Create 3395.Subsequences-with-a-Unique-Middle-Mode-I.cpp

Author: wisdompeak

Math/3395.Subsequences-with-a-Unique-Middle-Mode-I/3395.Subsequences-with-a-Unique-Middle-Mode-I.cpp

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+using LL = long long;
+LL M = 1e9+7;
+class Solution { 
+ long long comb[1005][6]; 
+public:
+ LL getComb(int m, int n)
+ {
+ if (m<n) return 0;
+ return comb[m][n];
+ }
+
+ int subsequencesWithMiddleMode(vector<int>& nums) 
+ {
+ int n = nums.size();
+ for (int i = 0; i <= n; ++i) 
+ {
+ comb[i][0] = 1; 
+ if (i==0) continue;
+ for (int j = 1; j <= 5; ++j) 
+ {
+ comb[i][j] = comb[i - 1][j - 1] + comb[i - 1][j];
+ comb[i][j] %= M;
+ }
+ } 
+ unordered_set<int>Set(nums.begin(), nums.end());
+
+ LL ret = 0; 
+
+ unordered_map<int,int>left;
+ unordered_map<int,int>right;
+ for (int x: nums) right[x]++;
+
+ for (int i=0; i<n; i++)
+ { 
+ int a = nums[i];
+ right[a]--;
+ if (i>=1) left[nums[i-1]]++;
+
+ ret += getComb(i - left[a], 2) * getComb(n-i-1-right[a], 2) %M; 
+ ret %= M; 
+
+ for (int b: Set)
+ { 
+ if (a==b) continue; 
+ ret += getComb(left[b],2) * getComb(right[a], 1) * getComb(n-i-1-right[a]-right[b], 1) %M; 
+ ret += getComb(right[b],2) * getComb(left[a], 1) * getComb(i-left[a]-left[b], 1) %M; 
+ ret %= M;
+ }
+
+ for (int b: Set)
+ { 
+ if (a==b) continue; 
+ ret += getComb(left[b],1) * getComb(i-left[b]-left[a], 1) * getComb(right[a], 1) * getComb(right[b], 1) %M; 
+ ret += getComb(right[b],1) * getComb(n-i-1-right[b]-right[a], 1) * getComb(left[a], 1) * getComb(left[b], 1) %M;
+ ret %= M;
+ }
+
+ for (int b: Set)
+ { 
+ if (a==b) continue; 
+ ret += getComb(left[b],2) * getComb(right[a], 1) * getComb(right[b], 1) %M; 
+ ret += getComb(right[b],2) * getComb(left[a], 1) * getComb(left[b], 1) %M;
+ ret %= M;
+ }
+ }
+
+ return (getComb(n, 5) - ret + M) % M;
+ }
+};