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            elva

            大數求和

            Declaration

              該文為本人原創,如需轉載,請注名原作者和本站地址,但未經本人同意,嚴禁用于商業途徑。

            Text

              由于系統硬件的限制,我們無法直接進行大數的求和,但是采取一些存儲方面的技術來解決這個問題。下面通過引入字符數組,并運用小學就學習過的進位求和算法來進行大數的求和運算。這里只實現了大整數的求和,如果需要運用到小數求和里頭,需要改動才行。

            Code

            /*
             * FILE: lns.c
             * Funciton: Count the sum of two large numbers
             */


            /*
             * Author: Wu Zhangjin, <zhangjinw@gmail.com>
             * (c) 2006-11-25 dslab.lzu.edu.cn Lanzhou University
             * License GPL Version 2
             */


            #include <stdio.h>        /* standard input/output functions */
            #include <string.h>         /* strlen function */
            #define MAX_DIGITS 10000    /* define your max digit here */

            /**
             * sumof_ln - count the sum of two large numbers
             * @ln_arr: the address of the array which store the two string of larger numbers
             *
             * Description:
             * For the restrictions of the hardware, we can not count the sum of two
             * large numbers directly, but we can use some skills to work it out.
             * This function use a char array to store the large numbers, and then
             * add every char digit with the carry, until the leftmost digit. Notes that
             * if the digit of two numbers is not equal,The left aligned digit should be
             * treated espectically--you should add a carry if it exist on every left digit.
             * And also if the last carry exist,the leftmost digit should be '1'
             *
             * Returns:
             * the address point of the string of sum
             *
             * Notes:
             * you can define the maximum digit of the number by the macro MAX_DIGITS
             */


            char* sumof_ln(char ln_arr[2][MAX_DIGITS])
            {
                int digit_arr[2], carry, sindex, lindex, i, tmp, align_lindex;
                
                carry = 0;
                digit_arr[0] = strlen(ln_arr[0]);
                digit_arr[1] = strlen(ln_arr[1]);
                sindex = (digit_arr[0] < digit_arr[1])?0:1;
                lindex = 1 - sindex;
                align_lindex = digit_arr[lindex] - digit_arr[sindex];

                for (i = digit_arr[sindex] - 1; i >= 0; i --) {
                    tmp = ln_arr[lindex][align_lindex + i] + ln_arr[sindex][i] + carry;
                    ln_arr[lindex][align_lindex + i] = tmp - 48 - 10 * (carry = (tmp >= 106?1:0));
                }

                if (digit_arr[0] != digit_arr[1])
                for (i = align_lindex - 1; i >= 0 && carry; i --)    {
                    tmp = ln_arr[lindex][i] + carry;
                    ln_arr[lindex][i] = tmp - 10 * (carry = (tmp >= 58?1:0));

                }

                if (carry) {
                    for (i = digit_arr[lindex] - 1; i >= 0; i --)
                        ln_arr[lindex][i+1] = ln_arr[lindex][i];
                    ln_arr[lindex][digit_arr[lindex] + 1] = '\0';
                    ln_arr[lindex][0] = '1';
                }    

                return ln_arr[lindex];
            }

            /**
             * main - main function to call function sumof_ln
             * Description:
             * compile and link this c program and input two larger numbers, you can get the sum of them
             *
             * Notes:
             * you cannot input a number whose digit is larger than MAX_DIGITS, but you can change by modifying the macro.
             */


            int main(int argc, char *argv[])
            {
                char ln_arr[2][MAX_DIGITS];

                printf("Please input two large numbers: \n");
                scanf("%s %s", ln_arr[0], ln_arr[1]);

                printf("The sum is:\n%s\n", sumof_ln( ln_arr ));    
            }


            Demo

            shell> make lns
            cc     lns.c   -o lns
            shell> ./lns
            Please input two large numbers:
            9
            1
            The sum is:
            10
            shell> ./lns
            Please input two large numbers:
            999999999999999999999999999999999999999999999999999999999999999999999999999999999
            1
            The sum is:
            1000000000000000000000000000000000000000000000000000000000000000000000000000000000
            shell> ./lns
            Please input two large numbers:
            5644687481748485751785757181534145412178758718715875187687867168716841687186716876841688676
            45848587878456465146861787116876871687168418178718718768465167867817617687116761867187187971971971954521278
            The sum is:
            45848587878456470791549268865362623472925599712864130947223886583692805374983930584028875158688848796209954
            shell> ./lns
            Please input two large numbers:
            144
            2546
            The sum is:
            2690

            posted on 2007-08-15 17:54 葉子 閱讀(1255) 評論(0)  編輯 收藏 引用 所屬分類: C\C++

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