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  • D. Flowers Codeforces Round #271(div2)

    D. Flowers
    time limit per test
    1.5 seconds
    memory limit per test
    256 megabytes
    input
    standard input
    output
    standard output

    We saw the little game Marmot made for Mole's lunch. Now it's Marmot's dinner time and, as we all know, Marmot eats flowers. At every dinner he eats some red and white flowers. Therefore a dinner can be represented as a sequence of several flowers, some of them white and some of them red.

    But, for a dinner to be tasty, there is a rule: Marmot wants to eat white flowers only in groups of size k.

    Now Marmot wonders in how many ways he can eat between a and b flowers. As the number of ways could be very large, print it modulo1000000007 (109 + 7).

    Input

    Input contains several test cases.

    The first line contains two integers t and k (1 ≤ t, k ≤ 105), where t represents the number of test cases.

    The next t lines contain two integers ai and bi (1 ≤ ai ≤ bi ≤ 105), describing the i-th test.

    Output

    Print t lines to the standard output. The i-th line should contain the number of ways in which Marmot can eat between ai and bi flowers at dinner modulo 1000000007 (109 + 7).

    Sample test(s)
    input
    3 2
    1 3
    2 3
    4 4
    
    output
    6
    5
    5
    
    Note
    • For K = 2 and length 1 Marmot can eat (R).
    • For K = 2 and length 2 Marmot can eat (RR) and (WW).
    • For K = 2 and length 3 Marmot can eat (RRR), (RWW) and (WWR).
    • For K = 2 and length 4 Marmot can eat, for example, (WWWW) or (RWWR), but for example he can't eat (WWWR).


    状态转移方程 dp[i]=dp[i-1]+dp[i-k]。

    取模要特别注意。


    代码:
    #include <cstdio>
    #include <algorithm>
    #include <iostream>
    #include <cstring>
    const long long mod = 1000000007;
    const int maxn=100000;
    long long dp[maxn+100];
    long long sum[maxn+100];
    using namespace std;
    int main(){
        int n,k;
        memset(sum, 0, sizeof(sum));
        scanf("%d %d",&n,&k);
        sum[0]=0;
        dp[0]=1;
        for(int i=1;i<k;++i){
            dp[i]=1;
            sum[i]=sum[i-1]+dp[i];
        }
        for(int i=k;i<=maxn;++i){
            dp[i]=dp[i-1]+dp[i-k];
            dp[i]%=mod;
            sum[i]=sum[i-1]+dp[i];
            sum[i]%=mod;
        }
        int a,b;
        for(int i=0;i<n;++i){
            scanf("%d %d",&a,&b);
            printf("%I64d
    ",(sum[b]-sum[a-1]+mod)%mod);
        }
        return 0;
    }
    



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  • 原文地址:https://www.cnblogs.com/yfceshi/p/6743229.html
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