动态规划之最大k乘积，编辑距离，k好数，节点选择，背包问题

         这几天真是闲的没事做了，都不知道干什么了，把自己之前的动态规划代码整理一遍，现在写代码也有了自己的风格。直接复制上去自己看吧，也懒得解释了

1.最短编辑距离，里面用到了重定向读写

#include <stdio.h>
#include <string.h>

#define MAXLEN 100
#define min(a,b,c) (((a<b?a:b)<c)?(a<b?a:b):(c))


int c[MAXLEN][MAXLEN] = {0};

void cls_length(char *sa,char *sb,int m,int n)
{
    int i = 0;
    int j = 0;
    int is_equal = 0;

    for(i = 0; i <= m; i++){
        c[i][0] = i;
    }//end for
    for(j = 0; j <= n; j++){
        c[0][j] = j;
    }//end for

    for(i = 1; i <= m; i++){
        for(j = 1; j <= n; j++){
                 is_equal = (sa[i-1] == sb[j-1])?0:1;
                 c[i][j] = min(c[i-1][j]+1,c[i][j-1]+1,
                               c[i-1][j-1] + is_equal);
        }//end for
    }//end for
}


void print_matrix_cls(int m,int n)
{
    int i = 0;
    int j = 0;

    for(i = 0; i <= m; i++){
        for(j = 0; j <= n; j++){
            printf("%d ",c[i][j]);
        }//end for 2
        printf("\n");
    }//end for 1
    printf("\n\n\nmin edit is %d\n\n\n",c[m][n]);
}

int main(int argc,char *argv[])
{
    char sa[MAXLEN] = {0};
    char sb[MAXLEN] = {0};
    int m = 0;
    int n = 0;

    freopen("D:\\in.txt","r",stdin);
    freopen("D:\\out.txt","w",stdout);


	while(scanf("%s %s",sa,sb)!=EOF){
      m = strlen(sa);
      n = strlen(sb);
      cls_length(sa,sb,m,n);
      print_matrix_cls(m,n);
	
	  memset(sa,0x00,m);
	  memset(sb,0x00,n);
	}//end while
    
    return 0;
}

2.最大K乘积

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define  MAXN  11
#define  MAXK  9


static int m[MAXN][MAXN];
static int w[MAXN][MAXN];


void MaxDp(int *a,int n,int k)
{
    int i = 0;
    int j = 0;
    int d = 0;
    int max = 0;
    int temp = 0;

    for(i = 1; i <= n; i++){
        m[i][1] = w[1][i];
    }//end for

    for(i = 1; i <= n; i++){
        for(j = 2; j <= k; j++){
            max = 0;
            for(d = 1; d < i; d++){
				temp = m[d][j-1]*w[d+1][i];
                if(temp > max){
                    max = temp;
                }//end if
                m[i][j] = max;
            }//end for 3
        }//end for 2
    }//end for 1
}

void init_matrix(int *a,int n)
{
	int i = 0;
	int j = 0;

    for(i = 1; i <= n; i++){
        w[i][i] = a[i];
        for(j = i+1; j <= n; j++){
            w[i][j] = w[i][j - 1]*10 + a[j];
        }//end for 2
    }//end for 1

}

int main(int argc,char *argv[])
{
    char c = '\0';
    int  i = 0;
    int  n = 0;
	int  k = 0;
    int  a[MAXN] = {0};

    scanf("%d%d",&n,&k);
    fflush(stdin);

    while((c=getchar())!= '\n'){
        a[++i] = c - '0';
    }//end while

    
	
<span style="font-family:SimSun;">    </span>init_matrix(a,n);

    MaxDp(a,n,k);

    printf("max %d is %d\n",k,m[n][k]);

    return 0;
}

3.蓝桥杯-k好数

#include <stdio.h>
#include <string.h>

#define mod 100000007 

long int sum = 0;

int dp[105][105] = {0};



void k_good_num(int k,int l)
{
    int i = 0;
    int j = 0;
    int x = 0;

    for(i = 0; i < k; i++){
        dp[1][i] = 1;
    }//end for 
    for(i = 2; i <= l; i++){
        for(j = 0; j < k; j++){
            for(x = 0; x < k; x++){
                if(x!=j-1 && x!=j+1){
                    dp[i][j] += dp[i-1][x];
                    dp[i][j] %= mod;
                }//end if
            }//end for3
        }//end for2
    }//end for 1
}

void print_k_num(int k,int l)
{
    int i = 0;

    for(i = 1; i < k; i++){
        sum += dp[l][i];
        sum %= mod;
    }//end for

	printf("sum = %d\n",sum);
}

int main(int argc,char *argv[])
{
    int k = 0;
    int l = 0;

    while(scanf("%d%d",&k,&l) != EOF){
        k_good_num(k,l);
        print_k_num(k,l);
        
		sum = 0;
		memset(dp,0x00,sizeof(dp));
    }

	return 0;
}

4.最长公共子串

#include <stdio.h>
#include <string.h>
#include <stdlib.h>

#define MAXLEN 100 


int b[MAXLEN][MAXLEN] = {0};
int c[MAXLEN][MAXLEN] = {0};


void lcs_length(char *sa,char *sb,int m,int n)
{
    int i = 0;
    int j = 0;

    for(i = 0; i <= m; i++){
        c[i][0] = 0;
    }//end for
    for(j = 0; j <= n; j++){
        c[0][j] = 0;
    }//end for

