打印出矩阵中最长的增加路径
Printing out the longest increasing path in a matrix
我在这里发表了类似的帖子，但没有得到任何反馈。问题来自这里。
我试图简单地打印出最长增加的矩阵的条目。我以为我在尝试以下矩阵时就知道了：
2 2 1
1 2 1
2 2 1
我得到了一个输出：
1
2
然后，当我增加n，m = 4时。我得到了这个矩阵：
2 2 1 1
2 1 2 2
1 2 2 3
1 2 1 3
和该路径条目的输出：
1
1
2
应该只是：
1
2
3
这是我的代码：
#include <algorithm>
#include <cmath>
#include <list>
#include <vector>
#include <stdio.h>
#include <random>
#include <utility>
#include <iostream>
void printPath(std::vector<int> &numPaths) {
std::sort(numPaths.begin(), numPaths.end());
for(int i = 0; i < numPaths.size(); i++) {
std::cout << numPaths[i] << std::endl;
}
}
int DFS(int i, int j, const std::vector<std::vector<int> > &matrix, std::vector<std::vector<int> > &length) {
std::vector<std::pair<int,int> > dics{{-1,0},{1,0},{0,-1},{0,1}}; // used to check the directions left, right, up, down
std::vector<int> path;
if(length[i][j] == -1) {
int len = 0;
for(auto p: dics) {
int x = i + p.first, y = j + p.second;
if(x < 0 || x >= matrix.size() || y < 0 || y >= matrix[0].size()) continue; // Check to make sure index is not out of boundary
if(matrix[x][y] > matrix[i][j]) { // compare number
len = std::max(len, DFS(x,y,matrix,length));
}
}
length[i][j] = len + 1;
}
return length[i][j];
}
int longestPath(std::vector<std::vector<int> > matrix) {
int n = matrix[0].size();
if (n == 0) {
return 0;
}
int m = matrix.size();
if (m == 0) {
return 0;
}
std::vector<std::vector<int> > length(m, std::vector<int>(n,-1));
std::vector<int> numPaths;
int len = 0;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
int newLen = DFS(i,j,matrix,length);
if(newLen > len) {
numPaths.push_back(matrix[i][j]);
}
len = std::max(len, DFS(i, j, matrix, length));
}
}
printPath(numPaths);
return len;
}
int main() {
// Specify the number of rows and columns of the matrix
int n = 4;
int m = 4;
// Declare random number generator
std::mt19937 gen(10);
std::uniform_int_distribution<> dis(1, 3);
// Fill matrix
std::vector<std::vector<int> > matrix;
for(int i = 0; i < m; i++) {
std::vector<int> row;
for(int j = 0; j < n; j++) {
row.push_back(0);
}
matrix.push_back(row);
}
// Apply random number generator to create matrix
for(int i = 0; i < m; i++) {
for(int j = 0; j < n; j++) {
matrix[i][j] = dis(gen);
}
}
// Print matrix to see contents
for(int i = 0; i < m; i++) {
for(int j = 0; j < n; j++) {
std::cout << matrix[i][j] << " ";
}
std::cout << std::endl;
}
std::cout << std::endl;
//std::vector<std::vector<int> > mat = {{1,2,3}};
int result = longestPath(matrix);
std::cout << "The longest path is " << result << std::endl;
}
如果有人能告诉我我出错了哪里，我真的很感激。
#include <algorithm>
#include <cmath>
#include <vector>
#include <stdio.h>
#include <random>
#include <utility>
#include <iostream>
#define MATRIX_SIZE 1000
void printPath(std::vector<int> &numPaths) {
std::sort(numPaths.begin(), numPaths.end());
for(int i = 0; i < numPaths.size(); i++) {
std::cout << numPaths[i] << std::endl;
}
}
int DFS(int i, int j, const std::vector<std::vector<int> > &matrix, std::vector<std::vector<int> > &length) {
std::vector<std::pair<int,int> > dics{{-1,0},{1,0},{0,-1},{0,1}}; // used to check the directions left, right, up, down
std::vector<int> path;
if(length[i][j] == -1) {
int len = 0;
for(auto p: dics) {
int x = i + p.first, y = j + p.second;
if(x < 0 || x >= matrix.size() || y < 0 || y >= matrix[0].size()) continue; // Check to make sure index is not out of boundary
if(matrix[x][y] > matrix[i][j]) { // compare number
len = std::max(len, DFS(x,y,matrix,length));
}
}
length[i][j] = len + 1;
}
return length[i][j];
}
void printMatrix(std::vector<std::vector<int>> &matrix) {
for (int i =0; i < matrix.size(); i++) {
for (int j =0; j < matrix[0].size(); j++) {
std::cout << matrix[i][j] << " ";
}
std::cout << std::endl;
}
}
std::vector<int> generatePath(int i, int j, const std::vector<std::vector<int>> &matrix, const std::vector<std::vector<int>> &length) {
int max_length = length[i][j];
std::vector<int> path(max_length, 0);
for (int current_length = max_length; current_length >= 1; current_length--) {
