/
main.go
79 lines (65 loc) · 1.2 KB
/
main.go
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package main
import (
"log"
"os"
"strconv"
"github.com/TomasCruz/projecteuler"
)
/*
Problem 76; Counting Summations
It is possible to write five as a sum in exactly six different ways:
4+1
3+2
3+1+1
2+2+1
2+1+1+1
1+1+1+1+1
How many different ways can one hundred be written as a sum of at least two positive integers?
*/
func main() {
var limit int
if len(os.Args) > 1 {
limit64, err := strconv.ParseInt(os.Args[1], 10, 64)
if err != nil {
log.Fatal("bad argument")
}
limit = int(limit64)
} else {
limit = 100
}
projecteuler.Timed(calc, limit)
}
func calc(args ...interface{}) (result string, err error) {
limit := args[0].(int)
m := generatePartitionMatrix(limit)
sum := 0
for i := 1; i < limit; i++ {
sum += m[limit][i]
}
result = strconv.Itoa(sum)
return
}
func generatePartitionMatrix(limit int) [][]int {
// init
m := make([][]int, limit+1)
for i := 0; i <= limit; i++ {
m[i] = make([]int, limit+1)
}
m[1][1] = 1
for i := 2; i <= limit; i++ {
m[i][1] = 1
m[i][2] = i / 2
m[i][i-1] = 1
m[i][i] = 1
}
for i := 5; i <= limit; i++ {
for j := 3; j < i-1; j++ {
sum := 0
for k := 1; k <= j; k++ {
sum += m[i-j][k]
}
m[i][j] = sum
}
}
return m
}