我正在开发一个wiki文章中描述的方法的实现，用于就地缓存 - 不规则转换方形矩阵。
https://en.wikipedia.org/wiki/In-place_matrix_transposition
该算法基本上递归地将矩阵分成四个，然后转换沿对角线的象限并交换其上下的象限。仅当矩阵的大小为2 * 2或更低时才会发生实际的转置/交换，否则会再次拆分。
我把它分成三个功能：
这将启动给定大小N的过程：
void SmartTranspose(int A[row][col]) {
Transpose(A, 0, 0, N, N);
}
然后：
void Transpose(int A[row][col], int x, int y, int w, int h) {
int Temp;
if ((w - x) * (h - y) <= 4){
for (int row1 = x ; row1 < w -1 ; row1++)
for (int col1 = y + 1 ; col1 < h ; col1++) {
Temp = A[row1][col1];
printf("transp: %d %d\n", A[row1][col1], A[col1] [row1]);
A[row1][col1] = A[col1][row1];
A[col1][row1] = Temp;
}
}
else {
int halfh = h / 2;
int halfw = w / 2;
Transpose(A, x, y, halfw , halfh);
Transpose(A, x + halfw, y + halfh, w , h);
TransposeSwap(A, x + halfw, y, w, halfh, x, y + halfh, halfw , h);
}
}
最后：
void TransposeSwap(int A[row][col], int x, int y, int w, int h,int x1, int y1, int w1, int h1) {
int Temp; int row2 = x1; int col2 = y1;
if ((w - x) * (h - y) <= 4 && (w1 - x1) * (h1 - y1) <= 4) {
for(row1 = x; row1 < w; row1++)
for(col1 = y; col1 < h; col1++)
{
Temp = A[row1][col1] ;
A[row1][col1] = A[col1][row1];
A[col1][row1] = Temp;
}
}
else {
printf("RECURSE");
int halfh = h / 2;
int halfw = w / 2;
int halfh1 = h1 / 2;
int halfw1 = w1 / 2;
TransposeSwap(A, x, y, halfw, halfh, x1, y1, halfw1, halfh1);
TransposeSwap(A, x + halfw, y, w, h - halfh, x1, y1 + halfh1, halfw1, h1);
TransposeSwap(A, x , y + halfh, halfw, h, x1 + halfw1, y1, w1, halfh1);
TransposeSwap(A, x + halfw, y + halfh, w, h, x1 + halfw1, y1 + halfh1, w1, h1);
}
}
然而，这不起作用，我很难看到我的逻辑在哪里出错了。
编辑：输出示例
Original matrix:
1948037971 40713922 986050715 74181839 943010147 1060710730
18590233 268906808 1966315840 1325423973 398061279 2047858287
513589654 1727398080 2016821685 277200601 1611383116 2000671901
228038281 1863845528 106517081 1934721636 745170263 1736525254
224427632 687572994 1249224754 1497415191 537022734 1443375385
1054092341 337577057 1484089307 2040143056 411758897 279615807
Transposed matrix:
1948037971 18590233 513589654 74181839 943010147 1060710730
40713922 268906808 1727398080 1325423973 398061279 2047858287
986050715 1966315840 2016821685 277200601 1611383116 2000671901
228038281 1863845528 106517081 1934721636 745170263 1736525254
224427632 687572994 1249224754 1497415191 537022734 1443375385
1054092341 337577057 1484089307 2040143056 411758897 279615807
正确的输出应该是转置矩阵。
编辑：主要功能和声明：
int row = 40000 , col = 40000;
static int A[40000][40000];
static int N[100] = {0};
void SmartTranspose(int A[row][col]);
void Transpose(int A[row][col], int x, int y, int w, int h);
void InitializeMatrix(int X[row][col]);
void PrintMatrix(int X[row][col]);
double pow(double x, double y);
int matrix = 0;
void TransposeSwap(int A[row][col], int x, int y, int w, int h,int x1, int y1, int w1, int h1);
