0-1背包问题

有n个物体，重量和价值已知，要放入容量为c的背包里，放入的时间，要求放入的总重量不能超过包的容量，同时保证价值最大。

动态规划：

#include <stdio.h>#define min(a,b) a>b?b:a#define max(a,b) a>b?a:bint main(){    int n,c;    int *w, *v,*flag; //w代表每个物品的容积，v代表价值, flag代表是否出现    int **m; //m[i,j]用来存储当剩余容量为j时，可选择的物品为i,i+1,...时，0-1背包问题的最优值    int i,j,k;    int jMax;       printf("please input the number of things and the volume of the knap:");    scanf("%d %d",&n,&c);    w=new int [n];    v=new int [n];    flag=new int [n];    m=new int *[n];    for(i=0;i<n;i++)        m[i]=new int [c+1];    printf("input the volume of each thing:");    for(i=0;i<n;i++)        scanf("%d", &w[i]);    printf("input the value of each thing:");    for(i=0;i<n;i++)        scanf("%d",&v[i]);    //从最后一个元素倒着推导，即第n-1个元素    jMax=min(w[n-1]-1,c);    for(j=0;j<=jMax;j++)        m[n-1][j]=0;    for(j=w[n-1];j<=c;j++)        m[n-1][j]=v[n-1];    for(i=n-2;i>0;i--)    {        jMax=min(w[i]-1,c);        for(j=0;j<jMax;j++)            m[i][j]=m[i+1][j];        for(j=jMax;j<=c;j++)            m[i][j]=max(m[i+1][j],m[i+1][j-w[i]]+v[i]);    }    m[0][c]=m[1][c];    if(c>=w[0])         m[0][c]=max(m[1][c],m[1][c-w[0]]+v[0]);     printf("the max value is %d. and the concrete are:\n",m[0][c]);    for(i=0;i<n-1;i++)    {        if(m[i][c]==m[i+1][c])             flag[i]=0;        else        {            flag[i]=1;            c=c-w[i];        }        flag[n-1]=(m[n-1][c])?1:0;    }    for(i=0;i<n;i++)        if (flag[i])            printf("%d ",v[i]);    printf("\n");    return 0;}

回溯法：

#include<stdio.h>int*w,*v,weigt,n,sumW,bestV,tempV;void backtrack(int t){    if(sumW<=weigt)    {        int i;        if(t>n)        {            for(i=0;i<n;i++)            {                if(tempV>bestV)                    bestV=tempV;            }        }else        {                sumW+=w[t];                tempV+=v[t];                backtrack(t+1);                sumW-=w[t];                tempV-=v[t];                backtrack(t+1);        }    }}int main(){    int i;    printf("Please enter the space of the backpack:");    scanf("%d",&weigt);    printf("Please input the number of objects:");    scanf("%d",&n);    w=new int[n];    v=new int[n];    printf("Please input the weigt of each object:\n");    for(i=0;i<n;i++)        scanf("%d",w+i);    printf("Please input the value of each object:\n");    for(i=0;i<n;i++)        scanf("%d",&v[i]);    sumW=0;    tempV=0;    bestV=0;    backtrack(0);    printf("%d\n",bestV);    return 0;}

分支限界法：

#include <stdio.h>#include <stdlib.h>typedef struct QNode{    int value;  //当前结点的总价值    int weight; //当前的总重量    struct QNode *next;}QNode, *QueuePtr;typedef struct{    QueuePtr front;    QueuePtr rear;}Queue;int initQueue(Queue &Q){    Q.front=Q.rear=(QueuePtr)malloc(sizeof(QNode));    if(!Q.front)        return -1;    Q.front->next=NULL;    return 1;}int emptyQueue(Queue Q){    if (Q.front==Q.rear)        return 1;    else        return 0;}int destroyQueue(Queue &Q){    while(Q.front){        Q.rear=Q.front->next;        free(Q.front);        Q.front=Q.rear;    }    return 1;}int enQueue(Queue &Q, int value, int weight){    QueuePtr p=(QueuePtr)malloc(sizeof(QNode));    if(!p)    <span style="white-space:pre">  </span>return -1;    p->value=value;     p->weight=weight;     p->next=NULL;    Q.rear->next=p;    Q.rear=p;    return 1;}int deQueue(Queue &Q, int &value, int &weight){    QueuePtr p;    if(Q.front==Q.rear)        return -1;    p=Q.front->next;    value=p->value;    weight=p->weight;    Q.front->next=p->next;    if(Q.rear==p) <span style="white-space:pre">      </span>Q.rear=Q.front;    free(p);    return 1;}Queue loadingQueue;int bestvalue, n;void inQueue(int value, int weight, int i){    if(i==n-1){    <span style="white-space:pre">  </span>if(value>bestvalue)            bestvalue=value;    }    else        enQueue(loadingQueue,value,weight);}int main(){    int i,j,k;    int *w, *v, ew, ev;    int c;    printf("input the number of things and the volume of ships:");    scanf("%d%d",&n,&c);    w=new int[n];    v=new int[n];    printf("input the weights:");    for(i=0;i<n;i++)        scanf("%d",&w[i]);    printf("input the values:");    for(i=0;i<n;i++)        scanf("%d",&v[i]);    initQueue(loadingQueue);    enQueue(loadingQueue,-1,0);         i=0;    //层数    ew=0;   //扩展结点对应的载重量    ev=0;       while(true){        if(ew+w[i]<=c)            inQueue(ev+v[i],ew+w[i],i);        inQueue(ev,ew,i);        deQueue(loadingQueue, ev,ew);        if(ev==-1) //同层结点尾部{            if(emptyQueue(loadingQueue)){                printf("the result is %d.\n",bestvalue);                break;            }            enQueue(loadingQueue,-1,0);            deQueue(loadingQueue, ev,ew);            i++;        }    }       <span style="white-space:pre">  </span>return 0;}

暴力搜索：

#include <stdio.h>#include <math.h>int main(){    int num,maxv=0;    int n, c, *w, *v, tempw, tempv;    int i,j,k;    scanf("%d%d",&n,&c);    w=new int [n];    v=new int [n];    for(i=0;i<n;i++)        scanf("%d",&w[i]);    for(i=0;i<n;i++)        scanf("%d",&v[i]);    for(num=0;num<pow(2,n);num++) //每一个num对应一个解    {        k=num; tempw=tempv=0;           for(i=0;i<n;i++)    //n位二进制        {            if(k%2==1){     //如果相应的位等于1，则代表物体放进去，如果是0，就不用放了                tempw+=w[i];                tempv+=v[i];            }            k=k/2;          //二进制转换的规则        }        //循环结束后，一个解空间生成，        //判断是否超过了背包的容积，        //如果没有超，判断当前解是否比最优解更好        if(tempw<=c){            if(tempv>maxv)                maxv=tempv;        }    }    printf("%d\n",maxv);    return 0;   }