Given 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
Given 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 can follow the following steps:
- Read the input values of N and S.
- Read the array A of N integers.
- Initialize X as 1, as it is the minimum possible value that divides all elements of A.
- Initialize the sum of quotients as 0.
- Iterate through each element in A. a. Calculate the quotient of the current element divided by X. b. Add the quotient to the sum of quotients.
- Check if the sum of quotients is less than or equal to S. a. If it is, then X is the minimum value that satisfies the condition. Print X and exit. b. If it is not, increment X by 1 and go back to step 5.
- If no X is found that satisfies the condition, it means that the sum of quotients will always exceed S. In this case, there is no solution.
Here is the implementation in Python:
# Step 1
N, S = map(int, input().split())
# Step 2
A = list(map(int, input().split()))
# Step 3
X = 1
# Step 4
sum_of_quotients = 0
# Step 5
for num in A:
# Step 5a
quotient = num // X
# Step 5b
sum_of_quotients += quotient
# Step 6
if sum_of_quotients <= S:
print(X)
else:
while sum_of_quotients > S:
X += 1
sum_of_quotients = 0
for num in A:
quotient = num // X
sum_of_quotients += quotient
print(X)
# Step 7
if sum_of_quotients > S:
print("No solution")
This program reads the input values, iterates through the array, calculates the sum of quotients, and checks if it satisfies the condition. If it does, it prints the minimum value of X. If not, it increments X and repeats the process until a solution is found or it determines that there is no solution.
Similar Questions
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