Leetcode

Minimum Swaps To Make Sequences Increasing

May 26, 2022 by aAshish

Approach 1: 2D DP

  • Time:O(n)
  • Space:O(n)

C++

 
class Solution {
 public:
  int minSwap(vector<int>& A, vector<int>& B) {
    vector<int> keepAt(A.size(), INT_MAX);
    vector<int> swapAt(A.size(), INT_MAX);
    keepAt[0] = 0;
    swapAt[0] = 1;

    for (int i = 1; i < A.size(); ++i) {
      if (A[i] > A[i - 1] && B[i] > B[i - 1]) {
        keepAt[i] = keepAt[i - 1];
        swapAt[i] = swapAt[i - 1] + 1;
      }
      if (A[i] > B[i - 1] && B[i] > A[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());
  }
};

JAVA

 
class Solution {
  public int minSwap(int[] A, int[] B) {
    final int n = A.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 (A[i] > A[i - 1] && B[i] > B[i - 1]) {
        keepAt[i] = keepAt[i - 1];
        swapAt[i] = swapAt[i - 1] + 1;
      }
      if (A[i] > B[i - 1] && B[i] > A[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]);
  }
}

Python

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

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

C++

 
class Solution {
 public:
  int minSwap(vector<int>& A, vector<int>& B) {
    int keepAt = 0;
    int swapAt = 1;
    int prevKeepAt = 0;
    int prevSwapAt = 1;

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

    return min(keepAt, swapAt);
  }
};

JAVA

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

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

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