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#include "leetcode.h"
/*
* given NxN array of integers 'matrix' return the minimum
* sum of any falling path through 'matrix'
*
* a falling path starts at any element in row 0 and chooses
* the element in the next row that is either directly below
* or diagonally left/right that obviously makes for the lowest sum
*/
class Solution {
public:
int minFallingPathSum(vvd(int) & matrix) {
vvd(int) dp(matrix.size(), vector<int>(matrix.size(), INT_MAX));
for (int i = 0; i < matrix.size(); i++)
dp[0][i] = matrix[0][i];
for (int i = 1; i < matrix.size(); i++) {
for (int j = 0; j < matrix.size(); j++) {
if (j > 0 && j < matrix.size() - 1) {
dp[i][j] =
min(dp[i - 1][j - 1] + matrix[i][j], dp[i - 1][j] + matrix[i][j]);
dp[i][j] = min(dp[i - 1][i + 1] + matrix[i][j], dp[i][j]);
} else if (j == 0)
dp[i][j] =
min(dp[i - 1][j + 1] + matrix[i][j], dp[i - 1][j] + matrix[i][j]);
else if (j == matrix.size() - 1)
dp[i][j] =
min(dp[i - 1][j - 1] + matrix[i][j], dp[i - 1][j] + matrix[i][j]);
}
}
int ans = INT_MAX;
for (auto &x : dp[dp.size() - 1])
ans = min(ans, x);
return ans;
}
};
int main() {
Solution obj;
vvd(int) matrix = {{2, 1, 3}, // 1
{6, 5, 4}, //-> 4
{7, 8, 9}}; // 8 <-
cout << obj.minFallingPathSum(matrix); // expect 13
}
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