找到大小为 2*N 的非递减数组 brr[],使得每个 arr[i] 等于 brr[i] 和 brr[2*n – i +1] 的总和
给定一个大小为N的数组arr[] ,任务是找到另一个大小为2*N的数组brr[] ,使得它不递减,并且对于从1到N的每个第 i个arr[i] = brr[i] + brr[2*n – i +1]。
例子:
Input: n = 2, arr[] = { 5, 6 }
Output: 0 1 5 5
Explanation: For i =1, arr[1] = 5, brr[1]+brr[2*2-1+1] = 5, so both are equal, For i =2, arr[2] = 6, brr[2]+brr[2*2-2+1] = 6, so both are equal.
Input: n = 3, arr[] = { 2, 1, 2 }
Output: 0 0 1 1 1 2
方法:数组brr[]的个数会成对恢复(brr[1], brr[2*n]), (brr[2], brr[2*n-1])等等。因此,满足上述条件brr[i]+brr[2*Ni-1]==arr[i]的这些值可能存在一定的限制。让l尽可能小, r是答案中可能的最大值。最初, l=0, r=10^18并且它们被更新为l=brr[i] , r=brr[2*ni-1] 。请按照以下步骤解决问题:
- 将变量l初始化为0 ,将r初始化为INF64。
- 将N的值乘以2以保留第二个数组大小的计数。
- 定义一个函数brute(ind, l, r)其中ind是要为其填充值的数组的索引, l和r是值的范围。递归调用此函数以计算第二个数组brr[] 中每一对的值。
- 在函数brute(ind, l, r)
- 定义基本情况,即当ind的值等于第一个数组arr[] 的大小时。
- 如果是,则打印第二个数组brr[]的元素并退出函数。
- 否则,在[l, arr[ind]/2]范围内迭代并执行以下步骤。
- 如果arr[ind]-i的值小于r,则将brr[ind]的值设置为i ,并将brr[n-ind-1]的值设置为arr[ind]-i。
- 将l的值设置为i并将r设置为arr[ind]-i作为l和r 的更新值。
- 为下一个索引递归地调用相同的函数brute(ind+1, l, r) 。
下面是上述方法的实现。
C++
// C++ program for the above approach.
#include
using namespace std;
const long long INF64 = 1000000000000000000ll;
const int N = 200 * 1000 + 13;
int n;
long long arr[N], brr[N];
// Function to find the possible
// output array
void brute(int ind, long long l, long long r)
{
// Base case for the recursion
if (ind == n / 2) {
// If ind becomes half of the size
// then print the array.
for (int i = 0; i < int(n); i++)
printf("%lld ", brr[i]);
puts("");
// Exit the function.
exit(0);
}
// Iterate in the range.
for (long long i = l; i <= arr[ind] / 2; ++i)
if (arr[ind] - i <= r) {
// Put the values in the respective
// indices.
brr[ind] = i;
brr[n - ind - 1] = arr[ind] - i;
// Call the function to find values for
// other indices.
brute(ind + 1, i, arr[ind] - i);
}
}
// Driver Code
int main()
{
n = 2;
n *= 2;
arr[0] = 5;
arr[1] = 6;
brute(0, 0, INF64);
return 0;
}
Java
// Java program for the above approach
import java.io.*;
class GFG{
static int INF64 = (int)1e10;
static int N = 200 * 1000 + 13;
static int n;
static int arr[] = new int[N];
static int brr[] = new int[N];
// Function to find the possible
// output array
static void brute(int ind, int l, int r)
{
// Base case for the recursion
if (ind == n / 2)
{
// If ind becomes half of the size
// then print the array.
for(int i = 0; i < (int)n; i++)
System.out.print(brr[i] + " ");
// Exit the function.
System.exit(0);
}
// Iterate in the range.
for(int i = l; i <= arr[ind] / 2; ++i)
if (arr[ind] - i <= r)
{
// Put the values in the respective
// indices.
brr[ind] = i;
brr[n - ind - 1] = arr[ind] - i;
// Call the function to find values for
// other indices.
brute(ind + 1, i, arr[ind] - i);
}
}
// Driver code
public static void main(String[] args)
{
n = 2;
n *= 2;
arr[0] = 5;
arr[1] = 6;
brute(0, 0, INF64);
}
}
// This code is contributed by sanjoy_62
Python3
# Python 3 program for the above approach.
N = 200 * 1000 + 13
n = 0
arr = [0 for i in range(N)]
brr = [0 for i in range(N)]
import sys
# Function to find the possible
# output array
def brute(ind, l, r):
# Base case for the recursion
if (ind == n / 2):
# If ind becomes half of the size
# then print the array.
for i in range(n):
print(brr[i],end = " ")
# Exit the function.
sys.exit()
# Iterate in the range.
for i in range(l,arr[ind] // 2 +1,1):
if (arr[ind] - i <= r):
# Put the values in the respective
# indices.
brr[ind] = i
brr[n - ind - 1] = arr[ind] - i
# Call the function to find values for
# other indices.
brute(ind + 1, i, arr[ind] - i)
# Driver Code
if __name__ == '__main__':
n = 2
n *= 2
arr[0] = 5
arr[1] = 6
INF64 = 1000000000000000000
brute(0, 0, INF64)
# This code is contributed by ipg2016107.
C#
// C# program for the above approach
using System;
using System.Collections.Generic;
class GFG{
static int INF64 = (int)1e8;
static int N = 200 * 1000 + 13;
static int n;
static int[] arr = new int[N];
static int[] brr = new int[N];
// Function to find the possible
// output array
static void brute(int ind, int l, int r)
{
// Base case for the recursion
if (ind == n / 2)
{
// If ind becomes half of the size
// then print the array.
for(int i = 0; i < (int)n; i++)
Console.Write(brr[i] + " ");
// Exit the function.
System.Environment.Exit(0);
}
// Iterate in the range.
for(int i = l; i <= arr[ind] / 2; ++i)
if (arr[ind] - i <= r)
{
// Put the values in the respective
// indices.
brr[ind] = i;
brr[n - ind - 1] = arr[ind] - i;
// Call the function to find values for
// other indices.
brute(ind + 1, i, arr[ind] - i);
}
}
// Driver Code
public static void Main()
{
n = 2;
n *= 2;
arr[0] = 5;
arr[1] = 6;
brute(0, 0, INF64);
}
}
// This code is contributed by target_2.
Javascript
输出
0 1 5 5
时间复杂度: O(N)
辅助空间: O(N)