从其所有对的给定按位异或和按位与值中找到三元组
给定六个正整数表示三重态 (a，b，c) 的所有可能对的位异或和位与，任务是找到三重态。
示例:
输入: aXORb = 30，aANDb = 0，aXORc = 10，aANDc = 20，aXORb = 20，aANDb = 10 输出: a = 10，b = 20，c = 30 T6】解释:t8】如果 a = 10，b = 20，c= 30 a ^ b = 30，a & b = 0 a ^ c = 10
输入: aXORb = 3，aANDb = 0，aXORc = 2，aANDc = 1，aXORb = 1，aANDb = 2 输出: a = 1，b = 2，c = 3
方法:想法是基于以下观察，使用它们的逐位异或和逐位与值来找到每一个可能的三元组对的和:
a + b = a ^ b + 2 * (a & b)
按照以下步骤解决问题:
- 用上面的公式求出每一对可能的三元组的和，即 (a + b，b + c，c + a) 。
- a 的值可以计算为((a+b)+(a+c)–(b+c))/2。
- b 的值可以计算为((a+b)–a)。
- c 的值可以计算为((b+ c)–b)。
- 最后，打印三元组 (a，b，c) 的值。
下面是上述方法的实现:
C++
// C++ program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to find the triplet with given
// Bitwise XOR and Bitwise AND values of all
// possible pairs of the triplet
void findNumbers(int aXORb, int aANDb, int aXORc, int aANDc,
int bXORc, int bANDc)
{
// Stores values of
// a triplet
int a, b, c;
// Stores a + b
int aSUMb;
// Stores a + c
int aSUMc;
// Stores b + c
int bSUMc;
// Calculate aSUMb
aSUMb = aXORb + aANDb * 2;
// Calculate aSUMc
aSUMc = aXORc + aANDc * 2;
// Calculate bSUMc
bSUMc = bXORc + bANDc * 2;
// Calculate a
a = (aSUMb - bSUMc + aSUMc) / 2;
// Calculate b
b = aSUMb - a;
// Calculate c
c = aSUMc - a;
// Print a
cout << "a = " << a;
// Print b
cout << ", b = " << b;
// Print c
cout << ", c = " << c;
}
// Driver Code
int main()
{
int aXORb = 30, aANDb = 0, aXORc = 20, aANDc = 10,
bXORc = 10, bANDc = 20;
findNumbers(aXORb, aANDb, aXORc, aANDc, bXORc, bANDc);
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java program to implement
// the above approach
class GFG{
// Function to find the triplet with given
// Bitwise XOR and Bitwise AND values of all
// possible pairs of the triplet
static void findNumbers(int aXORb, int aANDb,
int aXORc, int aANDc,
int bXORc, int bANDc)
{
// Stores values of
// a triplet
int a, b, c;
// Stores a + b
int aSUMb;
// Stores a + c
int aSUMc;
// Stores b + c
int bSUMc;
// Calculate aSUMb
aSUMb = aXORb + aANDb * 2;
// Calculate aSUMc
aSUMc = aXORc + aANDc * 2;
// Calculate bSUMc
bSUMc = bXORc + bANDc * 2;
// Calculate a
a = (aSUMb - bSUMc + aSUMc) / 2;
// Calculate b
b = aSUMb - a;
// Calculate c
c = aSUMc - a;
// Print a
System.out.print("a = " + a);
// Print b
System.out.print(", b = " + b);
// Print c
System.out.print(", c = " + c);
}
// Driver Code
public static void main(String[] args)
{
int aXORb = 30, aANDb = 0,
aXORc = 20, aANDc = 10,
bXORc = 10, bANDc = 20;
findNumbers(aXORb, aANDb, aXORc,
aANDc, bXORc, bANDc);
}
}
// This code is contributed by 29AjayKumar
Python 3
# Python program to implement
# the above approach
# Function to find the triplet with given
# Bitwise XOR and Bitwise AND values of all
# possible pairs of the triplet
def findNumbers(aXORb, aANDb, aXORc, aANDc, bXORc, bANDc):
