Leet_Code/0413_arithmitic_slices.py at master · Kcheung42/Leet_Code · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
# ------------------------------------------------------------------------------
# Question:
# ------------------------------------------------------------------------------
# tags:
'''

'''

# ------------------------------------------------------------------------------
# Solutions
# ------------------------------------------------------------------------------

import unittest
from typing import *


class SolutionLeetBrute:
    '''
    Time: O(n^3)
    Time: O(1)

    1 2 3 4 5
    s
        e
      i
    s: 0 -> n-2
    e: s+2 -> n
    i: s+1 -> e
    A[i] - A[i-1] == diff, count += 1
    '''
    def numberOfArithmeticSlices(self, A: List[int]) -> int:
        result = 0
        n = len(A)
        for s in range(n - 2):
            diff = A[s + 1] - A[s]
            for e in range(s + 2, n):
                for i in range(s + 1, e):
                    if A[i] - A[i - 1] != diff:
                        break
                else:
                    result += 1
        return result


class Solution:
    def numberOfArithmeticSlices(self, A: List[int]) -> int:
        '''
        [1 2 3 4 5 6]
         l   r     x

        sum([i for i in range(x-r+1, 1)])

        slices = 4 + 3 + 2 + 1
        1 2 3
        2 3 4
        3 4 5
        4 5 6
        1 2 3 4
        2 3 4 5
        3 4 5 6
        1 2 3 4 5
        2 3 4 5 6
        1 2 3 4 5 6

        A[i:j]

        is arithmitic: if len(A[i:j]) >= 3, diff between consecutive alement is the same

         0 1 2 3 4  5  6
        [1 3 5 7 9 10 14]
                    i j
         l
             r

         diff = 1

         from l -> i how many slices with len 3,4 -> i-l

        Arithmitic Sequences:
        A[0:3] -> diff = 2
        A[3:6] -> diff = 3
        '''

        n = len(A)

        if n < 3: return 0

        result = 0  #count of arithmitic slices
        diff = A[1] - A[0]
        l = 0
        for j in range(1, n):
            i = j-1
            delta = A[j] - A[i]
            if delta != diff:
                r = l + 2
                if r <= i:
                    result += sum([x for x in range(i - r + 1, 0, -1)])
                l = i
                diff = delta

                '''
         0 1 2 3 4
        [1 3 5 7 9 ]
                 i j
             l
               r
        1 3 5
        3 5 1
        5 7 9
        1 3 5 7
        3 5 7 9
                '''
        if l != n - 2:
            r = l + 2
            if r <= n-1:
                result += sum([x for x in range((n-1) - r + 1, 0, -1)])
        return result


# ------------------------------------------------------------------------------
# Tests
# ------------------------------------------------------------------------------


class TestSolution(unittest.TestCase):
    def test_simple(self):
        s = Solution()
        A = [1, 2, 3, 4]
        self.assertEqual(s.numberOfArithmeticSlices(A), 3)


unittest.main(verbosity=2)