[BZOJ 1026] [SCOI 2009] Windy数 【数位DP】

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>

using namespace std;

const int MaxBit = 13;

int A, B;
int f[MaxBit][11], Bit[MaxBit];

inline int Abs(int a) {
	return a >= 0 ? a : -a;
}

//计算小于x的数的答案 
int Get(int x) {
	if (x == 0) return 0;
	int ret = 0, l = 0;
	while (x) {
		Bit[++l] = x % 10;
		x /= 10;
	}
	//统计位数不足l位的答案 
	for (int i = 1; i <= l - 1; ++i) {
		for (int j = 1; j <= 9; ++j) {
			ret += f[i][j];
		}
	}
	//固定后面的(l-i)位，然后第i位可以在[0, Bit[i]-1]之间变化 
	for (int i = 1; i <= Bit[l] - 1; ++i) ret += f[l][i];
	for (int i = l - 1; i >= 1; --i) {
		for (int j = 0; j <= Bit[i] - 1; ++j) {
			if (Abs(j - Bit[i + 1]) >= 2) ret += f[i][j];
		}
		//无法固定第i位 
		if (Abs(Bit[i + 1] - Bit[i]) < 2) break;
	}
	return ret;
}

int main() 
{
	//f[i][j]表示第i位是j的答案数 
	for (int i = 0; i <= 9; ++i) f[1][i] = 1;
	for (int i = 1; i <= 10; ++i) {
		for (int j = 0; j <= 9; ++j) {
			for (int k = 0; k <= 9; ++k) {
				if (Abs(k - j) >= 2) f[i][j] += f[i - 1][k];
			}
		}
	}
	scanf("%d%d", &A, &B);
	//对询问进行差分，化繁为简 
	printf("%d\n", Get(B + 1) - Get(A));
	return 0;
}