# Stores values of
# a triplet
a, b, c = 0, 0, 0;
# Stores a + b
aSUMb = 0;
# Stores a + c
aSUMc = 0;
# Stores b + c
bSUMc = 0;
# Calculate aSUMb
aSUMb = aXORb + aANDb * 2;
# Calculate aSUMc
aSUMc = aXORc + aANDc * 2;
# Calculate bSUMc
bSUMc = bXORc + bANDc * 2;
# Calculate a
a = (aSUMb - bSUMc + aSUMc) // 2;
# Calculate b
b = aSUMb - a;
# Calculate c
c = aSUMc - a;
# Pra
print("a = " , a, end = "");
# Prb
print(", b = " , b, end = "");
# Prc
print(", c = " , c, end = "");
# Driver Code
if __name__ == '__main__':
aXORb = 30; aANDb = 0; aXORc = 20; aANDc = 10; bXORc = 10; bANDc = 20;
findNumbers(aXORb, aANDb, aXORc, aANDc, bXORc, bANDc);
# This code contributed by shikhasingrajput
C
// C# code for above approach
using System;
public class GFG
{
// Function to find the triplet with given
// Bitwise XOR and Bitwise AND values of all
// possible pairs of the triplet
static void findNumbers(int aXORb, int aANDb,
int aXORc, int aANDc,
int bXORc, int bANDc)
{
// Stores values of
// a triplet
int a, b, c;
// Stores a + b
int aSUMb;
// Stores a + c
int aSUMc;
// Stores b + c
int bSUMc;
// Calculate aSUMb
aSUMb = aXORb + aANDb * 2;
// Calculate aSUMc
aSUMc = aXORc + aANDc * 2;
// Calculate bSUMc
bSUMc = bXORc + bANDc * 2;
// Calculate a
a = (aSUMb - bSUMc + aSUMc) / 2;
// Calculate b
b = aSUMb - a;
// Calculate c
c = aSUMc - a;
// Print a
System.Console.Write("a = " + a);
// Print b
System.Console.Write(", b = " + b);
// Print c
System.Console.Write(", c = " + c);
}
// Driver code
static public void Main ()
{
int aXORb = 30, aANDb = 0,
aXORc = 20, aANDc = 10,
bXORc = 10, bANDc = 20;
findNumbers(aXORb, aANDb, aXORc,
aANDc, bXORc, bANDc);
}
}
// This code is contributed by offbeat.
java 描述语言
<script>
// JavaScript program to implement
// the above approach
// Function to find the triplet with given
// Bitwise XOR and Bitwise AND values of all
// possible pairs of the triplet
function findNumbers(aXORb, aANDb, aXORc, aANDc, bXORc, bANDc)
{
// Stores values of
// a triplet
let a, b, c;
// Stores a + b
let aSUMb;
// Stores a + c
let aSUMc;
// Stores b + c
let bSUMc;
// Calculate aSUMb
aSUMb = aXORb + aANDb * 2;
// Calculate aSUMc
aSUMc = aXORc + aANDc * 2;
// Calculate bSUMc
bSUMc = bXORc + bANDc * 2;
// Calculate a
a = Math.floor((aSUMb - bSUMc + aSUMc) / 2);
// Calculate b
b = aSUMb - a;
// Calculate c
c = aSUMc - a;
// Print a
document.write("a = " + a);
// Print b
document.write(", b = " + b);
// Print c
document.write(", c = " + c);
}
// Driver Code
let aXORb = 30, aANDb = 0, aXORc = 20, aANDc = 10,
bXORc = 10, bANDc = 20;
findNumbers(aXORb, aANDb, aXORc, aANDc, bXORc, bANDc);
// This code is contributed by Surbhi Tyagi.
</script>
Output:
a = 10, b = 20, c = 30
时间复杂度:O(1) T5辅助空间:** O(1)
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