PAT A1010

题目：https://pintia.cn/problem-sets/994805342720868352/problems/994805507225665536

二分查找时，left = 2， right = max(36，N).

转进制时，防止溢出。

#include <cstdio>
#include <cstring>
typedef long long LL;
const LL inf = (1LL << 63) - 1;
int change(char a){
	if (a >= '0' && a <= '9')
		return a - '0';
	else if(a >= 'a' && a <= 'z')
		return a - 'a' + 10;
}

LL todecimal(char a[], int len, LL radix){
	int num;
	LL result = 0;
	for(int i = 0; i < len; i++){
		num = change(a[i]);
		if(num >= radix)
			return -1;
		result = result * radix + num;
		if(result < 0)
			return inf;
	}
	return result;
}

LL max(LL a, LL b){
	if(a > b)
		return a;
	else
		return b;
}

LL binarySearch(LL x, char a[], int len){
	LL y, left = 2, right, mid;
	right = max(36, x);
	while(left < right){
		mid = (left + right) / 2;
		y = todecimal(a, len, mid);
		if(y >= x)
			right = mid;
		else
			left = mid + 1;
	}
	y = todecimal(a, len, left);
	if(y == x)
		return left;
	else
		return 0;
}

int main(){
	char a[2][15];
	int tag;
	LL radix, N;
	scanf("%s %s %d %lld", a[0], a[1], &tag, &radix);
	int len = strlen(a[--tag]);
	N = todecimal(a[tag], len, radix);
	len = strlen(a[!tag]);
	LL other_radix = binarySearch(N, a[!tag], len);
	if(other_radix){
		printf("%lld\n", other_radix);
	}
	else
		printf("Impossible\n");
	return 0;
}