CodeForces
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B. Non-square Equation
Let’s consider equation:
where x, n are positive integers, s(x) is the function, equal to the sum of digits of number x in the decimal number system.
You are given an integer n, find the smallest positive integer root of equation x, or else determine that there are no such roots.
A single line contains integer n (1 ≤ n ≤ 1018) — the equation parameter.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.
Print -1, if the equation doesn’t have integer positive roots. Otherwise print such smallest integer x (x > 0), that the equation given in the statement holds.
2
1
110
10
4
-1
In the first test case x = 1 is the minimum root. As s(1) = 1 and 12 + 1·1 - 2 = 0.
In the second test case x = 10 is the minimum root. As s(10) = 1 + 0 = 1 and 102 + 1·10 - 110 = 0.
In the third test case the equation has no roots.
枚举sx sx的范围可以看出最多不会超过100
由sx求x公式
#include <bits/stdc++.h>using namespace std;#define LL long longLL get(LL n) { LL sum=0; while(n) { sum += n%10; n /= 10; } return sum;}int main() { LL n, ans = -1; scanf("%lld",&n); for(int i = 1;i < 100; i++) { LL x = sqrt(i*i/4+n) - i/2; LL sx = get(x); if(x*x+sx*x==n) { ans = x; break; } } printf("%d\n",ans); }
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