divisible by 3, Then increase steps by 1 and reduce N to N/3
• Else, check if N is divisible by 2, Then increase steps by 1, and reduce N to N/2
• If at any step no operation can be applied then there is no possible set of operations to reach N from 1. Therefore, return -1.

Below is the implementation of the above approach:

C++

 // C++ implementation to find// minimum number of steps// to reach N from 1 #include  using namespace std; // Function to find a minimum number// of steps to reach N from 1int Minsteps(int n){    int ans = 0;     // Check until N is greater    // than 1 and operations    // can be applied    while (n > 1) {         // Condition to choose the        // operations greedily        if (n % 5 == 0) {             ans++;            n = n / 5;            continue;        }        else if (n % 4 == 0) {            ans++;            n = n / 4;            continue;        }        else if (n % 3 == 0) {            ans++;            n = n / 3;            continue;        }        else if (n % 2 == 0) {            ans++;            n = n / 2;            continue;        }        return -1;    }    return ans;} // Driver codeint main(){    int n = 10;    cout << Minsteps(n);    return 0;}

Java

 // Java implementation to find// minimum number of steps// to reach N from 1 import java.util.*; class GFG{ // Function to find a minimum number// of steps to reach N from 1static int Minsteps(int n){    int ans = 0;     // Check until N is greater    // than 1 and operations    // can be applied    while (n > 1)    {                 // Condition to choose the        // operations greedily        if (n % 5 == 0)        {            ans++;            n = n / 5;            continue;        }        else if (n % 4 == 0)        {            ans++;            n = n / 4;            continue;        }        else if (n % 3 == 0)        {            ans++;            n = n / 3;            continue;        }        else if (n % 2 == 0)        {            ans++;            n = n / 2;            continue;        }        return -1;    }    return ans;} // Driver codepublic static void main(String[] args){    int n = 10;    System.out.print(Minsteps(n));}} // This code is contributed by Amit Katiyar

Python3

 # Python3 implementation to find# minimum number of steps# to reach N from 1 # Function to find a minimum number# of steps to reach N from 1def Minsteps(n):     ans = 0     # Check until N is greater    # than 1 and operations    # can be applied    while (n > 1):         # Condition to choose the        # operations greedily        if (n % 5 == 0):            ans = ans + 1            n = n / 5            continue         elif (n % 4 == 0):            ans = ans + 1            n = n / 4            continue         elif (n % 3 == 0):            ans = ans + 1            n = n / 3            continue         elif (n % 2 == 0):            ans = ans + 1            n = n / 2            continue         return -1     return ans # Driver coden = 10print(Minsteps(n)) # This code is contributed by Pratik

C#

 // C# implementation to find// minimum number of steps// to reach N from 1using System; class GFG{ // Function to find a minimum number// of steps to reach N from 1static int Minsteps(int n){    int ans = 0;     // Check until N is greater    // than 1 and operations    // can be applied    while (n > 1)    {                 // Condition to choose the        // operations greedily        if (n % 5 == 0)        {            ans++;            n = n / 5;            continue;        }        else if (n % 4 == 0)        {            ans++;            n = n / 4;            continue;        }        else if (n % 3 == 0)        {            ans++;            n = n / 3;            continue;        }        else if (n % 2 == 0)        {            ans++;            n = n / 2;            continue;        }        return -1;    }    return ans;} // Driver codepublic static void Main(){    int n = 10;    Console.Write(Minsteps(n));}} // This code is contributed by rutvik_56

Javascript


Output:
2

Time Complexity: O(log n)

Auxiliary Space: O(1)

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