算法设计与分析（第二版）主编：吕国英习题答案第四章1.#include<stdio.h>int main(void){int buf[100];int n;int i,j,k;scanf("%d",&n);for(i=0;i<n;i++)buf[i]=2;for(i=0;i<n-1;i++){for(j=0;j<n-i-1;j++){buf[j]+=2;}}for(j=0;j<n;j++){if(buf[j]>=10){buf[j+1]+=buf[j]/10;buf[j]=buf[j]%10;}}for(i=n-1;i>=0;i--)printf("%d",buf[i]);printf("\n");return 0;}2.#include<stdio.h>int main(void){int n=2;int i;for(i=1;i<=9;i++){n=(n+2)*2;}printf("%d\n",n);return 0;}3.#include<stdio.h>int main(void){int a=54;int n;int m;printf("计算机先拿3牌\n"); a=a-3;while(a>=0){printf("还剩%d牌\n",a); printf("你拿几？请输入："); scanf("%d",&n);if(n>4||n<1||n>a){printf("错误！重新拿牌\n"); continue;}a=a-n;printf("还剩%d牌\n",a);if(a==0)break;m=5-n;printf("计算机拿%d\n",m);a=a-m;}return 0;}4.#include<stdio.h>int d;int a1,a2;int fun(int n);int main(void){int n;printf("n=?,d=?,a1=?,a2=?");scanf("%d%d%d%d\n",&n,&d,&a1,&a2); printf("%d\n",fun(n));return 0;}int fun(int n){if(n==1)return a1;if(n==2)return a2;return fun(n-2)-(fun(n-1)-d)*2;}5.#include<stdio.h>char chess[8][8];int is_safe(int row,int col);int queen(int row,int col,int n); int main(void){int i,j;for(i=0;i<8;i++)for(j=0;j<8;j++)chess[i][j]='X';queen(0,0,0);for(i=0;i<8;i++){for(j=0;j<8;j++)printf("%c ",chess[i][j]);printf("\n");}return 0;}int is_safe(int row,int col){int i,j;for(i=0;i<8;i++){if(chess[row][i]=='Q')return 0;if(chess[i][col]=='Q')return 0;}i=row;j=col;while(i!=-1&&j!=-1){if(chess[i--][j--]=='Q')return 0;}i=row;j=col;while(i!=-1&&j!=8){if(chess[i--][j++]=='Q')return 0;}i=row;j=col;while(i!=8&&j!=-1){if(chess[i++][j--]=='Q')return 0;}i=row;j=col;while(i!=8&&j!=8){if(chess[i++][j++]=='Q')return 0;}return 1;}int queen(int row,int col,int n) {int i,j;int result=0;if(n==8)return 1;elseif(is_safe(row,col)){chess[row][col]='Q';for(i=0;i<8;i++)for(j=0;j<8;j++){result+=queen(i,j,n+1);if(result>0)break;}if(result>0)return 1;else{chess[row][col]='X';return 0;}}elsereturn 0;}6.#include<stdio.h>int main(void){int i,j,k;for(i=1;i<=33;i++)for(j=1;j<=50;j++){k=100-i-j;if(k%2==0){if(3*i+2*j+k/2==100)printf("大马%d\n中马%d\n小马%d\n\n\n",i,j,k); }}return 0;}7.#include<stdio.h>int main(void){int i;for(i=1;i<=10000;i++){if(i%2==1&&i%3==2&&i%5==4&&i%6==5&&i%7==0) printf("%d\n",i);}return 0;}8.#include<stdio.h>int main(void){int i;int sum;int a1,a2,a3,a4;for(i=1000;i<=9999;i++){a1=i%10;a2=i/10%10;if(a1!=a2){a3=i/100%10;if(a1!=a3&&a2!=a3){a4=i/1000;if(a1!=a4&&a2!=a4&&a3!