所以我一直试图做一个子集求和问题的变体，我想用动态编程做。所以我的目标是，例如，输入
m = 25 // Target value
n = 7 // Size of input set
并将输入设置为例如{1, 3, 4, 6, 7, 10, 25}。所以想要的输出就像是
{1, 3, 4, 7, 10} and {25}.
这是代码
#include <stdio.h>
#include <stdlib.h>
int main()
{
// Get input sequence
int n = 7; // Size of input set
int m = 25; // Target value
int *S; // Input set
int **C; // Cost table
int i,j,potentialSum,leftover;
S=(int*) malloc((n+1)*sizeof(int));
C=malloc((m+1)*sizeof(int*));
for (int rows = 0; rows<=m; rows++) {
C[rows] = malloc((m+1)*sizeof(int));
}
if (!S || !C)
{
printf(" FAILED %d\n",__LINE__);
exit(0);
}
S[0] = 0;
S[1] = 1;
S[2] = 3;
S[3] = 4;
S[4] = 6;
S[5] = 7;
S[6] = 10;
S[7] = 25;
// Initialize table for DP
C[0][0]=0; // DP base case
// For each potential sum, determine the smallest index such
// that its input value is in a subset to achieve that sum.
for (potentialSum=1; potentialSum<=m; potentialSum ++)
{
for (j=1;j<=n;j++)
{
leftover=potentialSum-S[j]; // To be achieved with other values
if (leftover<0) // Too much thrown away
continue;
if (C[leftover][0] == (-1)) // No way to achieve leftover
continue;
if (C[leftover][0]<j) // Indices are included in
break; // ascending order.
}
C[potentialSum][0]=(j<=n) ? j : (-1);
}
// Output the input set
printf(" i S\n");
printf("-------\n");
for (i=0;i<=n;i++)
printf("%3d %3d\n",i,S[i]);
// Output the DP table
printf("\n\n i C\n");
printf("-------\n");
for (i=0;i<=m;i++)
printf("%3d %3d\n",i,C[i][0]);
if (C[m][m]==(-1))
printf("No solution\n");
else
{
printf("\n\nSolution\n\n");
printf("(Position) i S\n");
printf("------------------\n");
for (i=m;i>0;i-=S[C[i][0]])
printf(" %3d %3d\n",C[i][0],S[C[i][0]]);
}
}
这将输出以下内容
i S
-------
0 0
1 1
2 3
3 4
4 6
5 7
6 10
7 25
i C
-------
0 0
1 1
2 -1
3 2
4 2
5 3
6 4
7 3
8 3
9 4
10 4
11 4
12 5
13 4
14 4
15 5
16 5
17 5
18 5
19 6
20 5
21 5
22 6
23 6
24 6
25 6
Solution
(Position) i S
------------------
6 10
5 7
3 4
2 3
1 1
Program ended with exit code: 0
我的问题是我只能输出一个解决方案，这就是需要较小值并且最多可达25的解决方案，因此当使用25时，它不在解决方案中。代码中的C数组是一个二维数组，因为我认为在计算第一个数据时我可以做另一个回溯吗？我无法弄清楚如何这样做，所以我将C[i][0]固定在第一列，只是为了演示一个解决方案。任何正确方向的提示将不胜感激。我找到了一个使用Python的解决方案，但问题是递归解决的，我认为这对我没有帮助，但代码是here。
提前感谢所有帮助。
答案 0 :(得分：1)
我没有完全理解你的代码。但是这里有一个C代码，用于查找汇总到target的所有子集。
#include <stdio.h>
int a[] = { 0, 1, 3, 4, 6, 7, 10, 25 }; //-- notice that the input array is zero indexed
int n = 7;
int target = 25;
int dp[8][26];
int solutions[1 << 7][8]; //-- notice that the number of subsets could be exponential in the length of the input array a.
int sz[1 << 7]; //-- sz[i] is the length of subset solutions[i]
int cnt = 0; //-- number of subsets
void copy(int srcIdx, int dstIdx){
int i;
for (i = 0; i < sz[srcIdx]; i++)
solutions[dstIdx][i] = solutions[srcIdx][i];
sz[dstIdx] = sz[srcIdx];
}
//-- i, and j are indices of dp array
//-- idx is the index of the current subset in the solution array
void buildSolutions(int i, int j, int idx){
if (i == 0 || j == 0) return; // no more elements to add to the current subset
if (dp[i - 1][j] && dp[i - 1][j - a[i]]){ // we have two branches
cnt++; // increase the number of total subsets
copy(idx, cnt); // copy the current subset to the new subset. The new subset does not include a[i]
buildSolutions(i - 1, j, cnt); //find the remaining elements of the new subset
solutions[idx][sz[idx]] = a[i]; // include a[i] in the current subset
sz[idx]++; // increase the size of the current subset
buildSolutions(i - 1, j - a[i], idx); // calculate the remaining of the current subset
}
else if (dp[i - 1][j - a[i]]){ // we only have one branch
solutions[idx][sz[idx]] = a[i]; // add a[i] to the current subset
sz[idx]++;
buildSolutions(i - 1, j - a[i], idx); // calculate the remaining of the current subset
}
else buildSolutions(i - 1, j, idx); // a[i] is not part of the current subset
}
int main(){
int i, j;
// initialize dp array to 0
for (i = 0; i <= n; i++)
for (j = 0; j <= target; j++) dp[i][j] = 0;
//-- filling the dp array
for (i = 0; i <= n; i++)
dp[i][0] = 1;
for (i = 1; i <= n; i++){
for (j = 1; j <= target; j++){
if (j < a[i])
dp[i][j] = dp[i - 1][j];
else
dp[i][j] = dp[i - 1][j] || dp[i - 1][j - a[i]];
}
}
//-- building all the solutions
for (i = 0; i < sizeof(sz); i++) sz[i] = 0; //-- initializing the sz array to 0
buildSolutions(n, target, 0);
//-- printing all the subsets
for (i = 0; i <= cnt; i++){
for (j = 0; j < sz[i]; j++){
printf("%d ", solutions[i][j]);
}
printf("\n");
}
}
如果您对代码有任何疑问，请随时提出。