Adjacent Bit Counts HDU - 3284 [DP]
| <marquee width="600"> Fighting!~~ </marquee> |
Adjacent Bit CountsTime Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 497 Accepted Submission(s): 414 Problem Description For a string of n bits x 1, x 2, x 3, …, x n, the adjacent bit count of the string ( AdjBC(x)) is given by x1*x2 + x2*x3 + x3*x4 + … + xn-1*xn which counts the number of times a 1 bit is adjacent to another 1 bit. For example: AdjBC(011101101) = 3 AdjBC(111101101) = 4 AdjBC(010101010) = 0 Write a program which takes as input integers n and k and returns the number of bit strings x of n bits (out of 2 n) that satisfy AdjBC(x) = k. For example, for 5 bit strings, there are 6 ways of getting AdjBC(x) = 2: 11100, 01110, 00111, 10111, 11101, 11011 Input The first line of input contains a single integer P, (1 ≤ P ≤ 1000), which is the number of data sets that follow. Each data set is a single line that contains the data set number, followed by a space, followed by a decimal integer giving the number (n) of bits in the bit strings, followed by a single space, followed by a decimal integer (k) giving the desired adjacent bit count. The number of bits (n) will not be greater than 100 and the parameters n and k will be chosen so that the result will fit in a signed 32-bit integer. Output For each data set there is one line of output. It contains the data set number followed by a single space, followed by the number of n-bit strings with adjacent bit count equal to k. Sample Input 101 5 22 20 83 30 174 40 245 50 376 60 527 70 598 80 739 90 8410 100 90 Sample Output 1 62 634263 18612254 1682125015 448747646 1609167 229373088 991679 1547610 23076518 Source Recommend zhuweicong 题意:ans=sigma (x[i]*x[i-1]) 其中xi只能为0或者1,问长度为n,ans==k有多少种情况? 思路: dp[n][k][num]代表以num为结尾,长度为n,和为k的方案数.那么很容易有如下状态转移方程 dp[n][k][1]=dp[n-1][k][0]+dp[n-1][k-1][1]; dp[n][k][0]=dp[n-1][k][1]+dp[n-1][k][0]; |
查看30道真题和解析
投递字节跳动等公司8个岗位