=a4){sum=(a1+a2+a3+a4)*(a1+a2+a3+a4);if(i%sum==0)printf("%d\n",i);}}}}return 0;}9.#include<stdio.h>#define N 10void max_min(int *a,int m,int n,int *min1,int *min2,int *max1,int *max2); int main(void){int a[N]={2,3,4,5,34,7,9,6,43,21};int min1,min2;int max1,max2;max_min(a,0,N-1,&min1,&min2,&max1,&max2);printf("min1=%d\nmin2=%d\nmax1=%d\nmax2=%d\n",min1,min2,max1,max2);return 0;}void max_min(int *a,int m,int n,int *min1,int *min2,int *max1,int *max2) {int lmin1,lmin2,lmax1,lmax2;int rmin1,rmin2,rmax1,rmax2;int mid;if(m==n){*min1=*min2=*max1=*max2=a[m];}elseif(m==n-1){if(a[m]<a[n]){*min1=a[m];*min2=a[n];*max1=a[n];*max2=a[m];}else{*min1=a[n];*min2=a[m];*max1=a[m];*max2=a[n];}}else{mid=(m+n)/2;max_min(a,m,mid,&lmin1,&lmin2,&lmax1,&lmax2); max_min(a,mid+1,n,&rmin1,&rmin2,&rmax1,&rmax2); if(lmin1<rmin1){if(lmin2<rmin1){*min1=lmin1;*min2=lmin2;}else{*min1=lmin1;*min2=rmin1;}}elseif(rmin2<lmin1)*min1=rmin1;*min2=rmin2;}else{*min1=rmin1;*min2=lmin1;}if(lmax1>rmax1){if(lmax2>rmax1){*max1=lmax1;*max2=lmax2;}else{*max1=lmax1;*max2=rmax1;}}elseif(rmax2>lmax1){*max1=rmax1;*max2=rmax2;}else{*max1=rmax1;*max2=lmax1;}}}10.#include<stdio.h>int add(int *a,int flag,int right); int main(void){int a[10]={1,2,3,4,5,6,7,8,9,10}; int sum=add(a,0,9);printf("%d\n",sum);return 0;int add(int *a,int flag,int right){int mid;if(flag==right){return a[flag];}elseif(flag==right-1){return a[flag]+a[right];}else{mid=(flag+right)/2;return add(a,flag,mid)+add(a,mid+1,right); }}11.#include<stdio.h>int main(void){int a[5][3]={{-50,17,-42},{-47,-19,-3},{36,-34,-43},{-30,-43,34},{-23,-8,-45}};int i,j;int max,n;int sum=0;for(i=0;i<5;i++){max=a[i][0];n=0;for(j=1;j<3;j++){if(a[i][j]>max){max=a[i][j];n=j;}sum+=max;printf("a[%d][%d]=%d\n",i,n,max);}printf("%d\n",sum);return 0;}12./** File: newmain.c* Author: nirnava** Created on 2010年4月22日, 下午5:21*/#include<stdio.h>#include<stdlib.h>#define N 4void matrix_mul(int *mul1,int *mul2,int *mul3,int length); void matrix_add_sub(int * A,int * B,int * C,int m,char ch); void update_half_value(int * A,int * B,int m);void get_half_value(int * A,int * B,int m);int main(void){int i,j;int mul1[N*N]={1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6};int mul2[N*N]={7,8,9,10,1,2,3,4,5,6,7,8,9,10,1,2};int mul3[N*N];matrix_mul(mul1,mul2,mul3,N);for(i=0;i<N*N;i++){printf("%5d",mul3[i]);if((i+1)%N==0)printf("\n");}return 0;}void matrix_add_sub(int * A,int * B,int * C,int