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HDU 2451 Simple Addition Expression 组合数学

2018年01月19日 ⁄ 综合 ⁄ 共 3441字 ⁄ 字号 评论关闭

Simple Addition Expression

Time Limit: 5000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1506    Accepted Submission(s): 575

Problem Description
A luxury yacht with 100 passengers on board is sailing on the sea in the twilight. The yacht is ablaze with lights and there comes out laughers and singing from the hall where an evening party is in full swing. People are singing,
dancing and enjoying themselves.

The yacht is equipped with the most advanced navigation and driving system which can all be manipulated by a computer. When the captain notices that there is only gentle breeze and the sea waves are not high, he starts the autopilot. The yacht sails forward
smoothly, ploughs the waves. When it’s completely dark, the passengers start to feel a little funny for sudden forward rushes or sudden decelerations or slight swings. The captain immediately walks to the driving platform and switches the autopilot to human
manipulation. The yacht returns back to normal and the party restarts. Laughers come back, too.

The captain summons the engineer on board to do a thorough check of the navigation system. It turns out that only the computer is out of order, but the exact failure is still unclear. There is a computer scientist among the passengers who is also invited to
the cab to give a hand. He first inputs several groups of data to test the computer. When he inputs 1+2+3, the computer outputs 6, which is exactly right. But when he inputs 4+5+6, the computer outputs 5, which is wrong. Then he inputs 12+13+14, and gets 39,
another right answer, while he inputs 14+15+16, and gets 35, another wrong answer. After the test, the computer scientist says smilingly: “the failure is clear now. The computer's adder can not carry." After excluding the failure, the captain restarts the
autopilot and the yacht returns back to normal, sailing smoothly on the sea.

The captain and the engineer invite the computer scientist to sit down and have a talk. The computer scientist tells a story as following:

A former mathematician defined a kind of simple addition expression.
If there is an expression (i) + (i+1) + (i+2), i>=0, when carried out additive operations, no position has a carry, it is called simple addition expression.

For instance, when i equals 0, 0+1+2 is a simple addition expression, meanwhile when i equals 11, 11+12+13 is a simple addition expression, too. Because of that no position has a carry.

However, when i equals 3, 3+4+5 is not a simple addition expression, that is because 3+4+5 equals 12, there is a carried number from unit digit to tens digit. In the same way, when i equals 13, 13+14+15 is not a simple addition expression, either. However,
when i equals 112, 112+113+114 is a simple addition expression. Because 112+113+114 equals 339, there is no carry in the process of adding.

when the students have got the definition of simple addition expression, the mathematician puts forward a new question: for a positive integer n, how many simple addition expressions exist when i<n. In addition, i is the first number of a simple addition expression.

when the value of n is large enough, the problem needs to be solved by means of computer.

 

Input
There are several test cases, each case takes up a line, there is an integer n (n<10^10).

 

Output
Output the number of all simple addition expressions when i<n.
/*
HDOJ 2451 组合数学

题目是求i+(i+1)+(i+2)的结果中没有进位的 
最高位满足1,2,3;中间的数要满足0,1,2,3; 个位数满足0,1,2;
 
*/ 
#include<iostream>
#include<string.h>
#include<math.h>
#include<stdio.h>
using namespace std;
int main()
{
	int i,temp,len,ans;
	char str[15];
	while(scanf("%s",str)!=EOF)
	{
		len=strlen(str);
		ans=0;
		for(i=0;i<len;i++)
		{
			temp=str[i]-'0';
			if(i==len-1)//个位只能取012 
			{
				if(temp<3)
					ans+=temp;
				else
					ans+=3;
				continue;			
			}
			if(temp<4)//如果不是最后位 则判断第一位 
				ans+=temp*pow(4,(len-2-i))*3;//len-2-i就是除了当前位和个位,右边的位数
											//这里未结束 当前位<3 还需考虑下一位的个数 
			else
			{
				ans+=pow(4,len-1-i)*3;//包括当前位在内的,右边的个数 
				break;				//pow(4,len-1-i)表示的是每位取4个包括自己减去个位有len-1-i位,i从0开始的
			}						//乘3 是最后位012  break表示当前位大于3 后面都是饱满的 计算完毕 
				 
		}							
		printf("%d\n",ans);
	}
	return 0;
}

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