func (gen *Generator) LenOfNextCirInGroup(start, target int) (len uint64, sum uint64) {
if start == target {
sum, circled, ok := gen.groups[start].nextValue()
if !circled || !ok {
gen.groups[start].Undo()
fmt.Printf("Group %d ran out of accessible circled numbers\n", start)
return 0, 0
}
return 1, sum
}
newestCircled, _, _ := gen.groups[start].nextValue()
sum += newestCircled
nonCircledCount, circledCount := uint64(1), floorSqrt.SumFSqRange(newestCircled, 1)
//TODO: handle the ok
newestCircled, _, _ = gen.groups[start+1].peek()
gen.groups[start+1].skipCircled(circledCount)
sum = moduloMath.Sum(1e9, sum, moduloMath.SumRange(1e9, newestCircled, circledCount))
for ii := start + 2; ii <= target; ii++ {
nonCircledCount += circledCount
circledCount += floorSqrt.SumFSqRange(newestCircled, circledCount)
//TODO: handle the ok
newestCircled, _, _ = gen.groups[ii].peek()
gen.groups[ii].skipCircled(circledCount)
sum = moduloMath.Sum(1e9, sum, moduloMath.SumRange(1e9, newestCircled, circledCount))
}
len = nonCircledCount + circledCount
return
}
func SumFirstNGroups(nn int) (sum uint64) {
sum = 1
for ii := 0; ii < nn; ii++ {
sum = moduloMath.Sum(1e9, sum, moduloMath.SumRange(1e9, 1, groupLengths[ii]))
}
return
}
func sequenceSum(nn uint64) (sum uint64) {
gen := sequenceGenerator.NewGenerator()
//get the target group and length up to that point
targetGroup, len := sequenceGenerator.LastGroup(nn)
nRemain := nn - len
fmt.Printf("the %dth value of the sequence is the %dth value of group %d\n", nn, nRemain, targetGroup)
sum = sequenceGenerator.SumFirstNGroups(targetGroup)
for ii := 1; ii < targetGroup; ii++ {
numTests := 0
for gen.IsNextCircled(ii) {
numTests++
len, partialSum := gen.LenOfNextCirInGroup(ii, targetGroup)
if len > nRemain {
//fmt.Printf("next value from group %d comes after the target\n", ii)
gen.UndoUpTo(targetGroup)
break
} else {
nRemain -= len
//fmt.Printf("next value from group %d comes before the target with %d values accounted for and %d remaining\n", ii, len, nRemain)
sum = moduloMath.Sum(1e9, sum, partialSum)
if nRemain == 0 {
return
}
}
}
fmt.Printf("moving onto group %d after %d tests\n", ii+1, numTests)
}
finalSumStart := gen.NextCircled(targetGroup)
finalSum := moduloMath.SumRange(1e9, finalSumStart, nRemain)
fmt.Printf("final group sum over %d sequential values starting at %d\n", nRemain, finalSumStart)
sum = moduloMath.Sum(1e9, sum, finalSum)
return
}