给定两个数字A和K ,任务是找到第K个最小的正整数B,使得A + B = A | B ,其中|表示按位OR运算符。
例子:
Input: A = 10, K = 3
Output: 5
Explanation:
K = 1, 10 + 1 = 10 | 1 = 11
K = 2, 10 + 4 = 10 | 4 = 14
K = 3, 10 + 5 = 10 | 5 = 15
Input: A = 1, B = 1
Output: 2
方法:
- 当且仅当B在所有位置A都为1的所有位置都为0时,B才是给定方程的解(以二进制表示)。
- 因此,我们需要确定A的位置为0的B的位。让我们假设,如果A = 10100001,则B的最后八位必须为0_0____0,其中_表示0或1。用_或0替换所有_。 1给我们一个解决方案。
- 通过用数字k的二进制表示形式的数字替换y中的所有_,将接收第k个最小的数字。
下面是上述方法的实现:
C++
// C++ program for the
// above approach
#include
using namespace std;
// Function to find k'th
// smallest number such that
// A + B = A | B
long long kthSmallest(long long a, long long k)
{
// res will store
// final answer
long long res = 0;
long long j = 0;
for (long long i = 0; i < 32; i++) {
// Skip when j'th position
// has 1 in binary representation
// as in res, j'th position will be 0.
while (j < 32 && (a & (1 << j))) {
// j'th bit is set
j++;
}
// If i'th bit of k is 1
// and i'th bit of j is 0
// then set i'th bit in res.
if (k & (1 << i)) {
res |= (1LL << j);
}
// Proceed to next bit
j++;
}
return res;
}
// Driver Code
int main()
{
long long a = 5, k = 3;
cout << kthSmallest(a, k) << "\n";
return 0;
}
Python3
# Python3 program for the above approach
# Function to find k'th
# smallest number such that
# A + B = A | B
def kthSmallest(a, k):
# res will store
# final answer
res = 0
j = 0
for i in range(32):
# Skip when j'th position
# has 1 in binary representation
# as in res, j'th position will be 0.
while (j < 32 and (a & (1 << j))):
# j'th bit is set
j += 1
# If i'th bit of k is 1
# and i'th bit of j is 0
# then set i'th bit in res.
if (k & (1 << i)):
res |= (1 << j)
# Proceed to next bit
j += 1
return res
# Driver Code
a = 5
k = 3
print(kthSmallest(a, k))
# This code is contributed by himanshu77
输出:
10
时间复杂度: O(log(n))