UVA - 357 - Let Me Count The Ways （动态规划）

UVA - 357

Let Me Count The Ways

Time Limit: 3000MS

Memory Limit: Unknown

64bit IO Format: %lld & %llu

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Description

After making a purchase at a large department store, Mel's change was 17 cents. He received 1 dime, 1 nickel, and 2 pennies. Later that day, he was shopping at a convenience store. Again his change was 17 cents. This time he received 2 nickels and 7 pennies. He began to wonder ' "How many stores can I shop in and receive 17 cents change in a different configuration of coins? After a suitable mental struggle, he decided the answer was 6. He then challenged you to consider the general problem.

Write a program which will determine the number of different combinations of US coins (penny: 1c, nickel: 5c, dime: 10c, quarter: 25c, half-dollar: 50c) which may be used to produce a given amount of money.

Input

The input will consist of a set of numbers between 0 and 30000 inclusive, one per line in the input file.

Output

The output will consist of the appropriate statement from the selection below on a single line in the output file for each input value. The number m is the number your program computes, n is the input value.

There are mways to produce ncents change.

There is only 1 way to produce ncents change.

Sample input

17 
11
4

Sample output

There are 6 ways to produce 17 cents change. 
There are 4 ways to produce 11 cents change. 
There is only 1 way to produce 4 cents change.

Source

Root :: Competitive Programming: Increasing the Lower Bound of Programming Contests (Steven & Felix Halim) :: Chapter 3. Problem Solving Paradigms :: Dynamic Programming ::  Coin Change - Classical
Root :: AOAPC I: Beginning Algorithm Contests (Rujia Liu) ::  Volume 5. Dynamic Programming 
Root :: Competitive Programming 2: This increases the lower bound of Programming Contests. Again (Steven & Felix Halim) :: Problem Solving Paradigms :: Dynamic Programming ::  Coin Change (CC)
Root :: Competitive Programming 3: The New Lower Bound of Programming Contests (Steven & Felix Halim) :: Problem Solving Paradigms :: Dynamic Programming ::  Coin Change (CC)

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AC代码：

#include <cstdio>
#include <cstring>
#include <algorithm>
#define LL long long
using namespace std;

int val[5] = {1, 5, 10, 25, 50};
LL dp[30005][5];
int n;

void init() {
	memset(dp, 0, sizeof(dp));
	for(int i = 0; i < 5; i++) dp[0][i] = 1;
	for(int i = 1; i < 30005; i++) {
		for(int j = 0; j < 5; j++) {
			if(i >= val[j]) dp[i][j] = dp[i - val[j]][j];
			if(j != 0) dp[i][j] += dp[i][j - 1];
		}
	}
}

int main() {
	init();
	while(scanf("%d", &n) != EOF) {
		if(dp[n][4] == 1) printf("There is only 1 way to produce %d cents change.\n", n);
		else printf("There are %lld ways to produce %d cents change.\n", dp[n][4], n);
	}
	return 0;
}