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hdu1028 Ignatius and the Princess III && hdu2082 找单词 && poj1664 放苹果 && noj1046 正整数划分问题——整数划分

这种问题有两种做法，DP和母函数。

hdu1028 Ignatius and the Princess III

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1028

DP做法：

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstdlib>
 4 #include <cstring>
 5 #include <cctype>
 6 #include <stack>
 7 #include <queue>
 8 #include <deque>
 9 #include <map>
10 #include <set>
11 #include <vector>
12 #include <cmath>
13 #include <algorithm>
14 #define lson l, m, rt<<1
15 #define rson m+1, r, rt<<1|1
16 using namespace std;
17 typedef long long int LL;
18 const int MAXN =  0x7fffffff;
19 const int  MINN =  -0x7fffffff;
20 const double eps = 1e-9;
21 const int dir[8][2] = {{0,1},{1,0},{0,-1},{-1,0},{-1,1},
22   {1,1},{1,-1},{-1,-1}};
23 
24 int main(void){
25 #ifndef ONLINE_JUDGE
26   freopen("hdu1028.in", "r", stdin);
27 #endif
28   int i, j, dp[121][121], n;
29   dp[1][1] = 1; // WA!
30   for (i = 2; i < 121; ++i) {
31     dp[i][1] = dp[1][i] = 1;
32     for (j = 2; j < 121; ++j) {
33       if (i > j) dp[i][j] = dp[i-j][j] + dp[i][j-1];
34       else if (i == j) dp[i][j] = dp[i][j-1] + 1;
35       else dp[i][j] = dp[i][i];
36     }
37   }
38   while (~scanf("%d", &n)) {
39     printf("%d\n", dp[n][n]);
40   }
41 
42   return 0;
43 }

母函数做法：

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstdlib>
 4 #include <cstring>
 5 #include <cctype>
 6 #include <stack>
 7 #include <queue>
 8 #include <deque>
 9 #include <map>
10 #include <set>
11 #include <vector>
12 #include <cmath>
13 #include <algorithm>
14 #define lson l, m, rt<<1
15 #define rson m+1, r, rt<<1|1
16 using namespace std;
17 typedef long long int LL;
18 const int MAXN =  0x7fffffff;
19 const int  MINN =  -0x7fffffff;
20 const double eps = 1e-9;
21 const int dir[8][2] = {{0,1},{1,0},{0,-1},{-1,0},{-1,1},
22   {1,1},{1,-1},{-1,-1}};
23 
24 int a[121], b[121];
25 int main(void){
26 #ifndef ONLINE_JUDGE
27   freopen("hdu1028.in", "r", stdin);
28 #endif
29   int n;
30   while (~scanf("%d", &n)) {
31     int i, j, k;
32     for (i = 0; i <= n; ++i) a[i] = b[i] = 0;
33     a[0] = 1;
34     for (i = 1; i <= n; ++i) {
35       for (j = 0; j <= n; ++j) {
36         for (k = 0; k*i+j <= n; ++k) {
37           b[k*i+j] += a[j];
38         }
39       }
40       for (j = 0; j <= n; ++j) {
41         a[j] = b[j]; b[j] = 0;
42       }
43     }
44     printf("%d\n", a[n]);
45   }
46 
47   return 0;
48 }

hdu2082 找单词

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=2082

只写了母函数的。因为这个有个数限制。

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstdlib>
 4 #include <cstring>
 5 #include <cctype>
 6 #include <stack>
 7 #include <queue>
 8 #include <deque>
 9 #include <map>
10 #include <set>
11 #include <vector>
12 #include <cmath>
13 #include <algorithm>
14 #define lson l, m, rt<<1
15 #define rson m+1, r, rt<<1|1
16 using namespace std;
17 typedef long long int LL;
18 const int MAXN =  0x7fffffff;
19 const int  MINN =  -0x7fffffff;
20 const double eps = 1e-9;
21 const int dir[8][2] = {{0,1},{1,0},{0,-1},{-1,0},{-1,1},
22   {1,1},{1,-1},{-1,-1}};
23 
24 int a[51], b[51];
25 int main(void){
26 #ifndef ONLINE_JUDGE
27   freopen("hdu2082.in", "r", stdin);
28 #endif
29   int t; scanf("%d", &t);
30   while (t--) {
31     int i, j, k, num;
32     for (i = 0; i <= 50; ++i) {
33       a[i] = b[i] = 0;
34     }
35     a[0] = 1;
36     for (i = 1; i <= 26; ++i) {
37       scanf("%d", &num);
38       for (j = 0; j <= 50; ++j) {
39         for (k = 0; k <= num && k*i+j <= 50; ++k) {
40           b[k*i+j] += a[j];
41         }
42       }
43       for (j = 0; j <= 50; ++j) {
44         a[j] = b[j]; b[j] = 0;
45       }
46     }
47     int sum = 0;
48     for (i = 1; i <= 50; ++i) sum += a[i];
49     printf("%d\n", sum);
50   }
51 
52   return 0;
53 }

