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  • K-based Numbers

    K-based Numbers

    Time Limit:1000MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u

    Description

    Let’s consider K-based numbers, containing exactly N digits. We define a number to be valid if its K-based notation doesn’t contain two successive zeros. For example:
    • 1010230 is a valid 7-digit number;
    • 1000198 is not a valid number;
    • 0001235 is not a 7-digit number, it is a 4-digit number.
    Given two numbers N and K, you are to calculate an amount of valid K based numbers, containing N digits.
    You may assume that 2 ≤ K ≤ 10; N ≥ 2; N + K ≤ 18.

    Input

    The numbers N and K in decimal notation separated by the line break.

    Output

    The result in decimal notation.

    Sample Input

    inputoutput
    2
    10
    
    90
    

    例如:n = 3;

      dp[3] = 

          1, 2, 3 + (1, 2, 3 + 0, 1, 2, 3); k*dp[2];

          +

          10, 20, 30 + 1, 2, 3; k*dp[1];

    #include<cstdio>
    #include<cstring>
    #include<algorithm>
    using namespace std;
    int dp[15];
    int main(){
        int n, k;
        scanf("%d%d", &n, &k);
        dp[1] = k-1;
        dp[2] = k*(k-1);
        for(int i = 3; i <= n; i++){
            dp[i] = (k-1)*(dp[i-1] + dp[i-2]);
        }
        printf("%d
    ",dp[n]);
        return 0;
    }
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  • 原文地址:https://www.cnblogs.com/ACMessi/p/4896289.html
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