USACO 2.2 Subset Sums (DP动态规划)

#include <stdio.h>
#define DEBUG 1
#define TESTCASES 9
#define MAX 39

//partitions[preNums][sum]表示在前preNums个数中选取，使总和为sum的方案数
//注意：第preNums个数,也就是最后一个数，可以选或者不选
//要long long 才不溢出
long long partitions[MAX + 1][800];
int n;

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

scanf("%d", &n);

int total = ((1 + n) * n) >> 1;
if (total & 1){
printf("0\n");
#if DEBUG
continue;
#else
return 0；
#endif
}
total = total >> 1;

partitions[1][1] = 1;
partitions[1][0] = 1;
int max = 1;
int preNums, sum;
for (preNums = 2; preNums <= n; preNums++){
int lastNum = preNums;
max += lastNum;
int limitSum = total > max ? total : max;
for (sum = 0; sum <= limitSum ; sum++){
if (sum < lastNum)
partitions[preNums][sum] = partitions[preNums - 1][sum];
else
partitions[preNums][sum] = partitions[preNums - 1][sum] + partitions[preNums - 1][sum - lastNum];
}
}

printf("%d\n", partitions
[total] >> 1);

#if DEBUG
}
#endif
return 0;
}