C++实现两个大整数的相加（考虑到负数异常情况）
实现两个大整数的相加，首先应该排除直接使用int和long long的方法，这些方法很容易溢出，这里为了方便（是否可以使用更精简的结构存储？）采用char来存储整数，整体思路如下：
1. 对于整数n和m的字符串形式，按照数组索引的从大到小累加计算，直接将结果存储到对应的result字符串中，处理完毕后再将result逆序输出，需考虑0和-的输出情况；
2. 考虑到有负号的情况，一开始就需要判断负号字符，这里将(-,-)和(+,+)统一当成相加操作然后都是负号的话在结尾补上负号，对于(+,-)和(-,+)统一处理成（大-小）的形式然后在结尾补负号；比如对于20-500转换成-(-20+500)，对于-500+20准换成-(500-20)。
3. 这里需要使用标志位nTake记录是否进位或借位；
4. 还要考虑是否有异常字符出现，使用全局变量gInvalid记录有无异常。
1 #include<stdio.h> 2 #include<string.h> 3 4 #define Joshua_OJ 5 6 bool gInvalid = false; 7 8 // 0: equal, -1: n less m, 1: n bigger m 9 int AbsIsEqual(char* n, char* m, int n_start, int n_end, int m_start, int m_end) 10 { 11 if ((n_end - n_start) > (m_end - m_start)) return 1; 12 else if ((n_end - n_start) < (m_end - m_start)) return -1; 13 else 14 { 15 int i = n_start; 16 int j = m_start; 17 while (i <= n_end && j <= m_end) 18 { 19 if (n[i] > m[j]) return 1; 20 else if (n[i] < m[j]) return -1; 21 ++i; 22 ++j; 23 } 24 } 25 return 0; 26 } 27 28 void BigNumberAdd(char* n, char* m, char* result) 29 { 30 gInvalid = false; 31 32 if (n == NULL || m == NULL) 33 { 34 gInvalid = true; 35 return; 36 } 37 38 int n_index = strlen(n) - 1; 39 int m_index = strlen(m) - 1; 40 41 // 负数特别处理 42 int n_start = 0; 43 int m_start = 0; 44 int n_signed = 1; 45 int m_signed = 1; 46 if (n[0] == '-') 47 { 48 n_start = 1; 49 n_signed = -1; 50 } 51 if (m[0] == '-') 52 { 53 m_start = 1; 54 m_signed = -1; 55 } 56 // 如果只有一个负数，转换为大数减小数再取负号，这样方便异号借位相减 57 bool isResetPosNeg = false; 58 if (n_signed == 1 && m_signed == -1) 59 { 60 int tag = AbsIsEqual(n, m, n_start, n_index, m_start, m_index); 61 if (tag == -1) 62 { 63 n_signed = 0 - n_signed; 64 m_signed = 0 - m_signed; 65 isResetPosNeg = true; 66 } 67 else if (tag == 0) 68 { 69 result[0] = '0'; 70 result[1] = '\0'; 71 return; 72 } 73 } 74 else if (n_signed == -1 && m_signed == 1) 75 { 76 int tag = AbsIsEqual(n, m, n_start, n_index, m_start, m_index); 77 if (tag == 1) 78 { 79 n_signed = 0 - n_signed; 80 m_signed = 0 - m_signed; 81 isResetPosNeg = true; 82 } 83 else if (tag == 0) 84 { 85 result[0] = '0'; 86 result[1] = '\0'; 87 return; 88 } 89 } 90 91 int index = 0; 92 int nTake = 0; 93 while (n_index >= n_start || m_index >= m_start) 94 { 95 int op1, op2; 96 op1 = op2 = 0; 97 98 if (n_index >= n_start && (n[n_index] < '0' || n[n_index] > '9')) 99 { 100 gInvalid = true; 101 return; 102 } 103 if (m_index >= m_start && (m[m_index] < '0' || m[m_index] > '9')) 104 { 105 gInvalid = true; 106 return; 107 } 108 109 if (n_index >= n_start) op1 = n[n_index] - '0'; 110 if (m_index >= m_start) op2 = m[m_index] - '0'; 111 if (n_signed == 1 && m_signed == -1) op2 = m_signed * op2; 112 else if (m_signed == 1 && n_signed == -1) op1 = n_signed * op1; 113 114 int nSum = op1 + op2 + nTake; 115 if (nSum >= 10) 116 { 117 nSum -= 10; 118 result[index] = nSum + '0'; 119 nTake = 1; 120 } 121 else if (nSum >= 0) 122 { 123 result[index] = nSum + '0'; 124 nTake = 0; 125 } 126 else 127 { 128 nSum = 10 + nSum; 129 result[index] = nSum + '0'; 130 nTake = -1; 131 } 132 --n_index; 133 --m_index; 134 ++index; 135 } 136 137 if (nTake == 1) result[index++] = nTake + '0'; 138 else if (nTake == -1) result[index++] = '-'; 139 140 if (isResetPosNeg) result[index++] = '-'; 141 else if (n_signed == -1 && m_signed == -1) result[index++] = '-'; 142 143 result[index] = '\0'; 144 } 145 146 // 从后往前打印出这个数字，并忽略开头的0 147 void PrintNumber(char* number) 148 { 149 bool isBeginning0 = true; 150 int length = strlen(number); 151 152 for (int i = length - 1; i >= 0; --i) 153 { 154 if (i == length - 1 && number[i] == '-') 155 { 156 printf("%c", '-'); 157 continue; 158 } 159 160 if (isBeginning0 && number[i] != '0') 161 { 162 isBeginning0 = false; 163 } 164 165 if (!isBeginning0) 166 { 167 printf("%c", number[i]); 168 } 169 else 170 { 171 if (i == 0) printf("%c", '0'); 172 } 173 } 174 } 175 176 int main(void) 177 { 178 #ifdef Joshua_OJ 179 freopen("in.txt", "r", stdin); 180 #endif 181 int num; 182 char n[10000]; 183 char m[10000]; 184 char result[10002]; 185 186 scanf("%d", &num); 187 while (num--) 188 { 189 scanf("%s %s", n, m); 190 BigNumberAdd(n, m, result); 191 if (gInvalid) 192 { 193 printf("%s\n", "invalid number"); 194 continue; 195 } 196 PrintNumber(result); 197 printf("\n"); 198 } 199 200 #ifdef Joshua_OJ 201 fclose(stdin); 202 #endif 203 204 return 0; 205 }
输入第一个数表示有多少组数据，对于无效数据需要输出invalid number
Input：
15
200 -22
22 -200
-200 22
-22 200
0 0
000 000
-111 -111
-50 50
50 -50
-333 -333
222 -100
222.222 222
123222222222456 89701234562222222
11111111111111111 11111111111111100
9999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999
Output：
178
-178
-178
178
0
0
-222
0
0
-666
122
invalid number
89824456784444678
22222222222222211
19999999999999999999999999999999999999999999999999999998
