Problem Description
You are given a binary array nums. A subarray of an array is good if it contains exactly one element with the value 1. Return an integer denoting the number of ways to split the array nums into good subarrays. As the number may be too large, return it modulo 10^9 + 7. A subarray is a contiguous non-empty sequence of elements within an array.
Key Insights
- A good subarray contains exactly one
1. - The number of ways to split the array depends on the positions of
1s in the array. - For each pair of
1s, the elements between them (if any) can be included in different ways to form valid splits. - The count of
0s between two1s can be used to calculate the number of ways to choose where to split.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
To solve this problem, we can iterate through the array and keep track of the indices of 1s. For each pair of consecutive 1s, we can count the number of 0s between them, which will determine how many ways we can split the array. The ways to split between two 1s can be calculated as the number of 0s plus one (i.e., count of 0s + 1). We then multiply the number of ways for each pair of 1s to get the total number of ways to split the entire array. Finally, we return the result modulo 10^9 + 7.