poj 2282 The Counting Problem
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The Counting Problem
Time Limit: 3000MS Memory Limit: 65536KB 64bit IO Format: %I64d & %I64u
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Description
Given two integers a and b, we write the numbers between a and b, inclusive, in a list. Your task is to calculate the number of occurrences of each digit. For example, if a = 1024 and b = 1032, the list will be
1024 1025 1026 1027 1028 1029 1030 1031 1032
there are ten 0's in the list, ten 1's, seven 2's, three 3's, and etc.
there are ten 0's in the list, ten 1's, seven 2's, three 3's, and etc.
Input
The input consists of up to 500 lines. Each line contains two numbers a and b where 0 < a, b < 100000000. The input is terminated by a line `0 0', which is not considered as part of the input.
Output
For each pair of input, output a line containing ten numbers separated by single spaces. The first number is the number of occurrences of the digit 0, the second is the number of occurrences of the digit 1, etc.
Sample Input
1 1044 497346 5421199 17481496 14031004 5031714 1901317 8541976 4941001 19600 0
Sample Output
1 2 1 1 1 1 1 1 1 185 185 185 185 190 96 96 96 95 9340 40 40 93 136 82 40 40 40 40115 666 215 215 214 205 205 154 105 10616 113 19 20 114 20 20 19 19 16107 105 100 101 101 197 200 200 200 200413 1133 503 503 503 502 502 417 402 412196 512 186 104 87 93 97 97 142 196398 1375 398 398 405 499 499 495 488 471294 1256 296 296 296 296 287 286 286 247
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题意:
统计从a数到b中,数过的数里面各个位置上0-9的个数。
分析:
从这道题上更体现了数学的魅力。。。
先不论哪个方法,都是找一个f(n),统计从1数到n的情况,然后再f(b)-f(a-1)出结果。
f(2980)可以和f(298)建立递推(实际的时候用f(297)更好一点)。注意这里需要建立一个“乘子”,一开始为1,每次递推一层就*10,然后累加到0-9的记录上。
呵呵,没啥说的 。我整理的模版:
Problem: D User: sdau_09_zysMemory: 164 KB Time: 16 MSLanguage: C++ Result: AcceptedPublic:
#include <iostream>#include <string>using namespace std;int a,b;int ansa[10],ansb[10];void count_digits(int s,int ans[],int times=1)//{ int i,d,p; if (s <= 0)return ; d = s % 10; p = s / 10; for (i = 1;i <= d;i ++)ans[i] += times; while(p > 0) { ans[p % 10] += (d + 1) * times; p = p / 10; } for (i = 0;i <= 9;i ++)ans[i] += times * (s / 10); times *= 10; count_digits((s / 10)-1,ans,times); return ;}int main(){ int i,j;while(scanf("%d%d",&a,&b) != EOF && a + b > 0){ memset(ansb,0,sizeof(ansb)); memset(ansa,0,sizeof(ansa)); if (a >= b) { swap(a,b); } a --; if (b > a) { count_digits(b,ansb); count_digits(a,ansa); } for(i=0;i<10;i++) { printf("%d%c",ansb[i]-ansa[i],i==9?'\n':' '); } }return 0;}
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