LeetCode //C - 797. All Paths From Source to Target

797. All Paths From Source to Target

Given a directed acyclic graph (DAG) of n nodes labeled from 0 to n - 1, find all possible paths from node 0 to node n - 1 and return them in any order.

The graph is given as follows: graph[i] is a list of all nodes you can visit from node i (i.e., there is a directed edge from node i to node graph[i][j]).
 

Example 1:

Input: graph = [[1,2],[3],[3],[]]
Output: [[0,1,3],[0,2,3]]
Explanation: There are two paths: 0 -> 1 -> 3 and 0 -> 2 -> 3.

Example 2:

Input: graph = [[4,3,1],[3,2,4],[3],[4],[]]
Output: [[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4],[0,1,4]]

Constraints:

• n == graph.length
• 2 <= n <= 15
• 0 <= graph[i][j] < n
• graph[i][j] != i (i.e., there will be no self-loops).
• All the elements of graph[i] are unique.
• The input graph is guaranteed to be a DAG.

From: LeetCode
Link: 797. All Paths From Source to Target

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Solution:

Ideas:

• DFS traversal is used to explore every path from node 0 to node n-1.

• A path[] keeps track of the current path.

• When reaching the last node (n - 1), copy path into the result.

• result stores all valid paths.

• returnSize stores the number of paths found.

• returnColumnSizes records the length of each path.

Code:

#define INITIAL_CAPACITY 128
#define MAX_NODES 15

void dfs(int** graph, int* graphColSize, int node, int* path, int pathLen,
         int*** result, int* returnSize, int* capacity, int** returnColumnSizes, int target) {
    path[pathLen++] = node;

    if (node == target) {
        if (*returnSize >= *capacity) {
            *capacity *= 2;
            *result = realloc(*result, (*capacity) * sizeof(int*));
            *returnColumnSizes = realloc(*returnColumnSizes, (*capacity) * sizeof(int));
        }
        (*result)[*returnSize] = malloc(sizeof(int) * pathLen);
        memcpy((*result)[*returnSize], path, sizeof(int) * pathLen);
        (*returnColumnSizes)[*returnSize] = pathLen;
        (*returnSize)++;
        return;
    }

    for (int i = 0; i < graphColSize[node]; ++i) {
        dfs(graph, graphColSize, graph[node][i], path, pathLen,
            result, returnSize, capacity, returnColumnSizes, target);
    }
}

int** allPathsSourceTarget(int** graph, int graphSize, int* graphColSize,
                           int* returnSize, int** returnColumnSizes) {
    int capacity = INITIAL_CAPACITY;
    int** result = malloc(sizeof(int*) * capacity);
    *returnColumnSizes = malloc(sizeof(int) * capacity);
    *returnSize = 0;

    int* path = malloc(sizeof(int) * graphSize); // max path length is graphSize
    dfs(graph, graphColSize, 0, path, 0, &result, returnSize, &capacity, returnColumnSizes, graphSize - 1);
    free(path);
    return result;
}