【题解】P6218 [USACO06NOV] Round Numbers S

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洛谷 P6218 [USACO06NOV] Round Numbers S

洛谷 P6218 [USACO06NOV] Round Numbers S 题目描述如果一个正整数的二进制表示中,\(0\) 的数目不小于 \(1\) 的数目,那么它就被称为「圆数」. 例如,\(9\) 的二进制表示为 \(10011001\),其中有 \(2\) 个 \(0\) 与 \(2\) 个 \(1\).因此,\(9\) 是一个「圆数」. 请你计算,区间 \([l,r]\) 中有多少个「圆数」. 输入格式一行,两个整数 \(l,r\). 输出格式一行,一个整数,表示区间 \([l,…

【题解】P6218 [USACO06NOV] Round Numbers S

题目传送门这是一道数位DP. 令 \(dp_{i,j,k}\) 为满足由 \(i\) 位组成,且其中有 \(j\) 个1,第 i 位(从右往左数)为 \(k\) 的二进制数的数量. 可以得出状态转移方程: \(dp_{i,j,0}=dp_{i-1,j,1}+dp_{i-1,j,0}\;(2\le i,0\le j< i)\) \(dp_{i,j,1}=dp_{i-1,j-1,0}+dp_{i-1,j-1,1}\;(2\le i,0<j\le i)\) 边界:\(dp_{1,0,0}=1,dp…

POJ 3252 Round Numbers 数学题解

Description The cows, as you know, have no fingers or thumbs and thus are unable to play Scissors, Paper, Stone' (also known as 'Rock, Paper, Scissors', 'Ro, Sham, Bo', and a host of other names) in order to make arbitrary decisions such as who gets…

题解【POJ3252】Round Numbers

Description The cows, as you know, have no fingers or thumbs and thus are unable to play Scissors, Paper, Stone' (also known as 'Rock, Paper, Scissors', 'Ro, Sham, Bo', and a host of other names) in order to make arbitrary decisions such as who gets…

【BZOJ1662】[Usaco2006 Nov]Round Numbers 圆环数数位DP

[BZOJ1662][Usaco2006 Nov]Round Numbers 圆环数 Description 正如你所知,奶牛们没有手指以至于不能玩"石头剪刀布"来任意地决定例如谁先挤奶的顺序.她们甚至也不能通过仍硬币的方式. 所以她们通过"round number"竞赛的方式.第一头牛选取一个整数,小于20亿.第二头牛也这样选取一个整数.如果这两个数都是 "round numbers",那么第一头牛获胜,否则第二头牛获胜. 如果一个正整数N的二…

[BZOJ1662][POJ3252]Round Numbers

[POJ3252]Round Numbers 试题描述 The cows, as you know, have no fingers or thumbs and thus are unable to play Scissors, Paper, Stone' (also known as 'Rock, Paper, Scissors', 'Ro, Sham, Bo', and a host of other names) in order to make arbitrary decisions s…

Round Numbers(组合数学)

Round Numbers Time Limit: 2000MS Memory Limit: 65536K Total Submissions: 10484 Accepted: 3831 Description The cows, as you know, have no fingers or thumbs and thus are unable to play Scissors, Paper, Stone' (also known as 'Rock, Paper, Scissors', 'Ro…