Additive Number 306

题目链接：https://leetcode.com/problems/additive-number/

题目描述：一串数字是Additive number，必须存在一个划分将这一串数字分成n个数字，n必须大于3，并且除了前两个数字之外，每个数字都是前两个数字之和，此外，不存在包含前导零的数字。

题目分析：深度搜索

代码实现：

#include <map>
#include <vector>
#include <algorithm>
#include <cstring>
#include <cstdlib>
#include <cstdio>
#include <cmath>
#include <iostream>
#include <stack>

using namespace std;

bool judge(string a, string b, string sum) {
//cout<<a<<", "<<b<<", "<<sum<<endl;
int lena = a.length();
int lenb = b.length();
int lens = sum.length();

if (lens < lena || lens < lenb) return 0;
int c = 0;
while(lena > 0 && lenb > 0) {
int tmp = a[lena-1] + b[lenb-1] - '0' - '0' + c;
c = tmp / 10;
tmp = tmp % 10;
if (sum[lens-1] != tmp+'0') return 0;
lena--;
lenb--;
lens--;
}

while(lena > 0) {
int tmp = a[lena-1] + c -'0';
c = tmp / 10;
tmp = tmp % 10;
if (sum[lens-1] != tmp+'0') return 0;
lena--;
lens--;
}

while(lenb > 0) {
int tmp = b[lenb-1] + c - '0';
c = tmp /10;
tmp = tmp %10;
if (sum[lens-1] != tmp+'0') return 0;
lenb--;
lens--;
}

if ((c==0 && lens==0) || (lens==1 && sum[0]==c+'0'))
return 1;

return 0;
}

bool df(string a, string b, string num) {
int lena = a.length();
int lenb = b.length();
int lenn = num.length();
int len = max(lena, lenb);
if (!lenn) return 1;
if (len > lenn) return 0;
if ((a[0] == '0' && lena>1) || (b[0] == '0' && lenb>1) || (num[0] == '0' && lenn>1)) return 0;

bool ret = judge(a, b, num.substr(0, len));
//cout<<a<<", "<<b<<", "<<num.substr(0, len)<<", ret:"<<ret<<endl;
if (ret) {
if (df(b, num.substr(0, len), num.substr(len)))
return 1;
}

if (len+1 > lenn) return 0;

ret = judge(a, b, num.substr(0, len+1));
//cout<<a<<", "<<b<<", "<<num.substr(0, len+1)<<", ret:"<<ret<<endl;
if (ret) {
if (df(b, num.substr(0, len+1), num.substr(len+1)))
return 1;
}

return 0;
}

bool isAdditiveNumber(string num) {
int len = num.length();
for (int i = 0; i < len-2; i++) {
for (int j = i+1; j < len-1; j++) {
if (df(num.substr(0, i+1), num.substr(i+1, j-i), num.substr(j+1)))
return 1;
}
}

return 0;
}

int main()
{
string s;
while(cin>>s) {
cout<<s<<" is "<<isAdditiveNumber(s)<<endl;
}
return 0;
}