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801. Minimum Swaps To Make Sequences Increasing 👍

Approach 1: 2D DP

  • Time: $O(n)$
  • Space: $O(n)$
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class Solution {
 public:
  int minSwap(vector<int>& nums1, vector<int>& nums2) {
    vector<int> keepAt(nums1.size(), INT_MAX);
    vector<int> swapAt(nums1.size(), INT_MAX);
    keepAt[0] = 0;
    swapAt[0] = 1;

    for (int i = 1; i < nums1.size(); ++i) {
      if (nums1[i] > nums1[i - 1] && nums2[i] > nums2[i - 1]) {
        keepAt[i] = keepAt[i - 1];
        swapAt[i] = swapAt[i - 1] + 1;
      }
      if (nums1[i] > nums2[i - 1] && nums2[i] > nums1[i - 1]) {
        keepAt[i] = min(keepAt[i], swapAt[i - 1]);
        swapAt[i] = min(swapAt[i], keepAt[i - 1] + 1);
      }
    }

    return min(keepAt.back(), swapAt.back());
  }
};

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class Solution {
  public int minSwap(int[] nums1, int[] nums2) {
    final int n = nums1.length;
    int[] keepAt = new int[n];
    int[] swapAt = new int[n];
    Arrays.fill(keepAt, Integer.MAX_VALUE);
    Arrays.fill(swapAt, Integer.MAX_VALUE);
    keepAt[0] = 0;
    swapAt[0] = 1;

    for (int i = 1; i < n; ++i) {
      if (nums1[i] > nums1[i - 1] && nums2[i] > nums2[i - 1]) {
        keepAt[i] = keepAt[i - 1];
        swapAt[i] = swapAt[i - 1] + 1;
      }
      if (nums1[i] > nums2[i - 1] && nums2[i] > nums1[i - 1]) {
        keepAt[i] = Math.min(keepAt[i], swapAt[i - 1]);
        swapAt[i] = Math.min(swapAt[i], keepAt[i - 1] + 1);
      }
    }

    return Math.min(keepAt[n - 1], swapAt[n - 1]);
  }
}

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class Solution:
  def minSwap(self, nums1: list[int], nums2: list[int]) -> int:
    keepAt = [math.inf] * len(nums1)
    swapAt = [math.inf] * len(nums1)
    keepAt[0] = 0
    swapAt[0] = 1

    for i in range(1, len(nums1)):
      if nums1[i] > nums1[i - 1] and nums2[i] > nums2[i - 1]:
        keepAt[i] = keepAt[i - 1]
        swapAt[i] = swapAt[i - 1] + 1
      if nums1[i] > nums2[i - 1] and nums2[i] > nums1[i - 1]:
        keepAt[i] = min(keepAt[i], swapAt[i - 1])
        swapAt[i] = min(swapAt[i], keepAt[i - 1] + 1)

    return min(keepAt[-1], swapAt[-1])

Approach 2: 1D DP

  • Time: $O(n)$
  • Space: $O(1)$
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class Solution {
 public:
  int minSwap(vector<int>& nums1, vector<int>& nums2) {
    int keepAt = 0;
    int swapAt = 1;
    int prevKeepAt = 0;
    int prevSwapAt = 1;

    for (int i = 1; i < nums1.size(); ++i) {
      keepAt = INT_MAX;
      swapAt = INT_MAX;
      if (nums1[i] > nums1[i - 1] && nums2[i] > nums2[i - 1]) {
        keepAt = prevKeepAt;
        swapAt = prevSwapAt + 1;
      }
      if (nums1[i] > nums2[i - 1] && nums2[i] > nums1[i - 1]) {
        keepAt = min(keepAt, prevSwapAt);
        swapAt = min(swapAt, prevKeepAt + 1);
      }
      prevKeepAt = keepAt;
      prevSwapAt = swapAt;
    }

    return min(keepAt, swapAt);
  }
};

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class Solution {
  public int minSwap(int[] nums1, int[] nums2) {
    int keepAt = 0;
    int swapAt = 1;
    int prevKeepAt = 0;
    int prevSwapAt = 1;

    for (int i = 1; i < nums1.length; ++i) {
      keepAt = Integer.MAX_VALUE;
      swapAt = Integer.MAX_VALUE;
      if (nums1[i] > nums1[i - 1] && nums2[i] > nums2[i - 1]) {
        keepAt = prevKeepAt;
        swapAt = prevSwapAt + 1;
      }
      if (nums1[i] > nums2[i - 1] && nums2[i] > nums1[i - 1]) {
        keepAt = Math.min(keepAt, prevSwapAt);
        swapAt = Math.min(swapAt, prevKeepAt + 1);
      }
      prevKeepAt = keepAt;
      prevSwapAt = swapAt;
    }

    return Math.min(keepAt, swapAt);
  }
}