Choose Numbers From Two Arrays in Range — LeetCode 2143 Python Solution

The problem

You are given two 0-indexed integer arrays nums1 and nums2 of length n. A range [l, r] (inclusive) where 0 <= l <= r < n is balanced if: For every i in the range [l, r], you pick either nums1[i] or nums2[i].

Example

Input

nums1 = [1,2,5], nums2 = [2,6,3]

Output

3

Explanation

The balanced ranges are:

Python solution

class Solution:
    def countSubranges(self, nums1: List[int], nums2: List[int]) -> int:
        n = len(nums1)
        s1, s2 = sum(nums1), sum(nums2)
        f = [[0] * (s1 + s2 + 1) for _ in range(n)]
        ans = 0
        mod = 10**9 + 7
        for i, (a, b) in enumerate(zip(nums1, nums2)):
            f[i][a + s2] += 1
            f[i][-b + s2] += 1
            if i:
                for j in range(s1 + s2 + 1):
                    if j >= a:
                        f[i][j] = (f[i][j] + f[i - 1][j - a]) % mod
                    if j + b < s1 + s2 + 1:
                        f[i][j] = (f[i][j] + f[i - 1][j + b]) % mod
            ans = (ans + f[i][s2]) % mod
        return ans

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 2143. Choose Numbers From Two Arrays in Range is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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