POTD 2026-07-14 solved

src/3300-3399/3336.cpp

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+/*
+Tags
+level-hard
+array, math, dp, number-theory
+
+Problem Description
+3336. Find the Number of Subsequences With Equal GCD
+
+You are given an integer array nums.
+Your task is to find the number of pairs of non-empty subsequences (seq1, seq2) of nums that satisfy the following conditions:
+The subsequences seq1 and seq2 are disjoint, meaning no index of nums is common between them.
+The GCD of the elements of seq1 is equal to the GCD of the elements of seq2.
+Return the total number of such pairs.
+Since the answer may be very large, return it modulo 109 + 7.
+
+Example 1:
+Input: nums = [1,2,3,4]
+Output: 10
+Explanation:
+The subsequence pairs which have the GCD of their elements equal to 1 are:
+([1, 2, 3, 4], [1, 2, 3, 4])
+([1, 2, 3, 4], [1, 2, 3, 4])
+([1, 2, 3, 4], [1, 2, 3, 4])
+([1, 2, 3, 4], [1, 2, 3, 4])
+([1, 2, 3, 4], [1, 2, 3, 4])
+([1, 2, 3, 4], [1, 2, 3, 4])
+([1, 2, 3, 4], [1, 2, 3, 4])
+([1, 2, 3, 4], [1, 2, 3, 4])
+([1, 2, 3, 4], [1, 2, 3, 4])
+([1, 2, 3, 4], [1, 2, 3, 4])
+
+Example 2:
+Input: nums = [10,20,30]
+Output: 2
+Explanation:
+The subsequence pairs which have the GCD of their elements equal to 10 are:
+([10, 20, 30], [10, 20, 30])
+([10, 20, 30], [10, 20, 30])
+
+Example 3:
+Input: nums = [1,1,1,1]
+Output: 50
+
+Constraints:
+1 <= nums.length <= 200
+1 <= nums[i] <= 200
+*/
+
+#include <iostream>
+#include <vector>
+#include <string>
+#include <algorithm>
+#include <numeric>
+#include <cmath>
+#include <queue>
+#include <stack>
+#include <set>
+#include <map>
+#include <unordered_map>
+#include <unordered_set>
+#include <sstream>
+#include <limits>
+#include <iomanip>
+#include <functional>
+#include <cstring>
+#include <climits>
+#include "../core/core.h"
+using namespace std;
+
+class Solution
+{
+private:
+	static constexpr int mod = 1e9 + 7;
+public:
+	int subsequencePairCount(vector<int>& nums)
+	{
+		int m = *max_element(nums.begin(), nums.end());
+
+		vector<vector<int>> dp(m + 1, vector<int>(m + 1));
+		dp[0][0] = 1;
+
+		for (int num : nums)
+		{
+			vector<vector<int>> ndp(m + 1, vector<int>(m + 1));
+			for (int j = 0; j <= m; j++)
+			{
+				int divisor1 = gcd(j, num);
+				for (int k = 0; k <= m; k++)
+				{
+					int val = dp[j][k];
+					if (val == 0)
+					{
+						continue;
+					}
+
+					int divisor2 = gcd(k, num);
+					ndp[j][k] = (ndp[j][k] + val) % mod;
+					ndp[divisor1][k] = (ndp[divisor1][k] + val) % mod;
+					ndp[j][divisor2] = (ndp[j][divisor2] + val) % mod;
+				}
+			}
+			dp.swap(ndp);
+		}
+
+		int result = 0;
+		for (int j = 1; j <= m; j++)
+		{
+			result = (result + dp[j][j]) % mod;
+		}
+
+		return result;
+	}
+};
+
+int main()
+{
+	int n;
+	cin >> n;
+	vector<int> nums(n, 0);
+	Solution sol;
+	for (int i = 0; i < n; i++)
+	{
+		cin >> nums[i];
+	}
+	int result = sol.subsequencePairCount(nums);
+	cout << result << "\n";
+	return 0;
+}

tests/3300-3399/3336.txt

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+Test Case 1:
+Input:
+4
+1 2 3 4
+Output:
+10
+
+Test Case 2:
+Input:
+3
+10 20 30
+Output:
+2
+
+Test Case 2:
+Input:
+4
+1 1 1 1
+Output:
+50