推荐14-php算法题-306累加数

输入: "112358"
输出: true
解释: 累加序列为: 1, 1, 2, 3, 5, 8 。1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8

输入: "199100199"
输出: true
解释: 累加序列为: 1, 99, 100, 199。1 + 99 = 100, 99 + 100 = 199

/**
     * @param String $num
     * @return Boolean
     */
    function isAdditiveNumber($num) {
        $len = strlen($num);
        if($len < 3){
            return false;
        }
        $firstNum = 0;
        $secondNum = 0;
        $sumNum = 0;

        //回溯法，不断找出恰三个符合的累加数
        for ($i=2; $i<$len; $i++){
            $subLen = $i+1;
            for($j=1;$j<(int)(($subLen+1)/2);$j++){
                $firstNumLen = $j;
                for($k=1;$k<(int)(($subLen+1)/2);$k++){
                    $secondNumLen = $k;

                    if(0===strpos(substr($num,0,$firstNumLen),'0') && $firstNumLen != 1){
                        continue;
                    }
                    if(0===strpos(substr($num,$firstNumLen,$secondNumLen),'0') && $secondNumLen!= 1){
                        continue;
                    }
                    if(0===strpos(substr($num,$firstNumLen+$secondNumLen,$subLen-$firstNumLen-$secondNumLen),'0') && $subLen-$firstNumLen-$secondNumLen!= 1){
                        continue;
                    }
                    $firstNum = (int)substr($num,0,$firstNumLen);
                    $secondNum = (int)substr($num,$firstNumLen,$secondNumLen);
                    $sumNum =  (int)substr($num,$firstNumLen+$secondNumLen,$subLen-$firstNumLen-$secondNumLen);

                    if($firstNum+$secondNum == $sumNum){
                        $isAdditiveNumber = $this->verifyAdditiveNumber($num,$firstNum,$secondNum,$sumNum);
                        if($isAdditiveNumber){
                            return true;
                        }
                    }
                }
            }
        }
        return false;
    }

    //验证整个字符串是否为累加数字符串
    public function verifyAdditiveNumber($num,$firstNum,$secondNum,$sumNum){
        if($firstNum+$secondNum != $sumNum){
            return false;
        }
        $startIdx = 0;
        while(true){
            $tmpSumNum =  (string)($secondNum + $sumNum);
            $tmpStartLen = ($startIdx+strlen($firstNum)+strlen($secondNum)+strlen($sumNum));
            if($tmpStartLen  ==  strlen($num)){
                return true;
            }

            if(substr($num,$tmpStartLen,strlen($tmpSumNum)) != $tmpSumNum){
                return false;
            }

            $startIdx = $startIdx + strlen($firstNum);
            $firstNum = $secondNum;
            $secondNum = $sumNum;
            $sumNum = (int)$tmpSumNum;
        }

}

LeetCode：https://leetcode-cn.com/problems/additive-number/原文：https://segmentfault.com/a/1190000020426923