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confusing-number-ii.cpp
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confusing-number-ii.cpp
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// Time: O(logn)
// Space: O(logn)
class Solution {
public:
int confusingNumberII(int n) {
return totalCount(n) - validCountInLessLength(n) - validCountInFullLength(n);
}
private:
int totalCount(int n) { // count all numbers in the pattern of [01689]{1,len(n)} in the range of [1, n]
const auto& s = to_string(n);
int total = 0;
int p = pow(lookup.size(), s.length() - 1);
for (int i = 0; i <= s.length(); ++i, p /= lookup.size()) {
if (i == s.length()) {
++total;
break;
}
int smaller = 0;
for (const auto& kvp : lookup) {
smaller += int(kvp.first < s[i]);
}
total += smaller * p;
if (!lookup.count(s[i])) {
break;
}
}
return total - 1; // exclude 0
}
int validCountInLessLength(int n) { // count unconfusing numbers in the pattern of [01689]{1,len(n)-1} in the range of [1, n]
const auto& s = to_string(n);
int valid = 0;
int total = centers.size();
for (int i = 1; i < s.length(); i += 2) { // count unconfusing numbers for each odd length less than s
if (i == 1) {
valid += accumulate(cbegin(centers), cend(centers), 0,
[](const auto& total, const auto& kvp) {
return total + (kvp.first != '0');
});
} else {
valid += total * (lookup.size() - 1);
total *= lookup.size();
}
}
total = 1;
for (int i = 2; i < s.length(); i += 2) { // count unconfusing numbers for each even length less than s
valid += total * (lookup.size() - 1);
total *= lookup.size();
}
return valid;
}
int validCountInFullLength(int n) { // count unconfusing numbers in the pattern of [01689]{len(n)} in the range of [1, n]
const auto& s = to_string(n);
const auto& half_s = s.substr(0, (s.length() + 1) / 2);
int total = 0;
const auto& choices = (s.length() % 2) ? centers : lookup;
int p = pow(lookup.size(), int(half_s.length()) - 2) * choices.size();
for (int i = 0; i < half_s.length(); ++i, p /= lookup.size()) {
if (i == half_s.length() - 1) {
for (const auto& kvp : choices) {
if (kvp.first == '0' && i == 0) {
continue;
}
total += int(kvp.first < half_s[i]);
}
if (!choices.count(half_s[i])) {
break;
}
string tmp(half_s);
for (int i = half_s.length() - 1 - (s.length() % 2); i >= 0; --i) {
tmp.push_back(lookup.at(half_s[i]));
}
if (stoull(tmp) <= n && n != 0) {
++total;
}
break;
}
int smaller = 0;
for (const auto& kvp : lookup) {
if (kvp.first == '0' && i == 0) {
continue;
}
smaller += int(kvp.first < half_s[i]);
}
total += smaller * p;
if (!lookup.count(half_s[i])) {
break;
}
}
return total;
}
const unordered_map<char, char> lookup = {{'0', '0'}, {'1', '1'}, {'6', '9'},
{'8', '8'}, {'9', '6'}};
const unordered_map<char, char> centers = {{'0', '0'}, {'1', '1'}, {'8', '8'}};
};
// Time: O(logn)
// Space: O(logn)
class Solution2 {
public:
int confusingNumberII(int n) {
return f(n) - f(0); // f(0) is always 0 and could be ignored
}
private:
int f(int n) { // count confusing numbers in the range of [0, n]
return totalCount(n) - validCountInLessLength(n) - validCountInFullLength(n);
}
int totalCount(int n) { // count all numbers in the pattern of [01689]{1,len(n)} in the range of [0, n]
const auto& s = to_string(n);
int total = 0;
int p = pow(lookup.size(), s.length() - 1);
for (int i = 0; i <= s.length(); ++i, p /= lookup.size()) {
if (i == s.length()) {
++total;
break;
}
int smaller = 0;
for (const auto& kvp : lookup) {
smaller += int(kvp.first < s[i]);
}
total += smaller * p;
if (!lookup.count(s[i])) {
break;
}
}
return total;
}
int validCountInLessLength(int n) { // count unconfusing numbers in the pattern of [01689]{1,len(n)-1} in the range of [0, n]
const auto& s = to_string(n);
int valid = 0;
int total = centers.size();
for (int i = 1; i < s.length(); i += 2) { // count unconfusing numbers for each odd length less than s
if (i == 1) {
valid += centers.size();
} else {
valid += total * (lookup.size() - 1);
total *= lookup.size();
}
}
total = 1;
for (int i = 2; i < s.length(); i += 2) { // count unconfusing numbers for each even length less than s
valid += total * (lookup.size() - 1);
total *= lookup.size();
}
return valid;
}
int validCountInFullLength(int n) { // count unconfusing numbers in the pattern of [01689]{len(n)} in the range of [0, n]
const auto& s = to_string(n);
const auto& half_s = s.substr(0, (s.length() + 1) / 2);
int total = 0;
const auto& choices = (s.length() % 2) ? centers : lookup;
int p = pow(lookup.size(), int(half_s.length()) - 2) * choices.size();
for (int i = 0; i < half_s.length(); ++i, p /= lookup.size()) {
if (i == half_s.length() - 1) {
for (const auto& kvp : choices) {
if (kvp.first == '0' && s.length() == 2) {
continue;
}
total += int(kvp.first < half_s[i]);
}
if (!choices.count(half_s[i])) {
break;
}
string tmp(half_s);
for (int i = half_s.length() - 1 - (s.length() % 2); i >= 0; --i) {
tmp.push_back(lookup.at(half_s[i]));
}
if (stoull(tmp) <= n) {
++total;
}
break;
}
int smaller = 0;
for (const auto& kvp : lookup) {
if (kvp.first == '0' && i == 0) {
continue;
}
smaller += int(kvp.first < half_s[i]);
}
total += smaller * p;
if (!lookup.count(half_s[i])) {
break;
}
}
return total;
}
const unordered_map<char, char> lookup = {{'0', '0'}, {'1', '1'}, {'6', '9'},
{'8', '8'}, {'9', '6'}};
const unordered_map<char, char> centers = {{'0', '0'}, {'1', '1'}, {'8', '8'}};
};