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-rw-r--r--min_falling_path_sum.cpp45
1 files changed, 45 insertions, 0 deletions
diff --git a/min_falling_path_sum.cpp b/min_falling_path_sum.cpp
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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
+}