天梯习题——阶乘计算升级版（乘法原理、大数相乘）

缺乏、安全感 2022-12-20 02:53 78阅读 0赞

### [阶乘计算升级版][Link 1] ###

![题目][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1poZW5neWFuZ3hpbm4_size_16_color_FFFFFF_t_70_pic_center]  
![题目][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1poZW5neWFuZ3hpbm4_size_16_color_FFFFFF_t_70_pic_center 1]

#### 解题思路 ####

1000！估计需要2800以上的位来进行存储，很明显利用整型是无法将这些位存储起来，必须利用数组来进行存储，这里就涉及到大数相乘。

#### 乘法原理（图片来源于百度） ####

![乘法原理][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1poZW5neWFuZ3hpbm4_size_16_color_FFFFFF_t_70_pic_center 2]  
eg：23 \* 56  
23 \* 6 + 23 \* 50 = 1288

实现代码

void Print_Factorial ( const int N ){ 
     	if(N>0){ 
     		int ans[3000];	//确定 1000! 最大位数小于3000 
     		int d, k;		// d : 进位位 
     		k=1, d=0;		// k : 当前最高位 
     		ans[k]=1;		// ans : 存放结果 
     		
     		for(int i=2; i<=N; i++){ 
     			for(int j=1; j<=k; j++){ 
     				int tmp = i*ans[j]+d;	//临时存放 
     				ans[j] = tmp%10;		//确定当前第 j 位 
     				d = tmp/10;				//确定进位位 
    			}
     			
     			while(d>0){ 				//增位 
     				ans[++k] = d%10;
     				d /= 10;
    			}
    		}
    		
     		for(int i=k; i>0; i--)
     			printf("%d", ans[i]);
    		printf("\n");
    	}
    	else if(N==0)
    		printf("1\n");
    	else
    		printf("Invalid input\n");
     }

[参考博客][Link 2]

[Link 1]: https://pintia.cn/problem-sets/14/problems/742
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[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1poZW5neWFuZ3hpbm4_size_16_color_FFFFFF_t_70_pic_center 1]: https://img-blog.csdnimg.cn/20201110131112874.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1poZW5neWFuZ3hpbm4=,size_16,color_FFFFFF,t_70#pic_center
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[Link 2]: https://blog.csdn.net/wxx0136/article/details/52458170?ops_request_misc=%257B%2522request%255Fid%2522%253A%2522160498571719724836716752%2522%252C%2522scm%2522%253A%252220140713.130102334..%2522%257D&request_id=160498571719724836716752&biz_id=0&utm_medium=distribute.pc_search_result.none-task-blog-2~all~top_click~default-1-52458170.pc_first_rank_v2_rank_v28p&utm_term=%E9%98%B6%E4%B9%98%E8%AE%A1%E7%AE%97%E5%8D%87%E7%BA%A7%E7%89%88&spm=1018.2118.3001.4449