uva 1594 Ducci Sequence <queue,map>

Ducci Sequence

Description

A Ducci sequence is a sequence of n-tuples of integers. Given an n-tuple of integers (a1, a2, ... , an), the next n-tuple in the sequence is formed by taking the absolute differences of neighboring integers:

[align=CENTER]( a1, a2, ... , an) --- (| a1 - a2|,| a2 - a3|, ... ,| an - a1|)[/align]

Ducci sequences either reach a tuple of zeros or fall into a periodic loop. For example, the 4-tuple sequence starting with 8,11,2,7 takes 5 steps to reach the zeros tuple:

[align=CENTER](8, 11, 2, 7) --- (3, 9, 5, 1)--- (6, 4, 4, 2) --- (2, 0, 2, 4) --- (2, 2, 2, 2) --- (0, 0, 0, 0).[/align]

The 5-tuple sequence starting with 4,2,0,2,0 enters a loop after 2 steps:

[align=CENTER](4, 2, 0, 2, 0) --- (2, 2, 2, 2, 4) --- ( 0, 0, 0, 2, 2) --- (0, 0, 2, 0, 2) --- (0, 2, 2, 2, 2) --- (2, 0, 0, 0, 2) ---[/align]

[align=CENTER](2, 0, 0, 2, 0) --- (2, 0, 2, 2, 2) --- (2, 2, 0, 0, 0) --- (0, 2, 0, 0, 2) --- (2, 2, 0, 2, 2) --- (0, 2, 2, 0, 0) ---[/align]

[align=CENTER](2, 0, 2, 0, 0) --- (2, 2, 2, 0, 2) --- (0, 0, 2, 2, 0) --- (0, 2, 0, 2, 0) --- (2, 2, 2, 2, 0) --- ( 0, 0, 0, 2, 2) --- ... [/align]

Given an n-tuple of integers, write a program to decide if the sequence is reaching to a zeros tuple or a periodic loop.

Input

Your program is to read the input from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. Each test case starts with a line containing an integer n(3

n

15), which represents the size of a tuple in the Ducci sequences. In the following line, n integers are given which represents the n-tuple of integers. The range of integers are from 0 to 1,000. You may assume that the maximum number of steps of a Ducci sequence reaching zeros tuple or making a loop does not exceed 1,000.

Output

Your program is to write to standard output. Print exactly one line for each test case. Print `LOOP' if the Ducci sequence falls into a periodic loop, print `ZERO' if the Ducci sequence reaches to a zeros tuple.

The following shows sample input and output for four test cases.

Sample Input

4
4
8 11 2 7
5
4 2 0 2 0
7
0 0 0 0 0 0 0
6
1 2 3 1 2 3

Sample Output

ZERO
LOOP
ZERO
LOOP

开始想着用 队列 做，然后用 map 判断是否重复 ， 然而 出现问题了， 猜测应该是在map中查找重复数列 有问题，代码如下

#include <iostream>
#include <string>
#include <queue>
#include <cmath>
#include <map>            //vector判断是否重复
using namespace std;

typedef queue<int> Queue;
map<Queue,int> loop;
queue<int> ling;
int main()
{
int T;
cin >> T;
while(T--){
int n, a;
queue<int> ducci;
cin >> n;
for(int i = 0;i < n; i++)ling.push(0);
loop[ling] = 1;
for(int i = 0;i < n; i++){
cin >> a;
ducci.push(a);
}
int time = 0;
bool flag = false;
while(++time){
cout<<"----------------------------"<<endl;
cout<<time<<endl;
a = ducci.front();
cout<<a;
ducci.pop();
int start = a,t;
loop[ducci] = 1;
for(int i = 1;i < n; i++){
t = ducci.front();
cout<<"--"<<t;
ducci.pop();
ducci.push(abs(a-t));
a = t;
}
ducci.push(abs(start-t));
cout<<endl;
for(int i = 0;i < time;i++){
cout<< "i  "<<i<<endl;
if(loop[ducci]!=0){
if(i == 0)cout << "ZERO" << endl;
else cout << "LOOP" <<endl;
flag = true;
break;
}

}
if(flag)break;
}
}
// system("pause");
return 0;
}

然后 用数组做吧
用map判定老出现问题，然后就真的不会用stl做了

#include <iostream>
#include <cmath>
using namespace std;

int ducci[1000][20];

int main()
{
int T;
cin >> T;
while(T--){
int n;
cin >> n;
for(int i = 0;i < n; i++)ducci[0][i] = 0;
for(int i = 0;i < n; i++)cin >> ducci[1][i];
int time = 1;
bool flag = false;
while(++time){
//cout<<"----------------------------"<<endl;
//cout<<time<<endl;
int t;
for(int i = 0;i < n - 1; i++){
ducci[time][i] = abs(ducci[time-1][i+1] - ducci[time-1][i]);
//cout<<ducci[time][i]<<"--";
}
ducci[time][n-1] = abs(ducci[time-1][0] - ducci[time-1][n-1]);
//cout<<ducci[time][n-1]<<endl;
for(int i = 0;i < time;i++){
int flag1 = 1;
for(int j = 0;j < n;j++){
if(ducci[time][j] != ducci[i][j]){
flag1 = 0;
break;
}
}
if(flag1){
if(i == 0)cout << "ZERO" << endl;
else cout << "LOOP" <<endl;
flag = true;
break;
}

}
if(flag)break;
}
}
// system("pause");
return 0;
}

还是太不熟悉stl了
看别人的代码用stl做的

结构体 重载运算符什么的 都不熟唉

#include <cstdio>
#include <cstring>
#include <map>                      //map判断重复
#include <cmath>
#include <algorithm>
using namespace std;

struct Node{
int a[16];
int n;
void read() {
for (int i = 0; i < n; i++) {
scanf("%d", &a[i]);
}
}
void ducci() {
int tmp = a[0];
for (int i = 0; i < n-1; i++) {
a[i] = abs(a[i]-a[i+1]);
}
a[n-1] = abs(a[n-1]-tmp);
}

bool operator <(const Node &b) const {
for (int i = 0; i < n; i++) {
if (a[i] != b.a[i]) return a[i]<b.a[i];
}
return false;
}
bool iszero() {
for (int i = 0; i < n; i++) {
if (a[i] != 0) return false;
}
return true;
}
}lala;

map<Node, bool>vis;

int main() {
int t;
scanf("%d", &t);
while (t--) {
scanf("%d", &lala.n);
lala.read();
vis.clear();
vis[lala] = true;
bool isloop = false;
for (int i = 0; i < 1010; i++) {
lala.ducci();
if (vis[lala]) {
isloop = true;
break;
}
vis[lala] = true;
}

if (isloop && !lala.iszero()) puts("LOOP");
else puts("ZERO");
}
return 0;
}

还是强