Cp---dsa/58.cpp at master · Pushpendra100/Cp---dsa · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
#include <bits/stdc++.h>
using namespace std;
// Prime Check & Prime Factorisation


int main() {

/*
 n is a prime if its divisors are only 1 and n
 n --> 1, n
*/

    // bool is_prime = true;
    // int n;
    // cin>>n;
    // for (int i = 2; i < n; i++)
    // {
    //     if(n % i == 0){
    //         is_prime = false;
    //         break;
    //     }
    // }
    // // O(n)
    // cout<<is_prime<<endl;

    // this is brute force method


      /*
        SQRT Method
        1 * 24      1 * 36
        2 * 12      2 * 18
        3 * 8       3 * 12
        4 * 6       4 * 9
        6 * 4       6 * 6
        8 * 3       9 * 4
        12 * 2      12 * 3
        24 * 1      18 * 2
                    36 * 1

        Thus we can convert the loop from O(n) to O(sqrt(n))

        if a number is divided by 2 then it is fact then it is also divided by 18
        also if a number is not divided by 2 then it is also not divided by 18

        thus we can check upto sqrt(n)
    */


    // int n;
    // cin>>n;
    // if(n ==1){
    //     cout<<0<<endl;
    //     return 0;
    // }
    // bool is_prime = true;
    // for (int i = 2; i * i <= n; i++)
    // {
    //     if(n % i == 0){
    //         is_prime = false;
    //         break;
    //     }
    // }
    // // O(n)
    // cout<<is_prime<<endl;


    /*
    Finding Prime Factorisation

    ## in any number the smallest divisor other than 1 is a prime number
        ex. for 36 = 2 is prime
                25 = 5 is a prime
                91 = 7 is a prime

    ## 36 --2--> 18 --2--> 9 --3--> 3 --3--> 1
    */

//    int n;
//    cin>>n;
//    vector<int> prime_factors;
//    for (int i = 2; i <= n; i++)
//    {
//     while (n%i ==0)
//     {
//         prime_factors.push_back(i);
//         n /= i;
//     }
//    }
//    // O(n)
//    for (int &prime : prime_factors)
//    {
//     cout<<prime<<" ";
//    }


   /*
   for a composite number
   atleast one prime factor will lie from [2, sqrt(n)]
   */


    int n;
    cin>>n;
    vector<int> prime_factors;
    for (int i = 2; i*i <= n; i++)
    {
        while (n%i ==0)
        {
            prime_factors.push_back(i);
            n /= i;
        }
    }
    if(n > 1){
        prime_factors.push_back(n);
    }
    // TC:- O(sqrt(n))
    for (int &prime : prime_factors)
    {
        cout<<prime<<" ";
    }


    return 0;
}