NYOJ - 715 - Adjacent Bit Counts --第六届河南省程序设计大赛 (DP!!)
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Adjacent Bit Counts
- 描述
For a string of n bits x1, x2, x3, …, xn, the adjacent bit count of the string is given by fun(x) = x1*x2 + x2*x3 + x3*x 4 + … + xn-1*x n
which counts the number of times a 1 bit is adjacent to another 1 bit. For example:Fun(011101101) = 3
Fun(111101101) = 4
Fun (010101010) = 0
Write a program which takes as input integers n and p and returns the number of bit strings x of n bits (out of 2ⁿ) that satisfy Fun(x) = p.
For example, for 5 bit strings, there are 6 ways of getting fun(x) = 2:
11100, 01110, 00111, 10111, 11101, 11011
- 输入
- On the first line of the input is a single positive integer k, telling the number of test cases to follow. 1 ≤ k ≤ 10 Each case is a single line that contains a decimal integer giving the number (n) of bits in the bit strings, followed by a single space, followed by a decimal integer (p) giving the desired adjacent bit count. 1 ≤ n , p ≤ 100
- 输出
- For each test case, output a line with the number of n-bit strings with adjacent bit count equal to p.
- 样例输入
2
5 2
20 8
- 样例输出
663426
- 来源
- 第六届河南省程序设计大赛
简单DP题。。
定义数组dp[105][105][2];其中dp[i][j][0]代表第j位是0的时候长度为j的串组成值为i的串的种数,dp[i][j][1]代表
j位是1的时候长度为j的串组成值为i的串的种数,
容易看出dp[i][j][0]=dp[i][j-1][0]+dp[i][j-1][1]; dp[i][j][1]=dp[i-1][j-1][1]+dp[i][j-1][0];
所以,初始化先把f的值全部赋成0.然后dp[0][1][0]=dp[0][1][1]=1;然后再求出所有dp[0][j][0]和dp[0][j][1]的值;
之后两个for循环就ok了!AC代码:
#include <cstdio>#include <cstring>#include <algorithm>using namespace std;long long dp[105][105][2];void init(){memset(dp, 0, sizeof(dp));dp[0][1][0] = 1;dp[0][1][1] = 1;for(int i=2; i<=100; i++){dp[0][i][0] = dp[0][i-1][0] + dp[0][i-1][1];dp[0][i][1] = dp[0][i-1][0];}for(int i=1; i<=100; i++)for(int j=2; j<=100; j++){dp[i][j][0] = dp[i][j-1][1] + dp[i][j-1][0];dp[i][j][1] = dp[i-1][j-1][1] + dp[i][j-1][0];}} int main(){init();int k, n, p;scanf("%d", &k);while(k--){scanf("%d %d", &n, &p);printf("%I64d\n", dp[p][n][0]+dp[p][n][1]);}return 0;}
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