[Golang] Distinct powers - Problem 29 - Project Euler


Problem: [1]

Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

22=4, 23=8, 24=16, 25=32
32=9, 33=27, 34=81, 35=243
42=16, 43=64, 44=256, 45=1024
52=25, 53=125, 54=625, 55=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

Solution:

9183

Use big-number arithmetic [2] for power operations and Go built-in map [3] to count distinct items. It may takes several minutes to run the following code.

29.go | repository | view raw
  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
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
package main

import (
	"fmt"
	"strconv"
)

const MaxDigits = 201
const BASE = 10

func MakePositiveInt(s string) (n [MaxDigits]int) {
	// make n zero
	for i := 0; i < MaxDigits; i++ {
		n[i] = 0
	}

	for index, digit := range s {
		i := len(s) - index - 1
		switch digit {
		case '0':
			n[i] = 0
		case '1':
			n[i] = 1
		case '2':
			n[i] = 2
		case '3':
			n[i] = 3
		case '4':
			n[i] = 4
		case '5':
			n[i] = 5
		case '6':
			n[i] = 6
		case '7':
			n[i] = 7
		case '8':
			n[i] = 8
		case '9':
			n[i] = 9
		default:
			panic("invalid digit in number string")
		}
	}

	return
}

func AddPositiveInt(a, b [MaxDigits]int) (c [MaxDigits]int) {
	var carry, sum = 0, 0

	// make c zero
	for i := 0; i < MaxDigits; i++ {
		c[i] = 0
	}

	for i := 0; i < MaxDigits; i++ {
		sum = a[i] + b[i] + carry

		if sum >= BASE {
			carry = 1
			sum -= BASE
		} else {
			carry = 0
		}

		c[i] = sum
	}

	if carry != 0 {
		panic("overflow in addition")
	}

	return
}

func MultiplyOneDigit(a [MaxDigits]int, n int) (b [MaxDigits]int) {
	var carry = 0

	// make b zero
	for i := 0; i < MaxDigits; i++ {
		b[i] = 0
	}

	for i := 0; i < MaxDigits; i++ {
		b[i] = n * a[i]

		b[i] += carry

		if b[i] >= BASE {
			carry = b[i] / BASE
			b[i] %= BASE
		} else {
			carry = 0
		}
	}

	if carry != 0 {
		panic("overflow in multiplication")
	}

	return
}

func ShiftLeft(a [MaxDigits]int, n int) [MaxDigits]int {
	var i int

	for i = MaxDigits - 1; i >= n; i-- {
		a[i] = a[i-n]
	}
	for i >= 0 {
		a[i] = 0
		i -= 1
	}

	return a
}

func MultiplyPositiveInt(a, b [MaxDigits]int) (c [MaxDigits]int) {
	// make c zero
	for i := 0; i < MaxDigits; i++ {
		c[i] = 0
	}

	for i := 0; i < MaxDigits; i++ {
		tmp := MultiplyOneDigit(b, a[i])
		tmp = ShiftLeft(tmp, i)
		c = AddPositiveInt(c, tmp)
	}

	return
}

// a^b, b is integer and b>=2
func Power(a [MaxDigits]int, b int) (c [MaxDigits]int) {
	c = MultiplyPositiveInt(a, a)
	for i := 2; i < b; i++ {
		c = MultiplyPositiveInt(c, a)
	}
	return
}

func PositiveIntToString(a [MaxDigits]int) (s string) {
	isLeadingZero := true
	for i := MaxDigits - 1; i >= 0; i-- {
		if isLeadingZero && a[i] == 0 {
			continue
		} else {
			isLeadingZero = false
			s += strconv.Itoa(a[i])
		}
	}
	return
}

func main() {
	distinctNum := make(map[string]bool)
	for i := 2; i <= 100; i++ {
		a := MakePositiveInt(strconv.Itoa(i))
		for b := 2; b <= 100; b++ {
			c := Power(a, b)
			distinctNum[PositiveIntToString(c)] = true
		}
	}

	fmt.Println(len(distinctNum))
}

Test on:

  • Ubuntu 18.04, Go 1.11.1

References:

[1]Distinct powers - Problem 29 - Project Euler
[2][Golang] Large Positive Integer Multiplication
[3]Go maps in action - The Go Blog