51nod1042 数字0-9的数量（数位DP）

原题链接：https://www.51nod.com/onlineJudge/questionCode.html#!problemId=1042
思路：就是统计啦，有点麻烦，注意细节，看代码
AC代码：#include<bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7;
const int MAXN = 1e5 + 5;
long long dp[20][12][12]; //
long long ans[12];
void preProcess() {
long long num = 1;
dp[1][0][0] = 1;
for (int i = 1; i <= 19; i++) {
for (int j = 0; j <= 9; j++) {
for (int k = 0; k <= 9; k++) {
if (j == k) dp[i][j][k] = (j != 0 ? dp[i][j - 1][k] : 0) + dp[i - 1][9][k] + num;
else dp[i][j][k] = dp[i][j - 1][k] + dp[i - 1][9][k];
}
}
num *= 10;
}
}
int main() {
long long w;
string a, b;
preProcess();
cin >> w >> b;
int len1 = b.length();
w--;
stringstream ss;
ss << w;
ss >> a;
int len2 = a.length();
long long temp = 1;
for (int i = 0; i < len1; i++) {
for (int j = 0; j <= 9; j++) {
int v = b[i] - '0';
if (v == j) {
long long num = 0;
for (int j = i + 1; j < len1; j++) {
num = num * 10 + b[j] - '0';
}
ans[j] += num + 1;
if (j != 0) ans[j] += dp[len1 - i][v - 1][j];
}
else {
if (v != 0)ans[j] += dp[len1 - i][v - 1][j];
}
}
if (i)temp *= 10;
ans[0] -= temp;
}
temp = 1;
for (int i = 0; i < len2; i++) {
for (int j = 0; j <= 9; j++) {
int v = a[i] - '0';
if (v == j) {
long long num = 0;
for (int j = i + 1; j < len2; j++) {
num = num * 10 + a[j] - '0';
}
ans[j] -= num + 1;
if (j != 0) ans[j] -= dp[len2 - i][v - 1][j];
}
else {
if (v != 0)ans[j] -= dp[len2 - i][v - 1][j];
}
}
if (i)temp *= 10;
ans[0] += temp;
}
for (int i = 0; i <= 9; i++) {
printf("%lld\n", ans[i]);
}
return 0;
}