You are given two integer arrays of the same length nums1 and nums2. In one operation, you are allowed to swap nums1[i] with nums2[i].
nums1 = [1,2,3,8], and nums2 = [5,6,7,4], you can swap the element at i = 3 to obtain nums1 = [1,2,3,4] and nums2 = [5,6,7,8].Return the minimum number of needed operations to make nums1 and nums2 strictly increasing. The test cases are generated so that the given input always makes it possible.
An array arr is strictly increasing if and only if arr[0] < arr[1] < arr[2] < ... < arr[arr.length - 1].
Example 1:
Input: nums1 = [1,3,5,4], nums2 = [1,2,3,7] Output: 1 Explanation: Swap nums1[3] and nums2[3]. Then the sequences are: nums1 = [1, 3, 5, 7] and nums2 = [1, 2, 3, 4] which are both strictly increasing.
Example 2:
Input: nums1 = [0,3,5,8,9], nums2 = [2,1,4,6,9] Output: 1
Constraints:
2 <= nums1.length <= 105nums2.length == nums1.length0 <= nums1[i], nums2[i] <= 2 * 105#801 Minimum Swaps To Make Sequences Increasing asks you to transform two arrays so that both remain strictly increasing while minimizing the number of swaps at the same indices. A key observation is that at each index you have two choices: keep the elements as they are or swap them. This naturally leads to a dynamic programming approach.
Maintain two states for each index: the minimum swaps if you keep the current pair unchanged, and the minimum swaps if you swap the elements at that index. For each step, check whether the current elements maintain the increasing property with the previous elements in both swapped and non-swapped scenarios. Based on these conditions, update the two states accordingly.
This approach efficiently tracks the optimal decision at every step without recomputing previous states. With careful state transitions, the algorithm runs in O(n) time and can be optimized to O(1) space by only storing the previous state.
| Approach | Time Complexity | Space Complexity |
|---|---|---|
| Dynamic Programming with Swap/Keep States | O(n) | O(1) optimized (O(n) if full DP arrays are used) |
NeetCodeIO
Watch expert explanations and walkthroughs
Practice problems asked by these companies to ace your technical interviews.
Explore More ProblemsJot down your thoughts, approach, and key learnings
Yes, this problem reflects common interview themes like dynamic programming and state transitions. Variants of this question are frequently asked in interviews at top tech companies to test optimization and reasoning skills.
The problem primarily relies on dynamic programming with two variables or small arrays to track states. No complex data structures are required, making it efficient in both time and space.
The optimal approach uses dynamic programming by tracking two states at each index: keeping the elements as they are or swapping them. By comparing current and previous elements in both sequences, you update the minimum swaps needed. This results in an O(n) time solution.
A purely greedy solution is not reliable because local choices may break the increasing condition later. Dynamic programming works better because it tracks both swap and no-swap possibilities at each step.