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Count Numbers with Unique Digits
Bookmark
Brute Force
Combinatorial DP
Backtracking
Input
n = 3
n = 5
n = 8 (max)
n = 0 (edge)
Custom
n
=
3
n =
3
digits already seen in this number
0
1
2
3
4
5
6
7
8
9
number under test
-
count =
0
single digits
0–9
are all unique →
10
numbers
test every number below 10^n by peeling its digits off
n =
3
digits already seen in this number
0
1
2
3
4
5
6
7
8
9
number under test
-
count =
0
single digits
0–9
are all unique →
10
numbers
test every number below 10^n by peeling its digits off
n =
3
digits already seen in this number
0
1
2
3
4
5
6
7
8
9
number under test
10
count =
10
single digits
0–9
are all unique →
10
numbers
Test 10: peel its digits off from the right.
n =
3
digits already seen in this number
0
1
2
3
4
5
6
7
8
9
number under test
21
count =
21
single digits
0–9
are all unique →
10
numbers
count = 21.
n =
3
digits already seen in this number
0
1
2
3
4
5
6
7
8
9
number under test
33
count =
31
single digits
0–9
are all unique →
10
numbers
Test 33: peel its digits off from the right.
n =
3
digits already seen in this number
0
1
2
3
4
5
6
7
8
9
number under test
45
count =
41
single digits
0–9
are all unique →
10
numbers
Test 45: peel its digits off from the right.
n =
3
digits already seen in this number
0
1
2
3
4
5
6
7
8
9
number under test
56
count =
51
single digits
0–9
are all unique →
10
numbers
Digits 5, 6 are all distinct, so 56 counts.
n =
3
digits already seen in this number
0
1
2
3
4
5
6
7
8
9
number under test
68
count =
62
single digits
0–9
are all unique →
10
numbers
Test 68: peel its digits off from the right.
n =
3
digits already seen in this number
0
1
2
3
4
5
6
7
8
9
number under test
79
count =
72
single digits
0–9
are all unique →
10
numbers
Digits 7, 9 are all distinct, so 79 counts.
n =
3
digits already seen in this number
0
1
2
3
4
5
6
7
8
9
number under test
91
count =
83
single digits
0–9
are all unique →
10
numbers
Test 91: peel its digits off from the right.
n =
3
digits already seen in this number
0
1
2
3
4
5
6
7
8
9
number under test
-
count =
739
the scan ran to the end, the trace stops earlier
10 +
Done. Numbers below 10^3 with all-distinct digits = 739.
algo
master
.
io
Step:
Check every number x with 0 <= x < 10^3 and keep the ones with no repeated digit.
0 / 301
Input
n = 3
n = 5
n = 8 (max)
n = 0 (edge)
Custom
n
=
3
0 / 301
algo
master
.
io
Step:
Check every number x with 0 <= x < 10^3 and keep the ones with no repeated digit.