m,char ch) {int i;for(i=0;i<m*m;i++){if(ch=='+')C[i]=A[i]+B[i];C[i]=A[i]-B[i];}}void update_half_value(int * A,int * B,int m) {int i,j;for(i=0;i<m/2;i++){for(j=0;j<m/2;j++){B[i*m+j]=A[i*m/2+j];}}}void get_half_value(int * A,int * B,int m) {int i,j;for(i=0;i<m/2;i++){for(j=0;j<m/2;j++){A[i*m/2+j]=B[i*m+j];}}}void matrix_mul(int *A,int *B,int *C,int m) {if(m==2){int D,E,F,G,H,I,J;D=A[0]*(B[1]-B[3]);E=A[3]*(B[2]-B[0]);F=(A[2]+A[3])*B[0];G=(A[0]+A[1])*B[3];H=(A[2]-A[0])*(B[0]+B[1]);I=(A[1]-A[3])*(B[2]+B[3]);J=(A[0]+A[3])*(B[0]+B[3]);C[0]=E+I+J-G;C[1]=D+G;C[2]=E+F;C[3]=D+H+J-F;return ;}{int A1[m*m/4],A2[m*m/4],A3[m*m/4],A4[m*m/4];int B1[m*m/4],B2[m*m/4],B3[m*m/4],B4[m*m/4];int C1[m*m/4],C2[m*m/4],C3[m*m/4],C4[m*m/4];int D[m*m/4],E[m*m/4],F[m*m/4],G[m*m/4],H[m*m/4],I[m*m/4],J[m*m/4]; int temp1[m*m/4],temp2[m*m/4];get_half_value(A1,&A[0],m);get_half_value(A2,&A[m/2],m);get_half_value(A3,&A[m*m/2],m);get_half_value(A4,&A[m*m/2+m/2],m);get_half_value(B1,&B[0],m);get_half_value(B2,&B[m/2],m);get_half_value(B3,&B[m*m/2],m);get_half_value(B4,&B[m*m/2+m/2],m);matrix_add_sub(B2,B4,temp1,m/2,'-');matrix_mul(A1,temp1,D,m/2);matrix_add_sub(B3,B1,temp1,m/2,'-');matrix_mul(A4,temp1,E,m/2);matrix_add_sub(A3,A4,temp1,m/2,'+');matrix_mul(temp1,B1,F,m/2);matrix_add_sub(A1,A2,temp1,m/2,'+');matrix_mul(temp1,B4,G,m/2);matrix_add_sub(A3,A1,temp1,m/2,'-');matrix_add_sub(B1,B2,temp2,m/2,'+');matrix_mul(temp1,temp2,H,m/2);matrix_add_sub(A2,A4,temp1,m/2,'-');matrix_add_sub(B3,B4,temp2,m/2,'+');matrix_mul(temp1,temp2,I,m/2);matrix_add_sub(A1,A4,temp1,m/2,'+');matrix_add_sub(B1,B4,temp2,m/2,'+');matrix_mul(temp1,temp2,J,m/2);matrix_add_sub(E,I,temp1,m/2,'+');matrix_add_sub(J,G,temp2,m/2,'-');matrix_add_sub(temp1,temp2,C1,m/2,'+');matrix_add_sub(D,G,C2,m/2,'+');matrix_add_sub(E,F,C3,m/2,'+');matrix_add_sub(D,H,temp1,m/2,'+');matrix_add_sub(J,F,temp2,m/2,'-');matrix_add_sub(temp1,temp2,C4,m/2,'+');update_half_value(C1,&C[0],m);update_half_value(C2,&C[m/2],m);update_half_value(C3,&C[m*m/2],m);update_half_value(C4,&C[m*m/2+m/2],m);return ;}}13.