int main(){
srand(time(NULL));
double sizes = 0;
int count = 0;
for(sizes = 20; sizes < 30; sizes++)
{
N[count] = floor(pow(2, (sizes/9)));
printf("N %d\n", N[count]);
count++; }
for (matrix = 0; matrix <= count -1 ; matrix++){
InitializeMatrix(A);
printf("N %d\n",N[matrix]);
printf("\nOriginal matrix: \n");
SmartTranspose(A);
printf("E\n");
printf("\nTransposed matrix: \n");
PrintMatrix(A);
}
return 0;
}
指向完整代码的链接：https://jpst.it/QaBq
答案 0 :(得分：1)
这是我尝试演示一种工作算法。由于矩阵是方形的，我已经消除了一些函数参数。另外，我留下了一些调试代码，以显示每个递归级别的算法进度。
它可以转置任何对角线位于主对角线上的子矩阵。我在100x100阵列的0,0角测试了9x9矩阵。
#include <stdio.h>
int dbglvl;
void TransposeSwap(int dim, int A[dim][dim], int rs, int cs, int re, int ce) {
int Temp;
for (Temp = 0; Temp < dbglvl; Temp++) {
putchar('>');
}
printf("TransposeSwap(dim=%d, rs=%d, cs=%d, re=%d, ce=%d)\n", dim, rs, cs, re, ce);
if (re - rs <= 2 && ce - cs <= 2) {
for (int r = rs; r < re; r++)
for (int c = cs; c < ce; c++)
{
printf("transp %d %d: %d %d\n", r, c, A[r][c], A[c][r]);
Temp = A[r][c] ;
A[r][c] = A[c][r];
A[c][r] = Temp;
}
}
else {
int rm = (rs + re) / 2;
int cm = (cs + ce) / 2;
dbglvl++;
TransposeSwap(dim, A, rs, cs, rm, cm);
TransposeSwap(dim, A, rm, cs, re, cm);
TransposeSwap(dim, A, rs, cm, rm, ce);
TransposeSwap(dim, A, rm, cm, re, ce);
dbglvl--;
}
for (Temp = 0; Temp < dbglvl; Temp++) {
putchar('<');
}
printf("TransposeSwap\n");
}
void Transpose(int dim, int A[dim][dim], int s, int e) {
int Temp;
for (Temp = 0; Temp < dbglvl; Temp++) {
putchar('>');
}
printf("Transpose(dim=%d, s=%d, e=%d)\n", dim, s, e);
if (e - s <= 2) {
for (int r = s; r < e - 1 ; r++)
for (int c = s + 1 ; c < e ; c++) {
printf("transp %d %d: %d %d\n", r, c, A[r][c], A[c][r]);
Temp = A[r][c];
A[r][c] = A[c][r];
A[c][r] = Temp;
}
}
else {
int m = (s + e) / 2;
dbglvl++;
Transpose(dim, A, s, m);
Transpose(dim, A, m, e);
TransposeSwap(dim, A, m, s, e, m);
dbglvl--;
}
for (Temp = 0; Temp < dbglvl; Temp++) {
putchar('<');
}
printf("Transpose\n");
}
void Dump(int dim, int A[dim][dim], int rs, int cs, int re, int ce) {
int r, c;
for (r = rs; r < re; r++) {
for (c = cs; c < ce; c++) {
printf("%d ", A[r][c]);
}
putchar('\n');
}
}
#define N 100
int test[N][N] = {
{ 11, 12, 13, 14, 15, 16, 17, 18, 19 },
{ 21, 22, 23, 24, 25, 26, 27, 28, 29 },
{ 31, 32, 33, 34, 35, 36, 37, 38, 39 },
{ 41, 42, 43, 44, 45, 46, 47, 48, 49 },
{ 51, 52, 53, 54, 55, 56, 57, 58, 59 },
{ 61, 62, 63, 64, 65, 66, 67, 68, 69 },
{ 71, 72, 73, 74, 75, 76, 77, 78, 79 },
{ 81, 82, 83, 84, 85, 86, 87, 88, 89 },
{ 91, 92, 93, 94, 95, 96, 97, 98, 99 },
};
int main(void) {
puts("Original:");
Dump(N, test, 0, 0, 9, 9);
putchar('\n');
dbglvl = 1;
Transpose(N, test, 0, 9);
putchar('\n');
puts("Transposed:");
Dump(N, test, 0, 0, 9, 9);
return 0;
}