zoj 3149 Breadtree

D -Breadtree

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Time Limit:1000MS    Memory Limit:32768KB     64bit IO Format:%lld & %llu

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Description

Breadtree is a kind of tree that produces bread. At its first year, a breadtree is only a node with a bread of weight 0 on this node which is also called zeronode. Every year after that, the weight of bread on each node of the tree will increase by 1, and another branch with a zeronode will grow at the end of each node. However, there is a limit of branches on each node. That is, when the number of branches of a node reaches the limit, there won't be any more branches, but the weight of its bread will still increase. What's more, a breadtree remains unchanged when the total weight of bread is larger than 1234567890.

Input

There are two integers N and K on each line. N is a positive integer fit in signed 32-bit integer. K is a non-negative integer fit in signed 32-bit integer. An N equals to 0 signals the end of input, which should not be processed.

Output

Output the total weight of bread on a breadtree with branches limit K in the N-th year in a line for each case.

Sample Input

10000 0101 110 21221 1280 0

Sample Output

999950502212147483647

题意:

树上有节点，节点上有面包，节点每天分出一个分支（到达k后不再分），节点上面的面包每天增重1（到达1234567890后不增），给出n天和k，问第n天面包总重。（n、k都为32为整数）

思路：

开始想的是用一个dp[i]表示面包重为 i 的节点个数，一个sum[i]表示其前缀和，然后模拟树的伸张过程，复杂度有点高TLE了。

正确的思路为：dp[i]表示第i年的总重量（可将一开始看做第0年），则dp[0]=0, 在第i年根重 i ，其余子树重量为第(i-1)年..第(i-k)年的重量和，用一个sum[i]维护，然后直接循环就好了，注意k=0的特判就好了。

代码：

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <cmath>#include <string>#include <map>#include <stack>#include <vector>#include <set>#include <queue>#pragma comment (linker,"/STACK:102400000,102400000")#define maxn 100005#define MAXN 16005#define mod 1000000000#define INF 0x3f3f3f3f#define pi acos(-1.0)#define eps 1e-6typedef long long ll;using namespace std;ll n,m,k,ans,cnt,tot,flag;ll dp[maxn],sum[maxn];ll xx=1234567890;ll solve(){    ll i,j,d,t;    dp[0]=sum[0]=0;    for(i=1;i<=n;i++)    {        dp[i]=i+sum[i-1]-sum[max(0LL,i-k-1)];        sum[i]=sum[i-1]+dp[i];        if(dp[i]>xx) return dp[i];    }    return dp[n];}int main(){    ll i,j,t;    while(scanf("%lld%lld",&n,&k),n|k)    {        n--;        if(k==0)        {            printf("%lld\n",min(n,xx+1));            continue ;        }        ans=solve();        printf("%lld\n",ans);    }    return 0;}/*10000 0101 110 21221 1280 0*/