std::vector<std::pair<int,int> > dics{{-1,0},{1,0},{0,-1},{0,1}}; // used to check the directions left, right, up, down
int index = max_length - current_length;
for (auto p: dics) {
path[index] = matrix[i][j];
int x = i + p.first, y = j + p.second;
if(x < 0 || x >= matrix.size() || y < 0 || y >= matrix[0].size()) continue;
if (current_length - length[x][y] == 1) {
i = x;
j = y;
break;
}
}
}
printPath(path);
return path;
}
int longestPath(std::vector<std::vector<int> > matrix) {
int n = matrix[0].size();
if (n == 0) {
return 0;
}
int m = matrix.size();
if (m == 0) {
return 0;
}
std::vector<std::vector<int> > length(m, std::vector<int>(n,-1));
std::vector<int> numPaths;
int len = 0;
int maxRow = 0;
int maxCol = 0;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
int currentLength = DFS(i, j, matrix, length);
if (currentLength > len) {
len = currentLength;
maxRow = i;
maxCol = j;
}
}
}
generatePath(maxRow, maxCol, matrix,length);
return len;
}
int main(int argc, char *argv[]) {
std::mt19937 gen(10);
std::uniform_int_distribution<> dis(1, 1000000);
// Fill matrix
std::vector<std::vector<int> > matrix;
for(int i = 0; i < MATRIX_SIZE; i++) {
std::vector<int> row;
for(int j = 0; j < MATRIX_SIZE; j++) {
row.push_back(0);
}
matrix.push_back(row);
}
// Apply random number generator to create matrix
for(int i = 0; i < MATRIX_SIZE; i++) {
for(int j = 0; j < MATRIX_SIZE; j++) {
matrix[i][j] = dis(gen);
}
}
// Print matrix
//printMatrix(matrix);
timespec start, end;
clock_gettime(CLOCK_REALTIME, &start);
printf("the longest path is %dn", longestPath(matrix));
clock_gettime(CLOCK_REALTIME, &end);
printf("found in %ld microsn", (end.tv_sec * 1000000 + end.tv_nsec / 1000) - (start.tv_sec * 1000000 + start.tv_nsec / 1000));
return 0;
}
# Print the Longest Increasing Path in a Matrix #
class Solution:
# Possible directions allowed from the given question.
DIRECTIONS = [[1, 0], [-1, 0], [0, 1], [0, -1]]
def longestIncreasingPath(self, matrix):
# From the given question:
# ----- m = rows ----- i
# ----- n = cols ----- j
m = len(matrix)
if m == 0:
return 0
n = len(matrix[0])
if n == 0:
return 0
cache = [[0] * n for _ in range(m)]
longestPath = 0
maximum = 1
for i in range(m):
for j in range(n):
longestPath = self.depthFirstSearch(matrix, i, j, m, n, cache)
maximum = max(maximum, longestPath)
return (cache, maximum)
def depthFirstSearch(self, matrix, i, j, m, n, cache):
if cache[i][j] != 0:
return cache[i][j]
maxPath = 1
for direction in self.DIRECTIONS:
x = direction[0] + i
y = direction[1] + j
if x < 0 or y < 0 or x >= m or y >= n or matrix[x][y] <= matrix[i][j]:
continue
length = 1 + self.depthFirstSearch(matrix, x, y, m, n, cache)
maxPath = max(maxPath, length)
cache[i][j] = maxPath # Save the value at i, j for future usage.
return maxPath
def printPath(self, matrix):
# Check if longestPath is 0.
if not self.longestIncreasingPath(matrix):
return None
length = self.longestIncreasingPath(matrix)[1]
cache = self.longestIncreasingPath(matrix)[0]
# From the given question:
# ----- m = rows ----- i
# ----- n = cols ----- j
m = len(cache)
n = len(cache[0])
location = []
# Traverse the cache to obtain the location of the starting point of the longest increasing path in the matrix.
# Time complexity, T(n) = O(n*m) ----- if not a square matrix.
for i in range(m):
for j in range(n):
if cache[i][j] == length:
location.extend([i, j])
i, j = location[0], location[1]
result = [matrix[i][j]] # The result container is initialised with the element of the matrix at the obtained position
# Time complexity, T(n) = O(4n) ----- where n = length of longest increasing path in the given matrix and the 4 being the length of the DIRECTIONS matrix.
for _ in range(length):
for direction in self.DIRECTIONS:
x = direction[0] + i
y = direction[1] + j
if x < 0 or y < 0 or x >= m or y >= n or cache[i][j] - 1 != cache[x][y]:
continue
result.append(matrix[x][y])
i = x
j = y
return result
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