Problem Link - Fruit Basket in Combinatorics
Problem Statement:
Chef is preparing a fruit basket for Cheffina, he has N varieties of fruits. In particular, he has A_i number of fruits of the i-th varity.
In how many ways he can prepare the fruit basket?
Chef can add no more than A_i number of the i-th fruit in the basket. Chef can prepare an empty fruit basket.
Approach:
- Understanding the Combinations:
- For each variety of fruit i, Chef can choose from 0 to A[i] fruits. This gives A[i]+1 options (including choosing none).
- The total number of ways to prepare the fruit basket is the product of choices for all fruit varieties.
- Formula:
- Total Ways = ∏(A[i]+1) from i=1 to N. Here, N is the number of fruit varieties, and A[i] is the number of fruits of the i-th variety.
- Since the result can be very large, we will take the result modulo 10^9 + 7.
Complexity:
- Time Complexity:
O(N)For traversing the array once. - Space Complexity:
O(1)No extra space required.