快乐跳线序列

如果连续元素之间的差值的绝对值采用从 1 到 n-1 的所有可能值，则 n 个数字 (n < 3000) 的序列称为Jolly Jumper 。该定义意味着任何单个整数的序列都是一个快乐的跳线。

例子：

Input: 1 4 2 3
Output: True
This sequence 1 4 2 3 is Jolly Jumper because
the absolute differences are 3, 2, and 1.

Input: 1 4 2 -1 6  
Output: False
The absolute differences are 3, 2, 3, 7. 
This does not contain  all the  values from 1 
through n-1. So, this sequence is not Jolly.

Input: 11 7 4 2 1 6
Output: True

这个想法是维护一个布尔数组来存储连续元素的绝对差集。
a) 如果两个元素之间的绝对差值大于 n-1 或 0，则返回 false。
b) 如果一个绝对差重复，那么从 1 到 n-1 的所有绝对差都不存在（鸽子洞原理），返回 false。

下面是基于上述思想的实现。

C++

// Program for Jolly Jumper Sequence
#include
using namespace std;
 
// Function to check whether given sequence is
// Jolly Jumper or not
bool isJolly(int a[], int n)
{
    // Boolean vector to diffSet set of differences.
    // The vector is initialized as false.
    vector diffSet(n, false);
 
    // Traverse all array elements
    for (int i=0; i < n-1 ; i++)
    {
        // Find absolute difference between current two
        int d = abs(a[i]-a[i+1]);
 
        // If difference is out of range or repeated,
        // return false.
        if (d == 0 || d > n-1 || diffSet[d] == true)
            return false;
 
        // Set presence of d in set.
        diffSet[d] = true;
    }
 
    return true;
}
 
// Driver Code
int main()
{
    int a[] = {11, 7, 4, 2, 1, 6};
    int n = sizeof(a)/ sizeof(a[0]);
    isJolly(a, n)? cout << "Yes" : cout << "No";
    return 0;
}

Java

// Program for Jolly Jumper Sequence
import java.util.*;
 
class GFG
{
 
// Function to check whether given sequence
// is Jolly Jumper or not
static boolean isJolly(int a[], int n)
{
    // Boolean vector to diffSet set of differences.
    // The vector is initialized as false.
    boolean []diffSet = new boolean[n];
 
    // Traverse all array elements
    for (int i = 0; i < n - 1 ; i++)
    {
        // Find absolute difference
        // between current two
        int d = Math.abs(a[i] - a[i + 1]);
 
        // If difference is out of range or repeated,
        // return false.
        if (d == 0 || d > n - 1 ||
            diffSet[d] == true)
            return false;
 
        // Set presence of d in set.
        diffSet[d] = true;
    }
    return true;
}
 
// Driver Code
public static void main(String[] args)
{
    int a[] = {11, 7, 4, 2, 1, 6};
    int n = a.length;
    if(isJolly(a, n))
        System.out.println("Yes");
    else
        System.out.println("No");
}
}
 
// This code is contributed by Rajput-Ji

Python3

# Python3 Program for Jolly Jumper
# Sequence
 
# Function to check whether given
# sequence is Jolly Jumper or not
def isJolly(a, n):
 
    # Boolean vector to diffSet set
    # of differences. The vector is
    # initialized as false.
    diffSet = [False] * n
 
    # Traverse all array elements
    for i in range(0, n-1):
     
        # Find absolute difference between
        # current two
        d = abs(a[i]-a[i + 1])
 
        # If difference is out of range or
        # repeated, return false.
        if (d == 0 or d > n-1 or diffSet[d] == True):
            return False
 
        # Set presence of d in set.
        diffSet[d] = True
     
    return True
     
# Driver Code
a = [11, 7, 4, 2, 1, 6]
n = len(a)
 
print("Yes") if isJolly(a, n) else print("No")
 
# This code is contributed by
# Smitha Dinesh Semwal

C#

// Program for Jolly Jumper Sequence
using System;
 
class GFG
{
 
// Function to check whether given sequence
// is Jolly Jumper or not
static Boolean isJolly(int []a, int n)
{
    // Boolean vector to diffSet set of differences.
    // The vector is initialized as false.
    Boolean []diffSet = new Boolean[n];
 
    // Traverse all array elements
    for (int i = 0; i < n - 1 ; i++)
    {
        // Find absolute difference
        // between current two
        int d = Math.Abs(a[i] - a[i + 1]);
 
        // If difference is out of range or repeated,
        // return false.
        if (d == 0 || d > n - 1 ||
            diffSet[d] == true)
            return false;
 
        // Set presence of d in set.
        diffSet[d] = true;
    }
    return true;
}
 
// Driver Code
public static void Main(String[] args)
{
    int []a = {11, 7, 4, 2, 1, 6};
    int n = a.Length;
    if(isJolly(a, n))
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No");
}
}
 
// This code is contributed by PrinciRaj1992

Javascript

 
// Javascript program for Jolly Jumper Sequence
 
// Function to check whether given sequence is
// Jolly Jumper or not
function isJolly(a, n)
{
     
    // Boolean vector to diffSet set of
    // differences. The vector is
    // initialized as false.
    let diffSet = new Array(n).fill(false);
 
    // Traverse all array elements
    for(let i = 0; i < n - 1; i++)
    {
         
        // Find absolute difference between
        // current two
        let d = Math.abs(a[i] - a[i + 1]);
 
        // If difference is out of range or repeated,
        // return false.
        if (d == 0 || d > n - 1 ||
            diffSet[d] == true)
            return false;
 
        // Set presence of d in set.
        diffSet[d] = true;
    }
    return true;
}
 
// Driver Code
let a = [ 11, 7, 4, 2, 1, 6 ];
let n = a.length;
 
isJolly(a, n) ? document.write("Yes") :
                document.write("No");
                 
// This code is contributed by _saurabh_jaiswal
 

输出：

Yes

时间复杂度： O(n)
参考：
http://users.csc.calpoly.edu/~jdalbey/301/Labs/JollyJumpers.html