Given an integer, print the next smallest and next largest number that
have the same number of 1 bits in their binary representation.
Naive Solution:
For the next largest, keep adding 1 to the number until find the number that has same number of 1 bits. For the next smallest, keep decreasing 1.
boolean GetBit(int n, int index) {
return ((n & (1 << index)) > 0);
}
int SetBit(int n, int index, boolean b) {
if (b) {
return n | (1 << index);
} else {
int mask = ~(1 << index);
return n & mask;
}
}
int GetNext_NP(int n) {
if (n <= 0)
return -1;
int index = 0;
int countOnes = 0;
// Find first one.
while (!GetBit(n, index))
index++;
// Turn on next zero.
while (GetBit(n, index)) {
index++;
countOnes++;
}
n = SetBit(n, index, true);
// Turn off previous one
index--;
n = SetBit(n, index, false);
countOnes--;
// Set zeros
for (int i = index - 1; i >= countOnes; i--) {
n = SetBit(n, i, false);
}
// Set ones
for (int i = countOnes - 1; i >= 0; i--) {
n = SetBit(n, i, true);
}
return n;
}
int GetPrevious_NP(int n) {
if (n <= 0)
return -1; // Error
int index = 0;
int countZeros = 0;
// Find first zero.
while (GetBit(n, index))
index++;
// Turn off next 1.
while (!GetBit(n, index)) {
index++;
countZeros++;
}
n = SetBit(n, index, false);
// Turn on previous zero
index--;
n = SetBit(n, index, true);
countZeros--;
// Set ones
for (int i = index - 1; i >= countZeros; i--) {
n = SetBit(n, i, true);
}
// Set zeros
for (int i = countZeros - 1; i >= 0; i--) {
n = SetBit(n, i, false);
}
return n;
}
Naive Solution:
For the next largest, keep adding 1 to the number until find the number that has same number of 1 bits. For the next smallest, keep decreasing 1.
Advanced Solution:
- Traverse from right to left. Once we’ve passed a 1, turn on the next 0. We’ve now increased the number by 2^i. Yikes! Example: xxxxx011100 becomes xxxxx111100.
- Turn off the one that’s just to the right side of that. We’re now bigger by 2^i – 2^(i-1). Example: xxxxx111100 becomes xxxxx101100
- Make the number as small as possible by rearranging all the 1s to be as far right as possible: Example: xxxxx101100 becomes xxxxx100011
Code:
boolean GetBit(int n, int index) {
return ((n & (1 << index)) > 0);
}
int SetBit(int n, int index, boolean b) {
if (b) {
return n | (1 << index);
} else {
int mask = ~(1 << index);
return n & mask;
}
}
int GetNext_NP(int n) {
if (n <= 0)
return -1;
int index = 0;
int countOnes = 0;
// Find first one.
while (!GetBit(n, index))
index++;
// Turn on next zero.
while (GetBit(n, index)) {
index++;
countOnes++;
}
n = SetBit(n, index, true);
// Turn off previous one
index--;
n = SetBit(n, index, false);
countOnes--;
// Set zeros
for (int i = index - 1; i >= countOnes; i--) {
n = SetBit(n, i, false);
}
// Set ones
for (int i = countOnes - 1; i >= 0; i--) {
n = SetBit(n, i, true);
}
return n;
}
int GetPrevious_NP(int n) {
if (n <= 0)
return -1; // Error
int index = 0;
int countZeros = 0;
// Find first zero.
while (GetBit(n, index))
index++;
// Turn off next 1.
while (!GetBit(n, index)) {
index++;
countZeros++;
}
n = SetBit(n, index, false);
// Turn on previous zero
index--;
n = SetBit(n, index, true);
countZeros--;
// Set ones
for (int i = index - 1; i >= countZeros; i--) {
n = SetBit(n, i, true);
}
// Set zeros
for (int i = countZeros - 1; i >= 0; i--) {
n = SetBit(n, i, false);
}
return n;
}
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