zoukankan      html  css  js  c++  java
  • Milliard Vasya's Function-Ural1353动态规划

    Time limit: 1.0 second Memory limit: 64 MB

    Vasya is the beginning mathematician. He decided to make an important contribution to the science and to become famous all over the world. But how can he do that if the most interesting facts such as Pythagor’s theorem are already proved? Correct! He is to think out something his own, original. So he thought out the Theory of Vasya’s Functions. Vasya’s Functions (VF) are rather simple: the value of the Nth VF in the point S is an amount of integers from 1 to N that have the sum of digits S. You seem to be great programmers, so Vasya gave you a task to find the milliard VF value (i.e. the VF with N = 109) because Vasya himself won’t cope with the task. Can you solve the problem?
    Input
    Integer S (1 ≤ S ≤ 81).
    Output
    The milliard VF value in the point S.
    Sample

    input output
    1 10

    Problem Author: Denis Musin
    Problem Source: USU Junior Championship March’2005

    计算[0,10^9]之间有多少各数的各位之和为s,Dp[i][j]表示前i位中和为j的个数,则对于第i为k是它的个数为Dp[i][j]+=Dp[i-1][j-k].
    所以递推式就出来了。

    #include <cstdio>
    #include <cstring>
    #include <cstdlib>
    #include <cmath>
    #include <iostream>
    #include <algorithm>
    
    using namespace std;
    
    int Dp[10][83];
    
    int main()
    {
        memset(Dp,0,sizeof(Dp));
    
        for(int i = 0;i<=9;i++)//初始化第一位
        {
            Dp[1][i]=1;
        }
        for(int i=2;i<=9;i++)
        {
            for(int j=0;j<=81;j++)
            {
                Dp[i][j]=  Dp[i-1][j];
            }
            for(int j=0;j<=81;j++)
            {
                for(int s = 1;s<=9&&s<=j;s++)
                {
                    Dp[i][j] +=Dp[i-1][j-s];
                }
            }
        }
        int n;
        Dp[9][1]++;//因为1000000000计算不到,所以要加上
        while(~scanf("%d",&n))
        {
            printf("%d
    ",Dp[9][n]);
        }
        return 0;
    }
    
  • 相关阅读:
    ipad mini2 ios7 磁盘分析文件夹大小
    Qt设置horizontal line 和vertical line 的颜色
    剖析QMenu & Qt完全定制化菜单
    Django--Auth 模块
    Django --ORM常用的字段和参数 多对多创建形式
    Django--Ajax 提交
    Django--CSRF 跨站请求伪造
    Django--Session 操作
    css
    pycharm格式化代码 常用快捷键
  • 原文地址:https://www.cnblogs.com/juechen/p/5255864.html
Copyright © 2011-2022 走看看