USACO 2.3 Money Systems (DP 动态规划)

#include <stdio.h>
#define DEBUG 1
#define TESTCASES 9

//ways[coinageValueIndex][constructedMoney]表示考虑前coinageValueIndex种钱币凑成constructedMoney的数量的钱时的方案数，第coinageValueIndex种钱币可以选或者不选
//数组很大要声明为全局变量，如果声明为局部变量栈会溢出
long long ways[26][10001];

int main(){
#if DEBUG
int testCase;
for (testCase = 1; testCase <= TESTCASES; testCase++){
char inputFileName[20] = "inputX.txt";
inputFileName[5] = '1' +  (testCase - 1);
freopen(inputFileName, "r", stdin);
printf("\n#%d\n", testCase);
#endif

int typesOfCoins, moneyToConstruct;
scanf("%d%d", &typesOfCoins, &moneyToConstruct);

int coinageValueArray[26];
int coinageValueIndex;
for (coinageValueIndex = 1; coinageValueIndex <= typesOfCoins; coinageValueIndex++)
scanf("%d", &coinageValueArray[coinageValueIndex]);

int constructedMoney;
for (coinageValueIndex = 0; coinageValueIndex <= typesOfCoins; coinageValueIndex++)
for (constructedMoney = 0; constructedMoney <= moneyToConstruct; constructedMoney++)
if (constructedMoney == 0)
ways[coinageValueIndex][constructedMoney] = 1;
else
ways[coinageValueIndex][constructedMoney] = 0;

for (coinageValueIndex = 1; coinageValueIndex <= typesOfCoins; coinageValueIndex++)
for (constructedMoney = 1; constructedMoney <= moneyToConstruct; constructedMoney++)
if (constructedMoney < coinageValueArray[coinageValueIndex] )
ways[coinageValueIndex][constructedMoney] = ways[coinageValueIndex - 1][constructedMoney];
else
//ways[coinageValueIndex][constructedMoney - coinageValueArray[coinageValueIndex]]可以通过递增遍历constructedMoney的方式来优化ways空间成关于constructedMoney的一维数组,又因为当constructedMoney < coinageValueArray[coinageValueIndex]时，ways[coinageValueIndex][constructedMoney] = ways[coinageValueIndex - 1][constructedMoney]所以递增遍历constructedMoney的时候可以直接从constructedMoney = coinageValueArray[coinageValueIndex]开始遍历
ways[coinageValueIndex][constructedMoney] = ways[coinageValueIndex - 1][constructedMoney] +
ways[coinageValueIndex][constructedMoney - coinageValueArray[coinageValueIndex]];

printf("%lld\n", ways[typesOfCoins][moneyToConstruct]);

#if DEBUG
}
#endif
return 0;
}