# 801. Minimum Swaps To Make Sequences Increasing

We have two integer sequences `A` and `B` of the same non-zero length.

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.

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]`.)

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.

``````Example:
Input: A = [1,3,5,4], B = [1,2,3,7]
Output: 1
Explanation:
Swap A[3] and B[3].  Then the sequences are:
A = [1, 3, 5, 7] and B = [1, 2, 3, 4]
which are both strictly increasing.
``````

Note:

• `A, B` are arrays with the same length, and that length will be in the range `[1, 1000]`.
• `A[i], B[i]` are integer values in the range `[0, 2000]`.

0   4   4   5

0   1   6   8

0   4   4   7

0   1   6   5

``````class Solution {
public:
int minSwap(vector<int>& A, vector<int>& B) {
int n = A.size();
vector<int> swap(n, n), noSwap(n, n);
swap[0] = 1; noSwap[0] = 0;
for (int i = 1; i < n; ++i) {
if (A[i] > A[i - 1] && B[i] > B[i - 1]) {
swap[i] = swap[i - 1] + 1;
noSwap[i] = noSwap[i - 1];
}
if (A[i] > B[i - 1] && B[i] > A[i - 1]) {
swap[i] = min(swap[i], noSwap[i - 1] + 1);
noSwap[i] = min(noSwap[i], swap[i - 1]);
}
}
return min(swap[n - 1], noSwap[n - 1]);
}
};
``````

``````class Solution {
public:
int minSwap(vector<int>& A, vector<int>& B) {
int n1 = 0, s1 = 1, n = A.size();
for (int i = 1; i < n; ++i) {
int n2 = INT_MAX, s2 = INT_MAX;
if (A[i - 1] < A[i] && B[i - 1] < B[i]) {
n2 = min(n2, n1);
s2 = min(s2, s1 + 1);
}
if (A[i - 1] < B[i] && B[i - 1] < A[i]) {
n2 = min(n2, s1);
s2 = min(s2, n1 + 1);
}
n1 = n2;
s1 = s2;
}
return min(n1, s1);
}
};
``````

Github 同步地址：

https://github.com/grandyang/leetcode/issues/801

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https://leetcode.com/problems/minimum-swaps-to-make-sequences-increasing/solution/

https://leetcode.com/problems/minimum-swaps-to-make-sequences-increasing/discuss/119835/Java-O(n)-DP-Solution

https://leetcode.com/problems/minimum-swaps-to-make-sequences-increasing/discuss/120516/C++-solution-with-explanation

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