---
# System prepended metadata

title: UVA 100 The 3n + 1 problem

---

# UVA 100 The 3n + 1 problem
##  題目連結 [UVA 100](https://vjudge.net/problem/UVA-100)
### 題目內容
Problems in Computer Science are often classified as belonging to a certain class of problems (e.g., NP, Unsolvable, Recursive). In this problem you will be analyzing a property of an algorithm whose classification is not known for all possible inputs.
Consider the following algorithm:
1. input n
2. print n
3. if n = 1 then STOP
4. if n is odd then n ←− 3n + 1
5. else n ←− n/2
6. GOTO 2

Given the input 22, the following sequence of numbers will be printed
22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1
### 輸入限制
The input will consist of a series of pairs of integers i and j, one pair of integers per line. All integers will be less than 10,000 and greater than 0. You should process all pairs of integers and for each pair determine the maximum cycle length over all integers between and including i and j. You can assume that no operation overflows a 32-bit integer.
### 輸出限制
For each pair of input integers i and j you should output i, j, and the maximum cycle length for integers between and including i and j. These three numbers should be separated by at least one space with all three numbers on one line and with one line of output for each line of input. The integers i and j must appear in the output in the same order in which they appeared in the input and should be followed by the maximum cycle length (on the same line).
### 解題思路
a,b分別為大數與小數，從a到b算次數，輸出最大值。
### 程式碼
```cpp=
#include<bits/stdc++.h>
using namespace std;
int main(){
    long long n,m,cot,maxx;
    while(cin>>n>>m){
        int a=min(n,m);
        int b=max(m,n);
        maxx=0;
        for(int i=a;i<=b;i++){
            cot=1;
            int t=i;
            while(true){
                if(t==1){
                    break;
                }
                if(t%2==1){
                    t=3*t+1;
                    cot++;
                }
                else{
                    t/=2;
                    cot++;
                }
            }
            maxx=max(cot,maxx);
        }
        cout<<n<<" "<<m<<" "<<maxx<<endl;
    }
}

```
## 測資
### Sample input
1 10
100 200
201 210
900 1000
### Sample output
1 10 20
100 200 125
201 210 89
900 1000 174
##  中文題目連結 [zerojudge c039](https://zerojudge.tw/ShowProblem?problemid=c039)