Va 674 Coin Change (DP), 674 coin

Va 674 Coin Change (DP), 674 coin

Suppose there are 5 types of coins: 50-cent, 25-cent, 10-cent, 5-cent, and 1-cent. we want to make changes with these coins for a given amount of money.

For example, if we have 11 cents, then we can make changes with one 10-cent coin and one 1-cent coin, two 5-cent coins and one 1-cent coin, one 5-cent coin and six 1-cent coins, or eleven 1-cent coins. so there are four ways of making changes for 11 cents with the above coins. note that we count that there is one way of making change for zero cent.

Write a program to find the total number of different ways of making changes for any amount of money in cents. Your program shocould be able to handle up to 7489 cents.

Input The input file contains any number of lines, each one consisting of a number for the amount of money in cents.

Output For each input line, output a line containing the number of different ways of making changes with the above 5 types of coins.

Sample Input

1126

Sample Output

413

Five coins with a nominal value must be exchanged for a certain amount of money:

#include<iostream>#include<cstdio>#include<cstring>#include<algorithm>#include<limits.h>typedef long long LL;using namespace std;int v[5]={1,5,10,25,50};int dp[100000];int main(){    int n;    while(~scanf("%d",&n))    {        memset(dp,0,sizeof(dp));        dp[0]=1;        for(int i=0;i<5;i++)        {            for(int j=v[i];j<=n;j++)               dp[j]+=dp[j-v[i]];        }        printf("%d\n",dp[n]);    }    return 0;}

Sha 10599 Robots (II) -- Chapter Dp of Liu rujia -- Interpretation of the standard process --

The biggest feature of this program is to store each target point into an array without creating an adjacent matrix.
Why is LIS required. This seems that the route is not obvious, and LIS can implement nlogn using stacks. In this case, you can perform a memory-based search to traverse the vertices with a large serial number and determine whether they are in the lower right corner.