codeforce474D_组合

题目链接：http://codeforces.com/contest/474/problem/D

题目大意：用RW组成字符串，要求w的个数要k个连续出现，R任意，问字符串长度为[a, b]时，字符串的种类有多少

思路：dp[i] = dp[i - 1] + dp[i - k]

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define LL long long
using namespace std;

const int N = 1e5;
const int mod = 1e9 + 7;
LL num[N + 10], abc[N + 10];
int t, k, a, b;
void find()
{
    for(int i = 1; i < k; i++)
        num[i] = 1;
    num[0] = 0;
    num[k] = 2;
    for(int i = k + 1; i <= N; i++)
        num[i] = (num[i - 1] + num[i - k]) % mod;//num[i]表示长度为i时的种类有多少
    abc[0] = 0;
    for(int i = 1; i <= N; i++)
        abc[i] = (abc[i - 1] + num[i]) % mod;//长度为[1, i]时的种数
}
int main()
{
    scanf("%d %d", &t, &k);
    find();
    while(t--)
    {
        scanf("%d %d", &a, &b);
        LL res = (abc[b] - abc[a - 1]) % mod;
        if(res < 0)
            res = res + mod;
        printf("%I64d
", res);
    }
    return 0;
}