#include<stdio.h>int main(void){int a[6][7]={{16,4,3,12,6,0,3},{4,-5,6,7,0,0,2},{6,0,-1,-2,3,6,8},{5,3,4,0,0,-2,7},{-1,7,4,0,7,-5,6},{0,-1,3,4,12,4,2}};int b[6][7],c[6][7];int i,j,k;int max;int flag;int temp;for(i=0;i<6;i++)for(j=0;j<7;j++){b[i][j]=a[i][j];c[i][j]=-1;}for(i=1;i<5;i++){for(j=0;j<7;j++){max=0;for(k=j-2;k<=j+2;k++) {if(k<0)continue;elseif(k>6)break;else{if(b[i][j]+b[i-1][k]>max) {max=b[i][j]+b[i-1][k]; flag=k;}}}b[i][j]=max;c[i][j]=flag;}}for(j=1;j<=5;j++){max=0;for(k=j-2;k<=j+2;k++) {if(k<0)continue;elseif(k>6)break;else{if(b[i][j]+b[i-1][k]>max) {max=b[i][j]+b[i-1][k]; flag=k;}}}b[i][j]=max;c[i][j]=flag;}max=0;for(j=1;j<=5;j++){if(b[i][j]>max){max=b[i][j];flag=j;}}printf("%d\n",max);temp=c[i][flag];printf("%5d",a[i][temp]); for(j=i;j>0;j--){temp=c[j][temp];printf("%5d",a[j-1][temp]); }printf("\n");return 0;}14.#include<stdio.h>int main(void){int A[6]={0,3,7,9,12,13}; int B[6]={0,5,10,11,11,11}; int C[6]={0,4,6,11,12,12}; int AB[6][6];int temp[6];int abc[6];int max;int flag;int i,j,k;for(i=0;i<=5;i++){max=0;for(j=0;j<=i;j++){AB[i][j]=A[i-j]+B[j];if(AB[i][j]>max)max=AB[i][j];}temp[i]=max;}max=0;for(i=0;i<=5;i++){abc[i]=temp[i]+C[5-i];if(abc[i]>max){max=abc[i];flag=i;}}printf("max=%d\n",max); printf("c=%d\n",5-flag); max=max-C[5-flag];for(i=0;i<=flag;i++){if(AB[flag][i]==max){printf("b=%d\n",i);printf("a=%d\n",flag-i);break;}}return 0;}16.#include<stdio.h>#define N 100int search(int *a,int left,int right); int sum_buf(int *a,int left,int right); int main(void){int a[N];int i;int s;for(i=0;i<N;i++)a[i]=1;a[24]=2;s=search(a,0,N-1);printf("%d\n",s);return 0;}int sum_buf(int *a,int left,int right) {int i;int sum=0;for(i=left;i<=right;i++)sum+=a[i];return sum;}int search(int *a,int left,int right) {int mid=(left+right)/2;if(left==right-1){if(a[left]<a[right])return right;elsereturn left;}if(mid*2!=(right+left-1)){if(sum_buf(a,left,mid-1)>sum_buf(a,mid+1,right)) {return search(a,left,mid-1);}elseif(sum_buf(a,left,mid-1)<sum_buf(a,mid+1,right)) {return search(a,mid+1,right);}elsereturn mid;}else{if(sum_buf(a,left,mid)>sum_buf(a,mid+1,right)) return search(a,left,mid);elsereturn search(a,mid+1,right);}}17.#include<stdio.h>int job[6][2]={{3,8},{12,10},{5,9},{2,6},{9.3},{11,1}};int x[6],bestx[6],f1=0,bestf,f2[7]={0};void try(int i);void swap(int a,int b);int main(void){int i,j;bestf=32767;for(i=0;i<6;i++)x[i]=i;try(0);for(i=0;i<6;i++)printf("%d ",bestx[i]);printf("\nbestf=%d\n",bestf); return 0;}void try(int i){int j;if(i==6){for(j=0;j<6;j++)bestx[j]=x[j];bestf=f2[i];}else{for(j=i;j<6;j++){f1=f1+job[x[j]][0];if(f2[i]>f1)f2[i+1]=f2[i]+job[x[j]][1]; elsef2[i+1]=f1+job[x[j]][1];if(f2[i+1]<bestf){swap(i,j);try(i+1);swap(i,j);}f1=f1-job[x[j]][0];}}}void swap(int i,int j){int temp;temp=x[i];x[i]=x[j];x[j]=temp;}18.