UVA10943 How do you add?

题意： 求用K个不超过N的非负整数组成N的组合有多少种。

思路：瞎求。DP或者数论都行。本弱用了自顶向下的带备忘的DP，捡方便。设F（N，K）为答案，
那么F（N，K）=Sum(F（i，K-1）,0<=i<=N)

代码：

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <cmath>#include <queue>#include <vector>#define DB puts("**de**")#define WATCH(a) cout << a << endl#define REP(i,n) for(int i=0;i<n;++i)#define FF(i,a,b) for(int i=a;i<=b;++i)#define CL(a,b) memset(a,b,sizeof(a))#define LL long long#define FD(i,a,b) for(int i=a;i>=b;--i)#define pb push_back#define pr pair<int,int >//#pragma comment(linker, "/STACK:1024000000,1024000000")using namespace std;//constconst int MAXN=1e6+5;const int INF=0x3f3f3f3f;//struct//global//vector<int> edge[MAXN];int ti1,ti2,ti3,n,m,t,k,ncase,fa[105][105];double td1,td2,td3;char tc1,tc2;//funcLL f(int n,int k){    if(!k)        return 0;    if(fa[n][k])return fa[n][k];    if(k==1)    {        return 1;    }    if(k==2)    {        fa[n][k]=n+1;        return n+1;    }    LL tp=0;    for(int i=0;i<=n;i++)    {        tp+=f(n-i,k-1);        tp=tp%1000000;    }    fa[n][k]=tp%1000000;    return tp;}int main(){    //freopen("C:\\Users\\inkysakura\\Desktop\\testdata.txt","r",stdin);    while(scanf("%d %d",&n,&k),n||k)    {        cout << f(n,k)%1000000<<endl;    }    return 0;}