给定大小为N的数组arr [] ,范围[1,N]中的每个整数仅出现一次,除了A出现两次而B丢失了。任务是找到数字A和B。
例子:
Input: arr[] = {1, 2, 2, 3, 4}
Output:
A = 2
B = 5
Input: arr[] = {5, 3, 4, 1, 1}
Output:
A = 1
B = 2
方法:根据前N个自然数的总和,
SumN = 1 + 2 + 3 + … + N = (N * (N + 1)) / 2
And, let the sum of all the array elements be Sum. Now,
SumN = Sum – A + B
A – B = Sum – SumN …(equation 1)
根据前N个自然数的平方和
SumSqN = 12 + 22 + 32 + … + N2 = (N * (N + 1) * (2 * n + 1)) / 6
And, let the sum of the squares of all the array elements be SumSq. Now,
SumSq = SumSqN + A2 – B2
SumSq – SumSqN = (A + B) * (A – B) …(equation 2)
将等式2中等式1的(A – B)值
SumSq – SumSqN =(A + B)*(Sum – SumN)
A + B =(SumSq – SumSqN)/(Sum – SumN)…(等式3)
求解方程式1和方程式3将得出,
B = (((SumSq – SumSqN) / (Sum – SumN)) + SumN – Sum) / 2
And, A = Sum – SumN + B
下面是上述方法的实现:
C++
//C++ implementation of the approach
#include
#include
#include
using namespace std;
// Function to print the required numbers
void findNumbers(int arr[], int n)
{
// Sum of first n natural numbers
int sumN = (n * (n + 1)) / 2;
// Sum of squares of first n natural numbers
int sumSqN = (n * (n + 1) * (2 * n + 1)) / 6;
// To store the sum and sum of squares
// of the array elements
int sum = 0, sumSq = 0, i;
for (i = 0; i < n; i++) {
sum += arr[i];
sumSq = sumSq + (pow(arr[i], 2));
}
int B = (((sumSq - sumSqN) / (sum - sumN)) + sumN - sum) / 2;
int A = sum - sumN + B;
cout << "A = " ;
cout << A << endl;
cout << "B = " ;
cout << B << endl;
}
// Driver code
int main() {
int arr[] = { 1, 2, 2, 3, 4 };
int n = sizeof(arr)/sizeof(arr[0]);
findNumbers(arr, n);
return 0;
}
Java
// Java implementation of the approach
public class GFG {
// Function to print the required numbers
static void findNumbers(int arr[], int n)
{
// Sum of first n natural numbers
int sumN = (n * (n + 1)) / 2;
// Sum of squares of first n natural numbers
int sumSqN = (n * (n + 1) * (2 * n + 1)) / 6;
// To store the sum and sum of squares
// of the array elements
int sum = 0, sumSq = 0, i;
for (i = 0; i < n; i++) {
sum += arr[i];
sumSq += Math.pow(arr[i], 2);
}
int B = (((sumSq - sumSqN) / (sum - sumN)) + sumN - sum) / 2;
int A = sum - sumN + B;
System.out.println("A = " + A + "\nB = " + B);
}
// Driver code
public static void main(String[] args)
{
int arr[] = { 1, 2, 2, 3, 4 };
int n = arr.length;
findNumbers(arr, n);
}
}
Python3
# Python3 implementation of the approach
import math
# Function to print the required numbers
def findNumbers(arr, n):
# Sum of first n natural numbers
sumN = (n * (n + 1)) / 2;
# Sum of squares of first n natural numbers
sumSqN = (n * (n + 1) * (2 * n + 1)) / 6;
# To store the sum and sum of squares
# of the array elements
sum = 0;
sumSq = 0;
for i in range(0,n):
sum = sum + arr[i];
sumSq = sumSq + (math.pow(arr[i], 2));
B = (((sumSq - sumSqN) / (sum - sumN)) + sumN - sum) / 2;
A = sum - sumN + B;
print("A = ",int(A)) ;
print("B = ",int(B));
# Driver code
arr = [ 1, 2, 2, 3, 4 ];
n = len(arr);
findNumbers(arr, n);
#This code is contributed by Shivi_Aggarwal
C#
// C# implementation of the approach
using System;
public class GFG {
// Function to print the required numbers
static void findNumbers(int []arr, int n)
{
// Sum of first n natural numbers
int sumN = (n * (n + 1)) / 2;
// Sum of squares of first n natural numbers
int sumSqN = (n * (n + 1) * (2 * n + 1)) / 6;
// To store the sum and sum of squares
// of the array elements
int sum = 0, sumSq = 0, i;
for (i = 0; i < n; i++) {
sum += arr[i];
sumSq += (int)Math.Pow(arr[i], 2);
}
int B = (((sumSq - sumSqN) / (sum - sumN)) + sumN - sum) / 2;
int A = sum - sumN + B;
Console.WriteLine("A = " + A + "\nB = " + B);
}
// Driver code
public static void Main()
{
int []arr = { 1, 2, 2, 3, 4 };
int n = arr.Length;
findNumbers(arr, n);
}
}
// This code is contributed by PrinciRaj1992
PHP
Javascript
A = 2
B = 5
如果您希望与行业专家一起参加现场课程,请参阅《 Geeks现场课程》和《 Geeks现场课程美国》。