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| 1 | +## 801. Minimum Swaps To Make Sequences Increasing |
| 2 | + |
| 3 | +### Question |
| 4 | +We have two integer sequences A and B of the same non-zero length. |
| 5 | + |
| 6 | +We are allowed to swap elements A[i] and B[i]. Note that both elements are in the same index position in their respective sequences. |
| 7 | + |
| 8 | +At the end of some number of swaps, A and B are both strictly increasing. (A sequence is strictly increasing if and only if A[0] < A[1] < A[2] < ... < A[A.length - 1].) |
| 9 | + |
| 10 | +Given A and B, return the minimum number of swaps to make both sequences strictly increasing. It is guaranteed that the given input always makes it possible. |
| 11 | + |
| 12 | +``` |
| 13 | +Example: |
| 14 | +Input: A = [1,3,5,4], B = [1,2,3,7] |
| 15 | +Output: 1 |
| 16 | +Explanation: |
| 17 | +Swap A[3] and B[3]. Then the sequences are: |
| 18 | +A = [1, 3, 5, 7] and B = [1, 2, 3, 4] |
| 19 | +which are both strictly increasing. |
| 20 | +``` |
| 21 | + |
| 22 | +Note: |
| 23 | +* A, B are arrays with the same length, and that length will be in the range [1, 1000]. |
| 24 | +* A[i], B[i] are integer values in the range [0, 2000]. |
| 25 | + |
| 26 | +### Solution |
| 27 | +* Method 1: dp |
| 28 | + * we need to maintain 2 states: keep[i] and swap[i]. i means up to index i, two arrays are strictly increasing. |
| 29 | + * keep[i] means index i is not swapped. |
| 30 | + * swap[i] means index i is swapped. |
| 31 | + * Emample: |
| 32 | + * A: [x, x, x, 1 , 4] |
| 33 | + * B: [x, x, x, 2 , 3] |
| 34 | + * Two conditions: |
| 35 | + 1. A[i - 1] < A[i] && B[i - 1] < B[i] Up to current index, two arrays have already met the requirement. |
| 36 | + * keep[i] = keep[i - 1] Nothing changed |
| 37 | + * swap[i] = swap[i - 1] + 1 both changed |
| 38 | + * A: [x, x, x, 2, 3] |
| 39 | + * B: [x, x, x, 1, 4] |
| 40 | + 2. A[i - 1] < B[i] && B[i - 1] < A[i] |
| 41 | + * keep[i] = min(keep[i], swap[i - 1]) current i is not swapped, previous one swapped |
| 42 | + * A: [x, x, x, 2, 4] |
| 43 | + * B: [x, x, x, 1, 3] |
| 44 | + * swap[i] = min(swap[i], keep[i - 1] + 1) current is swapped, swap previous pair |
| 45 | + * A: [x, x, x, 2, 4] |
| 46 | + * B: [x, x, x, 1, 3] |
| 47 | + * Initialization |
| 48 | + * keep[0] = 0 |
| 49 | + * swap[0] = 1 |
| 50 | + ```Java |
| 51 | + class Solution { |
| 52 | + public int minSwap(int[] A, int[] B) { |
| 53 | + int len = A.length; |
| 54 | + if(len <= 1) return 0; |
| 55 | + int[] keep = new int[len]; |
| 56 | + int[] swap = new int[len]; |
| 57 | + Arrays.fill(keep, Integer.MAX_VALUE); |
| 58 | + Arrays.fill(swap, Integer.MAX_VALUE); |
| 59 | + keep[0] = 0; swap[0] = 0; |
| 60 | + for(int i = 1; i < len; i++){ |
| 61 | + if(A[i - 1] < A[i] && B[i - 1] < B[i]){ |
| 62 | + keep[i] = keep[i - 1]; |
| 63 | + swap[i] = swap[i - 1] + 1; |
| 64 | + } |
| 65 | + if(A[i] > B[i - 1] && B[i] > A[i - 1]){ |
| 66 | + keep[i] = Math.min(keep[i], swap[i - 1]); |
| 67 | + swap[i] = Math.min(swap[i], keep[i - 1] + 1); |
| 68 | + } |
| 69 | + } |
| 70 | + return Math.min(keep[len - 1], swap[len - 1]); |
| 71 | + } |
| 72 | + } |
| 73 | + ``` |
| 74 | + |
| 75 | +### Reference |
| 76 | +1. [花花酱 LeetCode 801. Minimum Swaps To Make Sequences Increasing - 刷题找工作 EP183](https://www.youtube.com/watch?v=__yxFFRQAl8) |
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