算法导论 练习题 15.2-2

#include <stdio.h>#include <limits.h>#include "矩阵栈.h"#include "字符栈.h"int m[7][7];int s[7][7];pMStack pm=initStackPM(20);pCStack pc=initStackPC(20);pMatrix A[4];pMatrix newMatrix(int row,int col){pMatrix c=(pMatrix)malloc(sizeof(MatrixNode));c->row=row;c->col=col;c->m=(int**)malloc(c->row*sizeof(int*));for(int i=0;i<c->row;i++){c->m[i]=(int*)malloc(c->col*sizeof(int));}return c;}void initA(){A[0]=newMatrix(1,3);A[0]->m[0][0]=1;A[0]->m[0][1]=2;A[0]->m[0][2]=3;A[1]=newMatrix(3,2);A[1]->m[0][0]=1;A[1]->m[0][1]=2;A[1]->m[1][0]=3;A[1]->m[1][1]=4;A[1]->m[2][0]=5;A[1]->m[2][1]=6;A[2]=newMatrix(2,3);A[2]->m[0][0]=1;A[2]->m[0][1]=2;A[2]->m[0][2]=3;A[2]->m[1][0]=4;A[2]->m[1][1]=5;A[2]->m[1][2]=6;A[3]=newMatrix(3,1);A[3]->m[0][0]=1;A[3]->m[1][0]=1;A[3]->m[2][0]=1;}pMatrix matrixMul(pMatrix a,pMatrix b){if(a->col != b->row){printf("矩阵乘法参数不合法！");return NULL;}pMatrix c=newMatrix(a->row,b->col);for(int i=0;i<a->row;i++){for(int j=0;j<b->col;j++){int sum=0;for(int k=0;k<a->col;k++){sum+=a->m[i][k]*b->m[k][j];}c->m[i][j]=sum;}}return c;}void matrixChainOrder(int p[],int len){int n=len-1,q;for(int i=1;i<=n;i++)m[i][i]=0;for(int l=2;l<=n;l++){for(int i=1;i<=n-l+1;i++){int j=i+l-1;m[i][j]=INT_MAX;for(int k=i;k<j;k++){int q=m[i][k]+m[k+1][j]+p[i-1]*p[k]*p[j];if(q<m[i][j]){m[i][j]=q;s[i][j]=k;}}}}}void printS(int i,int j){if(i==j)printf("A%d",i);else{printf("(");printS(i,s[i][j]);printS(s[i][j]+1,j);printf(")");}}void printM(pMatrix m){for(int i=0;i<m->row;i++){for(int j=0;j<m->col;j++){printf("%d ",m->m[i][j]);}printf("\n");}}void matrixChainMultiply(int i,int j){if(i==j)pushPM(pm,A[i-1]);else{pushPC(pc,'(');matrixChainMultiply(i,s[i][j]);matrixChainMultiply(s[i][j]+1,j);char c=popPC(pc);if(c=='('){pMatrix b=popPM(pm);pMatrix a=popPM(pm);pMatrix p=matrixMul(a,b);pushPM(pm,p);//printM(p);}}}void main(){initA();int p[5]={1,3,2,3,1};matrixChainOrder(p,5);printf("%d\n",m[1][4]);printS(1,4);printf("\n");matrixChainMultiply(1,4);pMatrix m=popPM(pm);printM(m);getchar();}