8.5矩阵运算，A是一个x行，y列矩阵，B是y行z列矩阵，把A和B相乘，结果是另外一个x行z列矩阵，每个位置的值由下公式决定,编写函数：
#include <stdio.h>
void matrix_mutiply(int *m1, int *m2, int *r, int x, int y, int z)
{
//sum为求和值
int i, j, k, sum;
for(i = 0; i < x; i++){
for(j = 0; j < z; j++){
//对i行j列的矩阵求值
for(sum = 0, k = 0; k < y; k++){
//由于m1 m2 r均为一维数组，矩阵上的i 行 j位，对应的一维坐标为 i * 列数 + j
sum += m1[ i * y + k ] * m2[ k * z + j ];
}
r[i * z + j] = sum;
}
}
}
int main()
{
int m1[6] = { 2, -6, 3, 5, 1, -1 };
int m2[8] = { 4, -2, -4, -5, -7, -3, 6, 7};
int r[12] = {};
matrix_mutiply(m1, m2, r, 3, 2, 4);
int x, y;
for(x = 0; x < 3; x++){
for(y = 0; y < 4; y++){
printf("%5d ", r[x * 4 + y]);
}
printf("
");
}
return 0;
}
输出：
8.6 编写函数array_offset，参数array_info数组中，第一个元素表示数组维数，第二个和第三个表示第一维的下标的最小和最大值，以此类推，...参数表示数组下标，函数返回下标对应的元素的的偏移量。
#include <stdarg.h>
int array_offset(int array_info[], ...)
{
int dimension = array_info[0];
//超出维度范围直接返回-1
if(1 > dimension || 10 < dimension){
return -1;
}
//当前维度和偏移量以及当前下标
int now;
int offset;
int index;
va_list arg;
va_start(arg, array_info);
//每次进两位，有上下限两个数
for(now = 1, offset = 0; now <= dimension * 2; now += 2){
//获取一个下标值
index = va_arg(arg, int);
//和对应的array_info中上下限对比，超过返回-1;
if(index < array_info[now] || index > array_info[now + 1]){
return -1;
}
//之前一维度的偏移量 乘以 维度 加上当前维度的偏移量
offset = offset * (array_info[now + 1] - array_info[now] + 1) + index - array_info[now];
}
va_end(arg);
return offset;
}
#include <stdio.h>
#include "function.c"
int main()
{
int array_info[] = {3, 4, 6, 1, 5, -3, 3};
printf("%d
", array_offset(array_info, 4, 1, -3));
printf("%d
", array_offset(array_info, 4, 1, 3));
printf("%d
", array_offset(array_info, 5, 1, -3));
printf("%d
", array_offset(array_info, 4, 1, -2));
printf("%d
", array_offset(array_info, 4, 2, -3));
printf("%d
", array_offset(array_info, 6, 3, 1));
return 0;
}
执行结果：
8.7 修改上一题，使左边的下标先变化
#include <stdio.h>
#include <stdarg.h>
int array_offset2(int array_info[], ...)
{
int dimension = array_info[0];
//超出维度范围直接返回-1
if(1 > dimension || 10 < dimension){
return -1;
}
//当前维度和偏移量以及当前下标
int now;
int offset;
int index;
int muti;
va_list arg;
va_start(arg, array_info);
//每次进两位，有上下限两个数
for(now = 1, offset = 0, muti = 1; now <= dimension * 2; now += 2){
//获取一个下标值
index = va_arg(arg, int);
//和对应的array_info中上下限对比，超过返回-1;
if(index < array_info[now] || index > array_info[now + 1]){
return -1;
}
//muti是一个乘积，代表一个下标位移要移动的位数。从左到右，越来越大。就是前一个维度的 阶乘
if(now == 1){
muti = 1;
}else{
muti *= array_info[now - 1] - array_info[now - 2] + 1;
}
offset += (index - array_info[now]) * muti;
}
va_end(arg);
return offset;
}
int main()
{
int array_info[] = {3, 4, 6, 1, 5, -3, 3};
printf("%d
", array_offset2(array_info, 4, 1, -3));
printf("%d
", array_offset2(array_info, 4, 2, -3));
printf("%d
", array_offset2(array_info, 4, 1, -1));
return 0;
}
运行结果：
8.8 八皇后，皇后的攻击范围像米字一样，在8 × 8的棋盘上，放8个皇后。使皇后直接无法相互攻击。
#include <stdio.h>
#define TRUE 1
#define FALSE 0
/*在8 * 8棋盘上， 0 代表空位置， 1 代表皇后
函数返回 1 表示(x, y) 安全， 返回 0 表示不安全
*/
//从上到下一行一行进行的，所以只要验证x,y的上方就可以了，下方还没有皇后
int safe(int chess[8][8], int x, int y)
{
int index;
for(index = 0; index < 8; index++){
//横向验证
if(chess[x][index]){
return FALSE;
}
//竖验证
if( index < x && chess[index][y]){
return FALSE;
}
//左上角验证
if(x >= index && y >= index && chess[x - index][y - index]){
return FALSE;
}
//右上角验证
if(x >= index && (y + index) < 8 && chess[x - index][y + index]){
return FALSE;
}
}
return TRUE;
}
//打印棋盘
void print_chess(int chess[8][8])
{
int x, y;
static int total = 0;;
printf("%d
", ++total);
for(x = 0; x < 8; x++){
for(y = 0; y < 8; y++){
printf("%-3d", chess[x][y]);
}
printf("
");
}
printf("
");
}
//递归查找八皇后
int eight_queen(int chess[8][8], int x)
{
//每行从左到右一个一个尝试
for(int index = 0; index < 8; index++){
//当此位置可以加入皇后的时候
if(safe(chess, x, index)){
//尝试设置皇后位置
chess[x][index] = 1;
//递归查找八皇后，如果是最后一行，找完，打印棋盘
if(x == 7){
print_chess(chess);
}else{
eight_queen(chess, x + 1);
}
}
//恢复棋盘，右移一位，再查找皇后位置
chess[x][index] = 0;
}
}
int main(int argc, char const *argv[])
{
int chess[8][8] = {};
eight_queen(chess, 0);
}
运行结果：
1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 5 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 6 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 7 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 8 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 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