#include<stdio.h>#define N 5 //N个数字#define M 2 //M个加号char buf[N];int a[N];char b[M+1][N];int c[M+1];int try(int t);void swap(int t1,int t2); int add();void output();int min=99999;int main(){int i;for(i=0;i<N;i++){scanf("%c",&buf[i]);}a[0]=0;for(i=1;i<=M;i++){a[i]=1;}for(;i<N;i++){a[i]=0;}try(1);output();printf("%d\n",min);return 0;}int try(int t){int j;int i;int sum;if(t>=N){sum=add();if(sum<min){min=sum;for(i=0;i<M+1;i++){c[i]=atoi(b[i]);}}/*for(i=0;i<N;i++){printf("%d",a[i]);}printf("\n");*/}else{for(j=t;j<N;j++){//if(a[t]!=a[j]){swap(t,j);try(t+1);swap(t,j);}//else//try(t+1);}}}void swap(int t1,int t2) {int t;t=a[t1];a[t1]=a[t2];a[t2]=t;}int add(){int sum=0;int i=0;int j;int k=0;int h=0;for(i=0;i<M+1;i++)for(j=0;j<N;j++)b[i][j]='Q';i=0;j=0;h=0;k=0;for(j=0;j<N;j++){if(a[j]==1){h=0;i++;b[i][h]=buf[j];//printf("%d ",atoi(b[i]));//printf("%d %d %c \n",i,h,b[i][h]); h++;}else{b[i][h]=buf[j];//printf("%d %d %c \n",i,h,b[i][h]); //printf("%d ",atoi(b[i]));h++;}}/*for(i=0;i<M+1;i++){for(j=0;j<N;j++)printf("%c ",b[i][j]);printf("\n");}*/for(i=0;i<M+1;i++){sum+=atoi(b[i]);}return sum;}void output(){int i;for(i=0;i<M+1;i++){printf("%d",atoi(b[i]));if(i!=M)printf("+");}printf("=");}19.#include<stdio.h>int main(void){int buf[100];int m,n;int i,j;buf[0]=1;buf[1]=1;scanf("%d%d",&n,&m);for(i=1;i<n;i++){buf[i+1]=buf[i];for(j=i;j>0;j--){buf[j]=buf[j]+buf[j-1];}}printf("%d\n",buf[m]);return 0;}20.#include<stdio.h>int max_sum4(int *a,int n);int max_sub_sum(int *a,int left,int right);int main(void){int a[6]={-2,11,-4,13,-5,-2};printf("%d\n",max_sum4(a,5));return 0;}int max_sum4(int *a,int n){return max_sub_sum(a,0,n);}int max_sub_sum(int *a,int left,int right){int center,i,max,left_sum,right_sum,s1,s2,s3,s4,lefts,rights,leftl,rightl; int buf[4];if(left==right)return a[left];else{center=(left+right)/2;left_sum=max_sub_sum(a,left,center); right_sum=max_sub_sum(a,center+1,right); s1=0;lefts=0;for(i=center;i>=left;i--){lefts+=a[i];if(lefts>s1)s1=lefts;}s2=0;rights=0;for(i=center+1;i<=right;i++){rights+=a[i];if(rights>s2)s2=rights;}s3=0;leftl=0;for(i=left;i<=center;i++){leftl+=a[i];if(leftl>s3)s3=leftl;}s4=0;rightl=0;for(i=right;i>=center+1;i--){rightl+=a[i];if(rightl>s4)s4=rightl;}buf[0]=s1+s2;buf[1]=s4+s3;buf[2]=left_sum;buf[3]=right_sum;max=0;for(i=0;i<=3;i++){if(buf[i]>max)max=buf[i];}return max; }}。