    for(i = 1; i <= m; i++){
        for(j = 1; j <= n; j++){
            if(sa[i-1] == sb[j-1]){
                c[i][j] = c[i-1][j-1] + 1; 
                b[i][j] = 0;
            }else if(c[i-1][j] >= c[i][j-1]){
                c[i][j] = c[i-1][j];
                b[i][j] = 1;
            }else{
                c[i][j] = c[i][j-1];
                b[i][j] = -1;
            }
        }//end for 2
    }//end for 1
}

void print_lcs(char *sa,int i,int j)
{
    if(i == 0 || j == 0){
        return;
    }
    if(b[i][j] == 0){
        print_lcs(sa,i-1,j-1);
        printf("%c ",sa[i-1]);
    }else if(b[i][j] == 1){
        print_lcs(sa,i-1,j);
    }else{
        print_lcs(sa,i,j-1);
    }


}


void print_matrix(int (*matrix)[MAXLEN],int m,int n)
{
    int i = 0;
    int j = 0;

    for(i = 0; i <= m; i++){
        for(j = 0; j <= n; j++){
            printf("%5d ",matrix[i][j]);
        }
        printf("\n");
    }

    printf("\n");
}

int main(int argc,char *argv[])
{
    char sa[MAXLEN] = "ABCBDAB";
    char sb[MAXLEN] = "BDCABA";
    int m = 0;
    int n = 0;

    m = strlen(sa);
    n = strlen(sb);


    // exec function
    lcs_length(sa,sb,m,n);

    print_matrix(b,m,n);

    print_matrix(c,m,n);

    print_lcs(sa,m,n);

    return 0;
}

5.n数最大乘积

#include <stdio.h>
#include <windows.h>
#include <string.h>

#define MAXLEN 500


int a[MAXLEN];
int b[MAXLEN];


void find_multify_value(int *a,int n,int *end)
{
      int i = 0;
	  int j = 0;
	  int len = 0;
	  int incr = 2;
	  int left = n;


	  if(n == 0 || n == 1 || n == 2 || n == 3 || n == 4){	         
		   a[0] = n;
		   *end = 1;
		   return ;
	  }//end if

	  a[0] = 1;

	  while(left >= incr){
		  a[i++] = incr;
		  left -= incr;
		  incr++;
	  }//end while

	  len = i;

	  //printf("len = %d,left = %d\n",len,left);

	  if(left != n && left != 0){
		  while(left){
			  if(i <= 0){
			     i = len;
			  }
			  a[--i]++;
			  left--;
		  }//end while
	  }//end if
      
      *end = len;
}

void calculate_array(int *a,int *b,int end,int *start)
{
	int i = 0;
	int temp = 0;
	int j = MAXLEN - 1;
	int k = MAXLEN - 2;
    int carry_bit = 0;

	b[j] = 1;

	for(i = 0; i < end; i++){
		for(j = MAXLEN -1; j > k; j--){
	       temp = b[j] * a[i] + carry_bit;
	       b[j] = temp % 10;
		   carry_bit = temp / 10;
		}//end for  
		while(carry_bit){
		   b[k--] += carry_bit % 10;
		   carry_bit /= 10;
		}//end while
	}//end for
	*start = k + 1;

}

void print_mutify_array(int *a,int end)
{
     int i = 0;

	 for(i = 0;i < end; i++){
	    printf("%d ",a[i]);
	 }//end for
	 printf("\n");
}

void print_multify_value(int *b,int start)
{
	int i = 0;

	for(i = start; i < MAXLEN; i++){
	     printf("%d",b[i]);
	}//end for
	printf("\n");

}
int main(int argc,char *argv[])
{
	int n = 0;
	int start = 0;
	int end = 0;

	freopen("D:\\out.txt","w",stdout);
	//while(scanf("%d",&n) != EOF){
      
	for(n = 1; n <= 100; n++){
        
		printf("n = %d\n",n);

		find_multify_value(a,n,&end);

		calculate_array(a,b,end,&start);

		print_mutify_array(a,end);
		
		print_multify_value(b,start);

		memset(a,0x00,sizeof(a));
		memset(b,0x00,sizeof(b));

		//	getchar();

	    //	Sleep(1500);
	}//end for

       
	return 0;
}

6.01背包问题

#include <stdio.h>

// 容量是10个
void backpack_01(int *w,int *v,int (*max)[11])
{
    int  i = 0;
    int  j = 0;

    for(i = 0; i <= 10; i++){
        if(i >= w[0]){
           max[0][i] = v[0];
        }
    }
    for(i = 1; i < 5; i++){
        for(j = 0; j <= 10; j++){
            if(j > w[i] && ((max[i-1][j-w[i]] + v[i]) > max[i-1][j])){
                max[i][j] = max[i-1][j-w[i]] + v[i];
            }else{
                max[i][j] = max[i-1][j];
            }
         }//end for 2
    }//end for 1

}

void print_backpack_01(int (*max)[11])
{
   int i = 0;
   int j = 0;

   for(i = 0; i < 5; i++){
      for(j = 0; j <= 10; j++){
        printf("%5d ",max[i][j]);
      }//end for 2
      printf("\n");
   }//end for 1
}

int main(int argc,char *argv[])
{
    int w[5] = {2,2,6,5,4};
    int v[5] = {6,3,5,4,6};
    int max[5][11] = {0};


    backpack_01(w,v,max);

    print_backpack_01(max);

    return 0;
}