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main2.cpp
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main2.cpp
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/// Source : https://leetcode.com/problems/minimum-incompatibility/
/// Author : liuyubobobo
/// Time : 2020-12-05
#include <iostream>
#include <vector>
#include <unordered_map>
using namespace std;
/// State Compression DP
/// Using __builtin_popcount
/// Time Complexity: O(2^n + 2^n * C(n, n / k))
/// Space Complexity: O(C(n, n / k))
class Solution {
public:
int minimumIncompatibility(vector<int>& nums, int k) {
int n = nums.size();
unordered_map<int, int> table;
int sz = n / k;
for(int state = 1; state < (1 << n); state ++)
if(__builtin_popcount(state) == sz)
deal(table, nums, state);
vector<int> dp(1 << n, -1);
int res = dfs(table, (1 << n) - 1, dp);
return res == INT_MAX ? -1 : res;
}
private:
int dfs(const unordered_map<int, int>& table, int state,
vector<int>& dp){
if(state == 0) return 0;
if(dp[state] != -1) return dp[state];
int res = INT_MAX;
for(const pair<int, int>& p: table)
if((state & p.first) == p.first) {
int t = dfs(table, state - p.first, dp);
if(t != INT_MAX) res = min(res, p.second + t);
}
return dp[state] = res;
}
void deal(unordered_map<int, int>& table, const vector<int>& nums, int state){
vector<int> v;
int index = 0, x = state;
while(x){
if(x & 1) v.push_back(nums[index]);
index ++;
x >>= 1;
}
sort(v.begin(), v.end());
for(int i = 1; i < v.size(); i ++)
if(v[i - 1] == v[i]) return;
table[state] = v.back() - v[0];
}
};
int main() {
vector<int> nums1 = {1, 2, 1, 4};
cout << Solution().minimumIncompatibility(nums1, 2) << endl;
// 4
vector<int> nums2 = {6,3,8,1,3,1,2,2};
cout << Solution().minimumIncompatibility(nums2, 4) << endl;
// 6
vector<int> nums3 = {5,3,3,6,3,3};
cout << Solution().minimumIncompatibility(nums3, 3) << endl;
// -1
vector<int> nums4 = {1};
cout << Solution().minimumIncompatibility(nums4, 1) << endl;
// 0
return 0;
}