poj1664 放苹果

题目链接：http://poj.org/problem?id=1664

这道也只写了DP的，用DP处理比较方便。

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstdlib>
 4 #include <cstring>
 5 #include <cctype>
 6 #include <stack>
 7 #include <queue>
 8 #include <deque>
 9 #include <map>
10 #include <set>
11 #include <vector>
12 #include <cmath>
13 #include <algorithm>
14 #define lson l, m, rt<<1
15 #define rson m+1, r, rt<<1|1
16 using namespace std;
17 typedef long long int LL;
18 const int MAXN =  0x7fffffff;
19 const int  MINN =  -0x7fffffff;
20 const double eps = 1e-9;
21 const int dir[8][2] = {{0,1},{1,0},{0,-1},{-1,0},{-1,1},
22   {1,1},{1,-1},{-1,-1}};
23 
24 int main(void){
25 #ifndef ONLINE_JUDGE
26   freopen("poj1664.in", "r", stdin);
27 #endif
28   int t, n, m; scanf("%d", &t);
29   int dp[11][11], i, j;
30   dp[1][1] = 1;
31   for (i = 2; i < 11; ++i) {
32     dp[i][1] = dp[1][i] = 1;
33     for (j = 2; j < 11; ++j) {
34       if (i > j) dp[i][j] = dp[i][j-1] + dp[i-j][j];
35       else if (i == j) dp[i][j] = dp[i][j-1] + 1;
36       else dp[i][j] = dp[i][i];
37     }
38   }
39   while (t--) {
40     scanf("%d%d", &m, &n);
41     printf("%d\n", dp[m][n]);
42   }
43 
44   return 0;
45 }

noj1046 正整数划分问题

题目链接：http://acm.nankai.edu.cn/p1046.html

跟hdu1028一样一样的……其实就是一道题目o(╯□╰)o

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstdlib>
 4 #include <cstring>
 5 #include <cctype>
 6 #include <stack>
 7 #include <queue>
 8 #include <deque>
 9 #include <map>
10 #include <set>
11 #include <vector>
12 #include <cmath>
13 #include <algorithm>
14 #define lson l, m, rt<<1
15 #define rson m+1, r, rt<<1|1
16 using namespace std;
17 typedef long long int LL;
18 const int MAXN =  0x7fffffff;
19 const int  MINN =  -0x7fffffff;
20 const double eps = 1e-9;
21 const int dir[8][2] = {{0,1},{1,0},{0,-1},{-1,0},{-1,1},
22   {1,1},{1,-1},{-1,-1}};
23 
24 int main(void){
25 #ifndef ONLINE_JUDGE
26   freopen("hdu1028.in", "r", stdin);
27 #endif
28   int i, j, dp[121][121], n;
29   dp[1][1] = 1; // WA!
30   for (i = 2; i < 121; ++i) {
31     dp[i][1] = dp[1][i] = 1;
32     for (j = 2; j < 121; ++j) {
33       if (i > j) dp[i][j] = dp[i-j][j] + dp[i][j-1];
34       else if (i == j) dp[i][j] = dp[i][j-1] + 1;
35       else dp[i][j] = dp[i][i];
36     }
37   }
38   while (~scanf("%d", &n)) {
39     printf("%d\n", dp[n][n]);
40   }
41 
42   return 0;
43 }

感觉这些基础的东西现在都不熟练……

哈哈，附上一首超级好听的钢琴曲~

某青推荐的……THX~

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原文地址：https://www.cnblogs.com/liuxueyang/p/3074503.html