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137 lines
3.5 KiB
137 lines
3.5 KiB
package cap3
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import "strings"
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// Ex19 高精度阶乘
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func Ex19(n uint64) string {
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result := []uint8{1}
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for i := uint64(2); i <= n; i++ {
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result = multiply(result, i)
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}
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return DigitSlice2String(result)
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}
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func multiply(a []uint8, b uint64) []uint8 {
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result := make([]uint8, len(a)+22)
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resultEndIdx := len(result) - 1
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bOffset := 0
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for i := b; i >= 1; i /= 10 {
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carry := uint8(0)
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bDigit := uint8(i % 10)
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aEnd, resultIdx := len(a)-1, 0
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for j := 0; j < len(a); j++ {
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// 字符转数字
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aDigit := a[aEnd-j]
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// 当前位计算结果 = 当前结果 + aDigit*bDigit + 进位
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resultIdx = resultEndIdx - (bOffset + j)
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num := result[resultIdx] + aDigit*bDigit + carry
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// 当前位为计算结果的个位，进位为十位上的数字
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result[resultIdx] = num % 10
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carry = num / 10
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}
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// 如果还有进位，则对下一个结果位添加进位，此时不会再有进位
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if carry != 0 {
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resultIdx--
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result[resultIdx] += carry
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}
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bOffset++
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}
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return result
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}
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func multiply2(a []uint8, b uint64) []uint8 {
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result := make([]uint8, len(a)+22)
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resultEndIdx := len(result)*2 - 1
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bOffset := 0
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for i := b; i >= 1; i /= 10 {
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carry := uint8(0)
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bDigit := uint8(i % 10)
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aEnd, resultIdx := len(a)*2-1, 0
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for j := 0; j < len(a); j++ {
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// 字符转数字
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aDigit := uint8(0)
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// 4,5 -> 37(0010,0101)
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aIdx := aEnd - j
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if aIdx%2 == 0 {
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aDigit = a[aIdx/2] >> 4
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} else {
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aDigit = a[aIdx/2] & 0b00001111
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}
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// 当前位计算结果 = 当前结果 + aDigit*bDigit + 进位
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resultIdx = resultEndIdx - (bOffset + j)
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bitIdx := resultIdx / 2
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if resultIdx%2 == 0 {
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num := (result[bitIdx] >> 4) + aDigit*bDigit + carry
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// 清位
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// 4,5 -> 37(0010,0101) => 0,5 -> 5(0000,0101)
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result[bitIdx] &= 0b00001111
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// 位赋值
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// 0,5 -> 5(0000,0101) => 5,5 -> 5(0101,0101)
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// 5(0000,0101) << 4 => 80(0101,0000)
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// 5(0000,0101) | 80(0101,0000) => 5,5 -> 5(0101,0101)
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result[bitIdx] |= (num % 10) << 4
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carry = num / 10
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} else {
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num := (result[bitIdx] & 0b00001111) + aDigit*bDigit + carry
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// 清位
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// 4,5 -> 37(0010,0101) => 4,0 -> 32(0010,0000)
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result[bitIdx] &= 0b11110000
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// 赋值
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// 4,0 -> 32(0010,0000) => 4,5 -> 37(0010,0101)
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// 32(0010,0000) | 5(0000,0101) => 4,5 -> 37(0010,0101)
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result[bitIdx] |= num % 10
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carry = num / 10
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}
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}
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// 如果还有进位，则对下一个结果位添加进位，此时不会再有进位
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if carry != 0 {
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resultIdx--
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bitIdx := resultIdx / 2
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if resultIdx%2 == 0 {
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// 4,5 -> 37(0010,0101) => 5,5 -> 37(0101,0101)
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// 4+1 -> 5(0000,0101) << 4 => 80(0101,0000)
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// 5(0000,0101) | 80(0101,0000) => 5,5 -> 5(0101,0101)
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result[bitIdx] &= 0b00001111
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num := (result[bitIdx] >> 4) + carry
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result[bitIdx] |= num << 4
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} else {
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result[bitIdx] &= 0b11110000
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num := (result[bitIdx] & 0b00001111) + carry
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result[bitIdx] |= num
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}
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}
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bOffset++
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}
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return result
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}
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// Ex19LowMem 低内存使用版，两位数字结果按位存在同一个uint8中，一个0~9数字只使用四字节，uint8可存两位，一个字节拆成两半用
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func Ex19LowMem(n uint64) string {
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result := []uint8{1}
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for i := uint64(2); i <= n; i++ {
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result = multiply2(result, i)
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}
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zeroPrefix := true
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sb := strings.Builder{}
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for _, num := range result {
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if zeroPrefix && num == 0 {
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continue
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} else {
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zeroPrefix = false
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}
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sb.WriteByte((num >> 4) + 48)
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sb.WriteByte((num & 0b00001111) + 48)
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}
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return sb.String()
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}
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