UVa 1640 The Counting Problem (数学,区间计数)

题意:给定两个数m, n,求从 m 到 n 中0-9数字各出现了多少次。

析:看起来挺简单的,其实并不好做,因为有容易想乱了。主要思路应该是这样的,分区间计数,先从个位进行计,一步一步的计算过来。都从0开始,最后用大数减小数的即可。

举个例子吧,容易理解。比如0-1234。

先计算个位数字,有1-4,然后计算123各出现了5次,注意是这里是5次,不是4次,因为我们要加上那个0,然后就剩下那个1230了,我们想那么现在个位数从开始到这,

重复了123次,然后再进行下一位,依次进行,直到0.

代码如下:

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <cstdio>
#include <string>
#include <functional>
#include <cstdlib>
#include <cmath>
#include <iostream>
#include <cstring>
#include <set>
#include <queue>
#include <algorithm>
#include <vector>
#include <deque>
#include <map>
#include <cctype>
#include <stack>
#include <sstream>
#include <cstdlib>
#define freopenr freopen("in.txt", "r", stdin)
#define freopenw freopen("out.txt", "w", stdout)
using namespace std;
#include <ctime> typedef long long LL;
typedef pair<int, int> P;
const int INF = 0x3f3f3f3f;
const LL LNF = 0x3f3f3f3f3f;
const double inf = 0x3f3f3f3f3f3f;
const double PI = acos(-1.0);
const double eps = 1e-8;
const int maxn = 1e5 + 5;
const int mod = 1e9 + 7;
const char *mark = "+-*";
const int dr[] = {-1, 0, 1, 0};
const int dc[] = {0, 1, 0, -1};
int n, m;
inline int Min(int a, int b){ return a < b ? a : b; }
inline int Max(int a, int b){ return a > b ? a : b; }
inline LL Min(LL a, LL b){ return a < b ? a : b; }
inline LL Max(LL a, LL b){ return a > b ? a : b; }
int ans[15]; void dfs(int n, int m, int ok){
if(-1 == n) return ;
int x = n / 10;
int y = n % 10;
for(int i = 1; i <= y; ++i) ans[i] += ok * m;
for(int i = 0; i < 10; ++i) ans[i] += ok * m * x;
int tmp = x;
while(tmp){
ans[tmp%10] += ok * (y+1) * m;
tmp /= 10;
}
dfs(x-1, m*10, ok);
} int main(){
while(scanf("%d %d", &m, &n) == 2){
if(!m && !n) break;
if(m < n) swap(m, n);
--n;
memset(ans, 0, sizeof ans);
dfs(m, 1, 1);
dfs(n, 1, -1); for(int i = 0; i < 10; ++i){
if(i) putchar(' ');
printf("%d", ans[i]);
}
printf("\n");
}
return 0;
}

  

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