Problem Link - Cutting Recipes in Number theory
Problem Statement:
The chef wants to reduce a recipe while maintaining the same ratios of ingredients, but without fractions, meaning all ingredient amounts must remain whole numbers. Given the quantities of ingredients, you need to find the smallest possible version of the recipe.
Approach:
- To maintain the same ratio between ingredients but reduce their overall quantities, the greatest common divisor of all the ingredient quantities needs to be calculated.
- By dividing each ingredient by the GCD, you ensure that the ratio of the ingredients remains intact while minimizing the total quantity.
- The GCD of all quantities is calculated, and each quantity is divided by this GCD to get the reduced ingredient values.
- See how to find gcd here:- Euclid Algorithm in Number theory
Complexity:
- Time Complexity: To compute the gcd of two numbers -
O(log(min(a,b))), We are computing the gcd of each element in the array by iterating over the array once -O(N log(max(A))) - Space Complexity:
O(1)No extra space needed.