79 lines
2.2 KiB
C++
79 lines
2.2 KiB
C++
// Source : https://leetcode.com/problems/number-of-different-subsequences-gcds/
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// Author : Hao Chen
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// Date : 2021-04-05
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/*****************************************************************************************************
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*
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* You are given an array nums that consists of positive integers.
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*
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* The GCD of a sequence of numbers is defined as the greatest integer that divides all the numbers in
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* the sequence evenly.
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*
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* For example, the GCD of the sequence [4,6,16] is 2.
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*
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* A subsequence of an array is a sequence that can be formed by removing some elements (possibly
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* none) of the array.
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*
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* For example, [2,5,10] is a subsequence of [1,2,1,2,4,1,5,10].
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*
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* Return the number of different GCDs among all non-empty subsequences of nums.
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*
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* Example 1:
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*
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* Input: nums = [6,10,3]
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* Output: 5
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* Explanation: The figure shows all the non-empty subsequences and their GCDs.
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* The different GCDs are 6, 10, 3, 2, and 1.
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*
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* Example 2:
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*
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* Input: nums = [5,15,40,5,6]
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* Output: 7
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*
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* Constraints:
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*
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* 1 <= nums.length <= 10^5
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* 1 <= nums[i] <= 2 * 10^5
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******************************************************************************************************/
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class Solution {
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private:
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// Euclidean algorithm
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// https://en.wikipedia.org/wiki/Euclidean_algorithm
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int gcd(int a, int b) {
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while ( b != 0 ) {
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int t = b;
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b = a % b;
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a = t;
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}
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return a;
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}
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public:
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int countDifferentSubsequenceGCDs(vector<int>& nums) {
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int len = nums.size();
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vector<int> gcds(200001, 0);
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for(int i=0; i<len; i++) {
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int n = nums[i];
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int m = sqrt(n);
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for(int g=1; g<=m; g++){
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if (n % g != 0) continue;
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int x = g, y = n/g;
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if (x != y ){
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gcds[x] = gcd(n, gcds[x]);
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gcds[y] = gcd(n, gcds[y]);
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}else {
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gcds[x] = gcd(n, gcds[x]);
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}
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}
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}
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int cnt = 0;
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for(int i=1; i<gcds.size(); i++){
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if (gcds[i]==i) cnt++;
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}
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return cnt;
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}
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};
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