Total sum of QuotientsMax. score: 40Given an array A of N integers and an integer S. Write an efficient program to find the minimum X such that X divides all the elements of A, the total sum of the quotients doesn’t exceed S. Consider integer division while dividing elements of the array.Input format:First line contains two spaced integers N and S.Second line contains N space separated integers of A.Output format:Print single integer representing X.SAMPLE INPUT 6 2710 8 8 11 14 19SAMPLE OUTPUT 3ExplanationIf N=6, S=27 and A=[10,8,8,11,14,19]If all elements are divided by 1, i.e, then the total sum of quotients of elements in A is 70, which is greater than S. So X shouldn’t be 1.If X=2, then the total sum of quotients of elements in A becomes 34, which is also greater than S.If X=3, the total sum becomes 20, which is less than S. Therefore the output is 3 because 3 is the minimum number where quotient’s sum goes less than S for the first time.Constraints:1<=N<=10^51<=A[i],S<=10^9
Question
Total sum of QuotientsMax. score: 40Given an array A of N integers and an integer S. Write an efficient program to find the minimum X such that X divides all the elements of A, the total sum of the quotients doesn’t exceed S. Consider integer division while dividing elements of the array.Input format:First line contains two spaced integers N and S.Second line contains N space separated integers of A.Output format:Print single integer representing X.SAMPLE INPUT 6 2710 8 8 11 14 19SAMPLE OUTPUT 3ExplanationIf N=6, S=27 and A=[10,8,8,11,14,19]If all elements are divided by 1, i.e, then the total sum of quotients of elements in A is 70, which is greater than S. So X shouldn’t be 1.If X=2, then the total sum of quotients of elements in A becomes 34, which is also greater than S.If X=3, the total sum becomes 20, which is less than S. Therefore the output is 3 because 3 is the minimum number where quotient’s sum goes less than S for the first time.Constraints:1<=N<=10^51<=A[i],S<=10^9
Solution
To solve this problem, we need to find the minimum value of X that divides all the elements of array A, while ensuring that the total sum of the quotients does not exceed S.
Let's start by reading the input values. The first line contains two integers N and S, representing the size of the array and the maximum sum of quotients, respectively. The second line contains N space-separated integers representing the elements of array A.
Next, we need to iterate through the array A and calculate the sum of quotients for each possible value of X. We will start with X = 2 and increment it until we find the minimum X that satisfies the given conditions.
For each value of X, we will initialize a variable sum to 0, which will store the sum of quotients. Then, we will iterate through each element of array A and calculate the quotient by dividing the element by X. We will add this quotient to the sum variable.
After calculating the sum of quotients for a particular value of X, we will check if it exceeds the maximum sum S. If it does, we will increment X and repeat the process. If it doesn't, we have found the minimum X that satisfies the conditions, and we can print it as the output.
Let's consider the given example to understand the process. We have N = 6, S = 27, and A = [10, 8, 8, 11, 14, 19].
If we start with X = 1, the sum of quotients is 70, which is greater than S. So X cannot be 1.
If we try X = 2, the sum of quotients is 34, which is still greater than S.
However, if we set X = 3, the sum of quotients becomes 20, which is less than S. Therefore, the output is 3, as it is the minimum value of X that satisfies the conditions.
The constraints for this problem are 1 <= N <= 10^5 and 1 <= A[i], S <= 10^9.
Similar Questions
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