給定一個(gè)十進(jìn)制正整數(shù)N，寫下從1開始，到N的所有整數(shù)，然后數(shù)一下其中出現(xiàn)的所有“1”的個(gè)數(shù).

暴力解法

最簡(jiǎn)單的辦法就是遍歷，分別統(tǒng)計(jì)每個(gè)數(shù)字出現(xiàn)的次數(shù):
<pre><code>` func sumls(num:Int) -> Int {
var count:Int = 0

    for i in 1...num {
        var temp:Int = i
        while temp != 0 {
            count += temp % 10 == 1 ? 1 : 0
            temp /= 10
        }
    }

    return count
}`</code></pre>

數(shù)學(xué)解法

數(shù)學(xué)解法需要比較常的分析，忽略證明過程，簡(jiǎn)單給出邏輯如下:
對(duì)于數(shù)abcde，c這位出現(xiàn)1的次數(shù)分以下情況:
1.若c == 0,結(jié)輪是 ab * 100;
2.若c == 1,結(jié)論是（ab）* 100 + de + 1;
3.若c > 1,結(jié)論是（ab + 1）* 100;
<pre><code>` func sumlsSimple(num:Int) -> Int {
if num <= 0 {
return 0
}
var factor = 1
var lowNum:Int = 0
var curNum:Int = 0
var highNum:Int = 0

    var count:Int = 0
    let n:Int = num
    
    while n / factor != 0 {
        lowNum = n - (n / factor) * factor
        curNum = (n / factor) % 10
        highNum = n / (factor * 10)
        
        if curNum == 0 {
            count += highNum * factor
        } else if curNum == 1 {
            count += highNum * factor + lowNum + 1
        } else {
            count += (highNum + 1) * factor
        }
        
        factor *= 10
    }
    
    return count
}`</code></pre>

通用解法

假設(shè)求解的不是1的數(shù)目，而是其他數(shù)字呢，限制范圍1~9，第二種解法稍微修改即可.
<pre><code>` func sumlsCommon(num:Int,target:Int) -> Int {
if num <= 0 || (target < 1 || target > 9){
return 0
}
var factor = 1
var lowNum:Int = 0
var curNum:Int = 0
var highNum:Int = 0

    var count:Int = 0
    let n:Int = num
    
    while n / factor != 0 {
        lowNum = n - (n / factor) * factor
        curNum = (n / factor) % 10
        highNum = n / (factor * 10)
        
        if curNum < target {
            count += highNum * factor
        } else if curNum == target {
            count += highNum * factor + lowNum + 1
        } else {
            count += (highNum + 1) * factor
        }
        
        factor *= 10
    }
    
    return count
}`</code></pre>

測(cè)試代碼:
<pre><code>var maxNum:Int = 123 var statisResult:Int = statis.sumls(num: maxNum) var statisResult2:Int = statis.sumlsSimple(num: maxNum) var statisResult3:Int = statis.sumlsCommon(num: maxNum, target: 2) print("FlyElephant--1...\(maxNum)中1的個(gè)數(shù)---\(statisResult)---\(statisResult2)") print("FlyElephant--1...\(maxNum)中2的個(gè)數(shù)---\(statisResult3)")</code></pre>

FlyElephant.png