算法基础-约数-编程新知

算法基础-约数

news/2024/10/11 19:44:23/文章来源:https://blog.csdn.net/qq_65186476/article/details/142099078

试除法求约数

public class Main {public static void main(String[] args){Scanner in = new Scanner(System.in);int n = in.nextInt();while(n -- > 0) {int x = in.nextInt();List<Integer> list = new ArrayList<>();for(int i = 1; i <= x / i; i ++) {if(x % i == 0) {list.add(i);if(x / i != i)list.add(x / i);}}Collections.sort(list);for (Integer num : list) {System.out.print(num + " ");}System.out.println();}}
}

基本思想

数的乘积的约数个数

public class Main {private static final int N = 1000000007;public static void main(String[] args) {Scanner in = new Scanner(System.in);Map<Integer, Integer> map = new HashMap<>();int n = in.nextInt();while(n -- > 0) {int x = in.nextInt();for(int i = 2; i <= x / i; i ++) {while(x % i == 0) {x /= i;map.put(i,map.getOrDefault(i,0) + 1);}}if(x > 1)map.put(x,map.getOrDefault(x,0) + 1);}long res = 1;for (Integer value : map.values())res = res * (value + 1) % N;System.out.println(res);}
}

数的乘积的约数之和

public class Main {private static final int N = 1000000007;public static void main(String[] args) {Scanner in = new Scanner(System.in);Map<Integer, Integer> map = new HashMap<>();int n = in.nextInt();while(n -- > 0) {int x = in.nextInt();for(int i = 2; i <= x / i; i ++) {while(x % i == 0) {x /= i;map.put(i,map.getOrDefault(i,0) + 1);}}if(x > 1)map.put(x,map.getOrDefault(x,0) + 1);}long res = 1;for (Map.Entry<Integer, Integer> entry : map.entrySet()) {long a = entry.getKey();long b = entry.getValue();long t = 1;while(b -- > 0)t = (t * a + 1) % N;res = res * t % N;}System.out.println(res);}
}