Is Choose Numbers From Two Arrays in Range easy or hard?

Choose Numbers From Two Arrays in Range is classified as a Hard problem because the brute-force approach is exponential and the correct solution requires modeling the process as dynamic programming over sum states with careful range management.

Choose Numbers From Two Arrays in Range Python/Java solution

The solution in Python or Java typically maintains a DP array indexed by shifted sums to handle negative values. For every index i, update the next DP state by adding nums1[i] and nums2[i] to existing sums, and finally count how many sums fall within [lower, upper].

How to solve Choose Numbers From Two Arrays in Range in O(n)?

A strict O(n) solution is generally not feasible because the algorithm must track multiple possible cumulative sums at every step. The practical optimal solution is O(n * R) using dynamic programming with state compression, where R represents the bounded sum range maintained during transitions.

What is the best approach for Choose Numbers From Two Arrays in Range?

The most effective approach uses dynamic programming on cumulative sums. Track how many ways each possible sum can be formed after processing each index, then update the states by adding either nums1[i] or nums2[i]. This reduces the exponential choice tree to O(n * R) time, where R is the sum range being tracked.

Is Choose Numbers From Two Arrays in Range asked at Google/Amazon/Meta?

Problems involving dynamic programming over cumulative sums and choice at each index frequently appear in interviews at companies like Google, Amazon, and Meta. Variants of this problem test understanding of state transitions, range handling, and DP optimization techniques.

What data structure is used in Choose Numbers From Two Arrays in Range?

The main structure is a dynamic programming array (or hash map) that stores counts of ways to reach each possible cumulative sum. Prefix sums may also be used to accelerate range updates during DP transitions.

What is the time complexity of Choose Numbers From Two Arrays in Range?

The optimized dynamic programming solution runs in O(n * R) time, where n is the array length and R is the range of possible cumulative sums considered in the DP state. Space complexity is O(R) because only the current set of reachable sums must be stored.

Description Hints 3 Solution

2143. Choose Numbers From Two Arrays in Range

Hard51.4% acceptance1 companyPremium elsewhere, free here

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].
The sum of the numbers you pick from nums1 equals to the sum of the numbers you pick from nums2 (the sum is considered to be 0 if you pick no numbers from an array).

Two balanced ranges from [l₁, r₁] and [l₂, r₂] are considered to be different if at least one of the following is true:

l₁ != l₂
r₁ != r₂
nums1[i] is picked in the first range, and nums2[i] is picked in the second range or vice versa for at least one i.

Return the number of different ranges that are balanced. Since the answer may be very large, return it modulo 10⁹ + 7.

Example 1:

Input: nums1 = [1,2,5], nums2 = [2,6,3]
Output: 3
Explanation: The balanced ranges are:
- [0, 1] where we choose nums2[0], and nums1[1].
  The sum of the numbers chosen from nums1 equals the sum of the numbers chosen from nums2: 2 = 2.
- [0, 2] where we choose nums1[0], nums2[1], and nums1[2].
  The sum of the numbers chosen from nums1 equals the sum of the numbers chosen from nums2: 1 + 5 = 6.
- [0, 2] where we choose nums1[0], nums1[1], and nums2[2].
  The sum of the numbers chosen from nums1 equals the sum of the numbers chosen from nums2: 1 + 2 = 3.
Note that the second and third balanced ranges are different.
In the second balanced range, we choose nums2[1] and in the third balanced range, we choose nums1[1].

Example 2:

Input: nums1 = [0,1], nums2 = [1,0]
Output: 4
Explanation: The balanced ranges are:
- [0, 0] where we choose nums1[0].
  The sum of the numbers chosen from nums1 equals the sum of the numbers chosen from nums2: 0 = 0.
- [1, 1] where we choose nums2[1].
  The sum of the numbers chosen from nums1 equals the sum of the numbers chosen from nums2: 0 = 0.
- [0, 1] where we choose nums1[0] and nums2[1].
  The sum of the numbers chosen from nums1 equals the sum of the numbers chosen from nums2: 0 = 0.
- [0, 1] where we choose nums2[0] and nums1[1].
  The sum of the numbers chosen from nums1 equals the sum of the numbers chosen from nums2: 1 = 1.

Constraints:

n == nums1.length == nums2.length
1 <= n <= 100
0 <= nums1[i], nums2[i] <= 100

Asked at 1 company

Adobe

Topics

Array Dynamic Programming

Hints open one at a time

Hint 1

If you know the possible sums you can get for a range [l, r], how can you use this information to calculate the possible sums you can get for a range [l, r + 1]?

Hint 2

For the range [l, r], if it is possible to choose elements such that the sum of elements you picked from nums1 is x and the sum of elements you picked from nums2 is y, then (x + nums1[r + 1], y) and (x, y + nums2[r + 1]) are possible sums you can get in the range [l, r + 1].

Hint 3

How can we save the possible sums obtainable at a given index so that we can reuse this information later?

Still stuck?Read the written solution.

Open solution