【动态规划】洛谷_1077 摆花

题意

给出$N$种花，其中第$i$种花的数量不能超过$a_i$个，求一共摆$M$个花的方案数模1000007。

思路

动态规划。设$f[i][j]$为前$i$种花摆$j$个的方案数，可得动态转移方程：
f[i][j]+=f[i][j−k]{k&lt;=a[i]}f[i][j]+=f[i][j-k]\{k&lt;=a[i]\}f[i][j]+=f[i][j−k]{k<=a[i]}

代码

#include<cstdio>

int N, M;
int a[1001], f[1001][1001];

int main() {
	scanf("%d %d", &N, &M);
	for (int i = 1; i <= N; i++) scanf("%d", &a[i]);
	f[0][0] = 1;
	for (int i = 1; i <= N; i++)
		for (int j = 0; j <= M; j++)
			for (int k = 0; k <= a[i]; k++)
				f[i][j] = (f[i][j] + f[i - 1][j - k]) % 1000007;
	printf("%d", f[N][M]);
}