UVA11038 How Many O's?题解

原文链接：http://www.algorithmist.com/index.php/User:Sweepline/UVa_11038.cpp

AC的C++语言程序如下：

// C++ solution for problem 11038 - "How Many 0's"
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

// Returns the number of zeroes in decimal representation of 0, 1, ..., b.
// Complexity: linear in the number of decimal digits of b.
long long solve(long long b) {
if (b < 0) return 0;

// Compute decimal representation of b
char s[20];
sprintf(s, "%lld", b);
int n = strlen(s);

// Compute powers of 10
long long ten[20] = { 1 };
for (int n = 1; n < 20; n++)
ten
= ten[n-1] * 10;

// Compute suffixes of b.suf[k] = atoll(s+k).
long long suf[20];
suf
= 0;
for (int i = n-1; i >= 0; i--)
suf[i] = suf[i+1] + (s[i] - '0') * ten[n-i-1];

long long res = 1, pref = 0;
for (int k = 1; k < n; k++) {
pref = pref * 10 + (s[k-1] - '0');
// pref is equal to integer, formed by first k digits of b.

if (s[k] != '0')
res += pref * ten[n-k-1];
else
res += (pref - 1) * ten[n-k-1] + suf[k+1] + 1;
}
return res;
}

int main() {
long long m, n;
while (scanf("%lld %lld", &m, &n) == 2 && m >= 0 && n >= 0)
printf("%lld\n", solve(max(m,n)) - solve(min(m,n)-1));
}