The sequence of integers a1,a2,…,ak is called a good array if a1=k?1 and a1>0. For example, the sequences [3,?1,44,0],[1,?99] are good arrays, and the sequences [3,7,8],[2,5,4,1],[0]
— are not.
A sequence of integers is called good if it can be divided into a positive number of good arrays. Each good array should be a subsegment of sequence and each element of the sequence should belong to exactly one array. For example, the sequences [2,?3,0,1,4]
, [1,2,3,?3,?9,4] are good, and the sequences [2,?3,0,1], [1,2,3,?3?9,4,1]
— are not.
For a given sequence of numbers, count the number of its subsequences that are good sequences, and print the number of such subsequences modulo 998244353.
Input
The first line contains the number n (1≤n≤103)
— the length of the initial sequence. The following line contains n integers a1,a2,…,an (?109≤ai≤109)
— the sequence itself.
Output
In the single line output one integer — the number of subsequences of the original sequence that are good sequences, taken modulo 998244353.
Examples
Input
32 1 1
Output
2
Input
41 1 1 1
Output
7
Note
In the first test case, two good subsequences — [a1,a2,a3]
and [a2,a3]
.
In the second test case, seven good subsequences — [a1,a2,a3,a4],[a1,a2],[a1,a3],[a1,a4],[a2,a3],[a2,a4]
and [a3,a4].
题意 ： 给你一串数字，并按照题目叙述，给出一个好序列的定义，并且任意个好序列之间可以合并起来，问最终好序列的个数。
思路分析：
dp[i] 表示以i位置开始的序列的最优解，倒着推一下就可以了， dp[i] += dp[j-i][i]*dp[j+1] (i+a[i] <= j <= n)
代码示例：
ll n;
ll a[1005];
ll c[1005][1005];
void init(){
for(ll i = 1; i <= 1000; i++){
c[i][0] = c[i][i] = 1;
for(ll j = 1; j < i; j++){
c[i][j] = (c[i-1][j]+c[i-1][j-1])%mod;
}
}
}
ll dp[1005];
int main() {
//freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
init();
cin >> n;
for(ll i = 1; i <= n; i++){
scanf("%lld", &a[i]);
}
dp[n+1] = 1;
ll ans = 0;
for(ll i = n-1; i >= 1; i--){
ll p = i+a[i];
if (a[i] <= 0) continue;
for(ll j = p; j <= n; j++){
dp[i] += (c[j-i][a[i]]*dp[j+1])%mod;
dp[i] %= mod;
}
ans += dp[i];
ans %= mod;
}
printf("%lld\n", ans);
return 0;
}
原文地址：https://www.cnblogs.com/ccut-ry/p/9249354.html