_931.java

package com.fishercoder.solutions;

/**
 * 931. Minimum Falling Path Sum
 *
 * Given a square array of integers A, we want the minimum sum of a falling path through A.
 * A falling path starts at any element in the first row, and chooses one element from each row.
 * The next row's choice must be in a column that is different from the previous row's column by at most one.
 *
 * Example 1:
 * Input: [[1,2,3],[4,5,6],[7,8,9]]
 * Output: 12
 * Explanation:
 * The possible falling paths are:
 * [1,4,7], [1,4,8], [1,5,7], [1,5,8], [1,5,9]
 * [2,4,7], [2,4,8], [2,5,7], [2,5,8], [2,5,9], [2,6,8], [2,6,9]
 * [3,5,7], [3,5,8], [3,5,9], [3,6,8], [3,6,9]
 * The falling path with the smallest sum is [1,4,7], so the answer is 12.
 *
 * Note:
 * 1 <= A.length == A[0].length <= 100
 * -100 <= A[i][j] <= 100
 * */
public class _931 {
    public static class Solution1 {
        public int minFallingPathSum(int[][] A) {
            int size = A.length;
            int[][] dp = new int[size][size];
            for (int i = 0; i < size; i++) {
                for (int j = 0; j < size; j++) {
                    if (i == 0) {
                        dp[i][j] = A[i][j];
                    } else {
                        int lastRow = dp[i - 1][j];
                        if (j - 1 >= 0) {
                            lastRow = Math.min(dp[i - 1][j - 1], lastRow);
                        }
                        if (j + 1 < size) {
                            lastRow = Math.min(dp[i - 1][j + 1], lastRow);
                        }
                        dp[i][j] = lastRow + A[i][j];
                    }
                }
            }
            int minSum = Integer.MAX_VALUE;
            for (int i = 0; i < size; i++) {
                minSum = Math.min(minSum, dp[size - 1][i]);
            }
            return minSum;
        }
    }
}