【leetcode】1187. Make Array Strictly Increasing

题目如下：

Given two integer arrays arr1 and arr2, return the minimum number of operations (possibly zero) needed to make arr1 strictly increasing.

In one operation, you can choose two indices 0 <= i < arr1.length and 0 <= j < arr2.length and do the assignment arr1[i] = arr2[j].

If there is no way to make arr1 strictly increasing, return -1.

Example 1:

Input: arr1 = [1,5,3,6,7], arr2 = [1,3,2,4]
Output: 1
Explanation: Replace 5 with 2, then arr1 = [1, 2, 3, 6, 7].

Example 2:

Input: arr1 = [1,5,3,6,7], arr2 = [4,3,1]
Output: 2
Explanation: Replace 5 with 3 and then replace 3 with 4. arr1 = [1, 3, 4, 6, 7].

Example 3:

Input: arr1 = [1,5,3,6,7], arr2 = [1,6,3,3]
Output: -1
Explanation: You can't make arr1 strictly increasing.

Constraints:

• 1 <= arr1.length, arr2.length <= 2000
• 0 <= arr1[i], arr2[i] <= 10^9

解题思路：如果arr1[i]个元素需要交换的话，那么一定是和arr2中大于arr1[i-1]的所有值中最小的那个交换。在这个前提下，可以利用动态规划的思想来解决这个问题。首先对arr2去重排序，记dp[i][j] = v 表示使得arr1在0~i区间递增需要的最小交换次数为v，并且最后一个交换的操作是 arr1[i] 与 arr2[j]交换,由于存在不需要交换的情况，所以令 dp[i][len(arr2)]为arr1[i]为不需要交换。因为题目要保证递增，所以只需要关注arr1[i-1]与arr[i]的值即可，而两者之间只有以下四种情况：

1. arr1[i] 与 arr1[i-1]都不交换，这个的前提是 arr1[i]  > arr1[i-1]，有 dp[i][len(arr2)] = dp[i-1][len(arr2)] ;

2. 只有arr1[i] 需要交换，对于任意的arr2[j] > arr1[i-1]，都有 dp[i][j] = dp[i-1][len(arr2)] + 1;

3. 只有arr1[i-1] 需要交换，对于任意的 arr2[j] < arr1[i]，都有 dp[i][len(arr2)]  = dp[i-1][j] + 1;

4.两者都要交换，如果i-1与j-1交换，那么i就和j交换，有dp[i][j] = dp[i-1][j-1] + 1

最后的结果只需要求出四种情况的最小值即可。

代码如下：

class Solution {
public:
    int makeArrayIncreasing(vector<int>& arr1, vector<int>& arr2) {
        set<int> st(arr2.begin(), arr2.end());
        //arr2.clear();
        arr2.assign(st.begin(), st.end());
        //arr2.sort();
        sort(arr2.begin(), arr2.end());
        vector <vector<int>> dp ;for (int i =0;i< arr1.size();i++){
            vector<int> v2 (arr2.size()+1,2001);
            dp.push_back(v2);
        }
        for (int i = 0 ;i < arr2.size();i++){
            dp[0][i] = 1;
        }
        int res = 2001;
        int LAST_INDEX = arr2.size();
        dp[0][arr2.size()] = 0;
        //int ] = 0;
        for (int i =1 ;i < arr1.size();i++){
            for (int j = 0;j < arr2.size();j++){
                //only [i] exchange
                if (arr2[j] > arr1[i-1]){
                    dp[i][j] = min(dp[i][j],dp[i-1][LAST_INDEX] + 1);
                }
                //both [i] and [i-1] exchange
                if(j > 0){
                    dp[i][j] = min(dp[i][j],dp[i-1][j-1] + 1);
                }
                //only [i-1] change
                if (arr1[i] > arr2[j]){
                    dp[i][LAST_INDEX] = min(dp[i][LAST_INDEX],dp[i-1][j]);
                }
            }
            // no exchange
            if (arr1[i] > arr1[i-1]){
                dp[i][LAST_INDEX] = min(dp[i][LAST_INDEX],dp[i-1][LAST_INDEX]);
            }
        }
        for (int i = 0; i <= arr2.size();i++){
            res = min(res,dp[arr1.size()-1][i]);
        }
        return res == 2001 ? -1 : res;
    }
};