分段打表,适用于求一段和。
题意: 判断[A, B] (1 <= A <= B <= 10^9)中有多少个哈沙德数。
解法:把 1~10^9 分成 10^4 段,每段 10^5 个数。用数组 s 存储每段中哈沙德数个数。比如 s[1]为 1~10^5 中哈沙德数个数,s[2]为 10^5+1~2*10^5 间哈沙德数个数。打表出每段哈沙德数个数后判断输入的数在哪段,将这段之前所有数加一起后,再从这段的起点开始一直判断到这个数。
#include <cstdio> #include <iostream> using namespace std; //每10^5个数中哈沙德数个数 int s[] = 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int q[10001]; //标记每段的终点 int f(int x){ if(!x) return 0; return f(x/10) + x%10; } void init(){ q[0] = 0; for(int i = 1; i <= 10000; i++){ q[i] = q[i-1] + 100000; } } int cal(int x){ int sum = 0; int i; for(i = 0; i <= 10000; i++){ //找到x在哪个段并把这段之前的哈沙德数个数加起来 if(x > q[i]) sum += s[i]; else break; } for(int j = q[--i]+1; j <= x; j++) //在这个段的起点开始扫描到x if(j%f(j) == 0) sum++; return sum; } int main(){ //freopen("a.txt", "r", stdin); init(); int t; scanf("%d", &t); for(int i = 1; i <= t; i++){ int a, b; scanf("%d %d", &a, &b); if(a>b) swap(a,b); printf("Case %d: ", i); printf("%dn", cal(b) - cal(--a)); } return 0; }