Created
June 9, 2022 05:54
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class Solution { | |
public: | |
int permutation(int m, int n) { | |
// m number with len n | |
// m * (m - 1) * (m - 2) .. * (m - n + 1) | |
int res = 1; | |
while (n) { | |
res *= m; | |
m--; | |
n--; | |
} | |
return res; | |
} | |
int numDupDigitsAtMostN(int n) { | |
vector<int> digits; // to store each digit | |
for (int x = n + 1; x > 0; x /= 10) { | |
digits.push_back(x % 10); | |
} | |
// make it from high to low | |
// e.g., n=137 => [7, 1, 3] => [1, 3, 7] | |
reverse(digits.begin(), digits.end()); | |
// get the # of digits | |
int size = digits.size(); | |
// to count the number without duplicates | |
int res = 0; | |
// one digit to (size - 1) digits | |
// e.g, n=8759 (4 digits), ignore leading 8 here | |
// so the last 3 digits have 9 * (9 * 8) permutations | |
// the last 2 digits have 9 * (9) permutations | |
// the last 1 digits have 9 permutations | |
for (int i = 1; i < size; i++) { | |
res += 9 * permutation(9, i - 1); | |
} | |
// consider the leading digit | |
unordered_set<int> st; // to store the leading fixed one | |
// for each digit | |
for (int i = 0; i < size; i++) { | |
// i = 0 (first digit) e.g., n=8759 | the free will be | |
// 1xxx, 2xxx, ..., 7xxx | |
// i > 0 e.g., n=8759 | the free will be | |
// 80xx, 81xx, ...86xx | |
for (int j = i > 0 ? 0 : 1; j < digits[i];j++) { | |
// the current digit should not duplicated with the fixed one | |
if (st.find(j) != st.end()) continue; | |
res += permutation(9 - i, size - i - 1); | |
} | |
// if the current leading digit duplicate with previous ones => break | |
if (st.find(digits[i]) != st.end()) break; | |
// insert the current leading digit to the hash table | |
st.insert(digits[i]); | |
} | |
return n - res; | |
} | |
}; |
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