Algorithm note _077: Blue Bridge cup practice K good number (Java)

Directory

1 Problem Description

2 Solutions

  1 problem description Problem Description

If an arbitrarily contiguous two-bit in the K-binary representation of a natural number n is not an adjacent number, then we say that this number is a K-good number. Ask for the number of K good numbers in the L-bit K-binary number. For example k = 4,l = 2, all k good numbers are 11, 13, 20, 22, 30, 31, 33 total 7. Since this is a large number, please output it to 1000000007 after the modulo value.

Input Format

The input contains two positive integers, K and L.

output Formatoutputs an integer that represents the value after which the answer is modulo 1000000007. Sample Input4 2Sample Output7data size and conventions

For 30% of data, KL <= 106;

For 50% data, K <=, L <= 10;

For 100% of data, 1 <= k,l <= 100.

  2 Solutions

This paper mainly examines the application of dynamic planning ideas.

The specific code is as follows:

ImportJava.util.Scanner; Public classMain { Public Static intMoD = 1000000007;  Public int[] DP =New int[102] [102];//dp[3][4] = num indicates that the 3rd digit size in the L-bit K-decimal number is 4, so that the 3-digit number is in num case         Public voidPrintresult (intKintL) { for(inti = 0;i < k;i++) dp[1][i] = 1;//target number lowest bitInitialize to 0~k-1 in turn, with each number appearing only once         for(inti = 2;i <= l;i++) {//the position of the number, the highest bit is L, the lowest bit is 1             for(intj = 0;j < k;j++) {                   for(intF = 0;f < k;f++) {                    if(F-1! = J && F + 1! =j) {Dp[i][j]+ = Dp[i-1][f]; DP[I][J]%=MoD; }                }            }        }        intsum = 0;  for(inti = 1;i < k;i++) {//removal of the highest bit of 0Sum + =Dp[l][i]; Sum%=MoD;        } System.out.println (sum); }         Public Static voidMain (string[] args) {main test=NewMain (); Scanner in=NewScanner (system.in); intK =In.nextint (); intL =In.nextint ();    Test.printresult (K, L); }}

Resources:

1. algorithm Training k good number

Algorithm note _077: Blue Bridge cup practice K good number (Java)