hdu 1545 01-K Code

01-K Code

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 406    Accepted Submission(s): 96


Problem Description
Consider a code string S of N symbols, each symbol can only be 0 or 1. In any consecutive substring of S, the number of 0's differs from the number of 1's by at most K. How many such valid code strings S are there? 

For example, when N is 4, and K is 3, there are two invalid codes: 0000 and 1111. 
 

Input
The input consists of several test cases. For each case, there are two positive integers N and K in a line.

N is in the range of [1, 62].

K is in the range of [2, 5].
 

Output
Output the number of valid code strings in a line for each case.
 

Sample Input
1 2 4 3
 

Sample Output
2 14
 


分析:dp[i][j][k] 表示遍历到第i位(从1开始),当前0-1的最小值为j,0-1的最大值为k,可知j的最大值为0,k的最小值为0;
            dp[0][0][0]表示空串
转移方程:dp[i+1][min(j+1,0)][k+1]+=dp[i][j][k];//第i+1位添0
                    dp[i+1][j-1][max(k-1,0)]+=dp[i][j][k];//第i+1位添1
由于j可能为负数,故加一个偏移值5
#include<cstdio>
#include<cstring>
#define ll __int64
const int W=5;
int n,k;
int max(int a,int b){return a>b?a:b;}
int min(int a,int b){return a<b?a:b;}
ll dp[63][10][10];
int main(){
	int i,j,p;
	while(~scanf("%d%d",&n,&k)){
		memset(dp,0,sizeof(dp));
		dp[0][W][W]=1;
		for(i=0;i<n;i++){
			for(j=-k+W;j<=W;j++)for(p=W;p<=k+W;p++){
				dp[i+1][min(j+1,W)][p+1]+=dp[i][j][p];
				dp[i+1][j-1][max(p-1,W)]+=dp[i][j][p];
			}
		}
		ll ans=0;
		for(i=-k+W;i<=W;i++)for(j=W;j<=k+W;j++)ans+=dp[n][i][j];
		printf("%I64d\n",ans);
	}
	return 0;
}


### HDU OJ 2089 Problem Solution and Description The problem titled "不高兴的津津" (Unhappy Jinjin) involves simulating a scenario where one needs to calculate the number of days an individual named Jinjin feels unhappy based on certain conditions related to her daily activities. #### Problem Statement Given a series of integers representing different aspects of Jinjin's day, such as homework completion status, weather condition, etc., determine how many days she was not happy during a given period. Each integer corresponds to whether specific events occurred which could affect her mood positively or negatively[^1]. #### Input Format Input consists of multiple sets; each set starts with two positive integers n and m separated by spaces, indicating the total number of days considered and types of influencing factors respectively. Following lines contain details about these influences over those days until all cases are processed when both numbers become zero simultaneously. #### Output Requirement For every dataset provided, output should be formatted according to sample outputs shown below: ```plaintext Case k: The maximum times of appearance is x, the color is c. ``` Where `k` represents case index starting from 1, while `x` stands for frequency count and `c` denotes associated attribute like colors mentioned earlier but adapted accordingly here depending upon context i.e., reasons causing unhappiness instead[^2]. #### Sample Code Implementation Below demonstrates a simple approach using Python language to solve this particular challenge efficiently without unnecessary complexity: ```python def main(): import sys input = sys.stdin.read().strip() datasets = input.split('\n\n') results = [] for idx, ds in enumerate(datasets[:-1], start=1): data = list(map(int, ds.strip().split())) n, m = data[:2] if n == 0 and m == 0: break counts = {} for _ in range(m): factor_counts = dict(zip(data[2::2], data[3::2])) for key, value in factor_counts.items(): try: counts[key] += value except KeyError: counts[key] = value max_key = max(counts, key=lambda k:counts[k]) result_line = f'Case {idx}: The maximum times of appearance is {counts[max_key]}, the reason is {max_key}.' results.append(result_line) print("\n".join(results)) if __name__ == '__main__': main() ```
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