LeetCode //C - 1301. Number of Paths with Max Score

1301. Number of Paths with Max Score

You are given a square board of characters. You can move on the board starting at the bottom right square marked with the character 'S'.

You need to reach the top left square marked with the character 'E'. The rest of the squares are labeled either with a numeric character 1, 2, ..., 9 or with an obstacle 'X'. In one move you can go up, left or up-left (diagonally) only if there is no obstacle there.

Return a list of two integers: the first integer is the maximum sum of numeric characters you can collect, and the second is the number of such paths that you can take to get that maximum sum, taken modulo 10^9 + 7.

In case there is no path, return 0, 0.

Example 1:

Input: board = "E23","2X2","12S"

Output: 7,1

Example 2:

Input: board = "E12","1X1","21S"

Output: 4,2

Example 3:

Input: board = "E11","XXX","11S"

Output: 0,0

Constraints:

• 2 <= board.length == boardi.length <= 100

From: LeetCode

Link: 1301. Number of Paths with Max Score

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Solution:

Ideas:

Use dynamic programming to store the maximum score and number of maximum-score paths reaching each cell.

Code:

#include <stdlib.h>
#include <string.h>

#define MOD 1000000007

/**
 * Note: The returned array must be malloced, assume caller calls free().
 */
int* pathsWithMaxScore(char **board, int boardSize, int* returnSize) {
    int maxScore[100][100];
    int pathCount[100][100];

    for (int i = 0; i < boardSize; i++) {
        for (int j = 0; j < boardSize; j++) {
            maxScore[i][j] = -1;
            pathCount[i][j] = 0;
        }
    }

    maxScore[0][0] = 0;
    pathCount[0][0] = 1;

    for (int i = 0; i < boardSize; i++) {
        for (int j = 0; j < boardSize; j++) {
            if (board[i][j] == 'X' || (i == 0 && j == 0)) {
                continue;
            }

            int best = -1;
            long long ways = 0;

            /* Cell above */
            if (i > 0 && maxScore[i - 1][j] > best) {
                best = maxScore[i - 1][j];
                ways = pathCount[i - 1][j];
            } else if (i > 0 && maxScore[i - 1][j] == best && best != -1) {
                ways += pathCount[i - 1][j];
            }

            /* Cell to the left */
            if (j > 0 && maxScore[i][j - 1] > best) {
                best = maxScore[i][j - 1];
                ways = pathCount[i][j - 1];
            } else if (j > 0 && maxScore[i][j - 1] == best && best != -1) {
                ways += pathCount[i][j - 1];
            }

            /* Upper-left diagonal cell */
            if (i > 0 && j > 0 && maxScore[i - 1][j - 1] > best) {
                best = maxScore[i - 1][j - 1];
                ways = pathCount[i - 1][j - 1];
            } else if (i > 0 && j > 0 &&
                       maxScore[i - 1][j - 1] == best && best != -1) {
                ways += pathCount[i - 1][j - 1];
            }

            if (best == -1) {
                continue;
            }

            int value = 0;

            if (board[i][j] >= '1' && board[i][j] <= '9') {
                value = board[i][j] - '0';
            }

            maxScore[i][j] = best + value;
            pathCount[i][j] = ways % MOD;
        }
    }

    int* result = (int*)malloc(2 * sizeof(int));
    *returnSize = 2;

    if (maxScore[boardSize - 1][boardSize - 1] == -1) {
        result[0] = 0;
        result[1] = 0;
    } else {
        result[0] = maxScore[boardSize - 1][boardSize - 1];
        result[1] = pathCount[boardSize - 1][boardSize - 1];
    }

    return result;
}