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refactor 357
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  • src/main/java/com/fishercoder/solutions

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src/main/java/com/fishercoder/solutions/_357.java

Lines changed: 27 additions & 24 deletions
Original file line numberDiff line numberDiff line change
@@ -19,31 +19,34 @@ Let f(k) = count of numbers with unique digits with length equals k.
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*/
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public class _357 {
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/**reference: https://discuss.leetcode.com/topic/47983/java-dp-o-1-solution
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* Following the hint. Let f(n) = count of number with unique digits of length n.
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f(1) = 10. (0, 1, 2, 3, ...., 9)
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f(2) = 9 * 9. Because for each number i from 1, ..., 9, we can pick j to form a 2-digit number ij and there are 9 numbers that are different from i for j to choose from.
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f(3) = f(2) * 8 = 9 * 9 * 8. Because for each number with unique digits of length 2, say ij, we can pick k to form a 3 digit number ijk and there are 8 numbers that are different from i and j for k to choose from.
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Similarly f(4) = f(3) * 7 = 9 * 9 * 8 * 7....
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...
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f(10) = 9 * 9 * 8 * 7 * 6 * ... * 1
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f(11) = 0 = f(12) = f(13)....
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any number with length > 10 couldn't be unique digits number.
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The problem is asking for numbers from 0 to 10^n. Hence return f(1) + f(2) + .. + f(n)
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As @4acreg suggests, There are only 11 different ans. You can create a lookup table for it. This problem is O(1) in essence.*/
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public int countNumbersWithUniqueDigits(int n) {
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if (n == 0) {
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return 1;
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public static class Solution1 {
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/**
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* reference: https://discuss.leetcode.com/topic/47983/java-dp-o-1-solution Following the hint.
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* Let f(n) = count of number with unique digits of length n. f(1) = 10. (0, 1, 2, 3, ...., 9)
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* f(2) = 9 * 9. Because for each number i from 1, ..., 9, we can pick j to form a 2-digit
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* number ij and there are 9 numbers that are different from i for j to choose from. f(3) = f(2)
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* * 8 = 9 * 9 * 8. Because for each number with unique digits of length 2, say ij, we can pick
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* k to form a 3 digit number ijk and there are 8 numbers that are different from i and j for k
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* to choose from. Similarly f(4) = f(3) * 7 = 9 * 9 * 8 * 7.... ... f(10) = 9 * 9 * 8 * 7 * 6 *
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* ... * 1 f(11) = 0 = f(12) = f(13).... any number with length > 10 couldn't be unique digits
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* number. The problem is asking for numbers from 0 to 10^n. Hence return f(1) + f(2) + .. +
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* f(n) As @4acreg suggests, There are only 11 different ans. You can create a lookup table for
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* it. This problem is O(1) in essence.
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*/
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public int countNumbersWithUniqueDigits(int n) {
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if (n == 0) {
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return 1;
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}
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int res = 10;
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int uniqueDigits = 9;
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int availableNumber = 9;
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while (n-- > 1 && availableNumber > 0) {
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uniqueDigits = uniqueDigits * availableNumber;
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res += uniqueDigits;
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availableNumber--;
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}
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return res;
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}
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int res = 10;
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int uniqueDigits = 9;
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int availableNumber = 9;
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while (n-- > 1 && availableNumber > 0) {
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uniqueDigits = uniqueDigits * availableNumber;
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res += uniqueDigits;
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availableNumber--;
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}
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return res;
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}
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}

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