簡單的以附於頁尾的程式計算，會發現當 n <= 100 時 f91(n) = 91。由於就算如此運算時間仍不甚理想，故使用了一些 I/O 優化，才能用 0.000 sec 完成。
Using the simple program at the end of this page, you’ll find out that f91(n) = 91 if n <= 100. The execution time, however, is still quite high when this is applied. Thus, I used some I/O optimizations to make the execution time 0.000 seconds.
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#include <iostream>
static inline int fast_atoi(const char *p, unsigned int len) {
int res = 0;
switch (len) {
case 7: res += (*p++ & 15) * 1000000;
case 6: res += (*p++ & 15) * 100000;
case 5: res += (*p++ & 15) * 10000;
case 4: res += (*p++ & 15) * 1000;
case 3: res += (*p++ & 15) * 100;
case 2: res += (*p++ & 15) * 10;
case 1: res += (*p & 15);
}
return res;
}
bool getInt(int *res) {
char numBuf[11], tmp;
unsigned int i = 0;
while (true) {
static char buf[1 << 20], *p = buf, *end = buf;
if (p == end) {
if ((end = buf + fread(buf, 1, 1 << 20, stdin)) == buf) break;
p = buf;
}
tmp = *p++;
if ((unsigned)(tmp - '0') > 10u && i) break;
numBuf[i++] = tmp;
}
if (!i) return false;
*res = fast_atoi(numBuf, i);
return true;
}
static inline int intLen(int n) {
if (n >= 1000000) return 7;
if (n >= 100000) return 6;
if (n >= 10000) return 5;
if (n >= 1000) return 4;
if (n >= 100) return 3;
if (n >= 10) return 2;
return 1;
}
static inline void itoa(int n, char *dst) {
int len = intLen(n);
dst[len] = '\0';
switch (len) {
case 7: dst[6] = n % 10 + '0'; n /= 10;
case 6: dst[5] = n % 10 + '0'; n /= 10;
case 5: dst[4] = n % 10 + '0'; n /= 10;
case 4: dst[3] = n % 10 + '0'; n /= 10;
case 3: dst[2] = n % 10 + '0'; n /= 10;
case 2: dst[1] = n % 10 + '0'; n /= 10;
case 1: dst[0] = n % 10 + '0';
}
}
int main() {
int n;
while (getInt(&n) && n) {
char numStr[11];
fputs("f91(", stdout);
itoa(n, numStr);
fputs(numStr, stdout);
if (n > 100) {
fputs(") = ", stdout);
itoa(n - 10, numStr);
fputs(numStr, stdout);
putchar('\n');
} else {
fputs(") = 91\n", stdout);
}
}
}
Calculating f91(n) for n <=100
#include <iostream>
int f91(int n) {
if (n > 100) return n - 10;
return f91(f91(n + 11));
}
int main() {
std::cout << "int arr[] = {";
for (int i = 0; i <= 100; i++) {
std::cout << f91(i) << ", ";
}
std::cout << "};";
}