Given a right triangle of numbers, find the largest of the sum of numbers that appear on the paths starting from the top towards the base, so that on each path the next number is located directly below or below-and-one-place-to-the-right.
Input : 1 1 2 4 1 2 2 3 1 1 Output : 9 Explanation : 1 + 1 + 4 + 3 Input : 2 4 1 1 2 7 Output : 10 Explanation : 2 + 1 + 7
The idea is to find largest sum ending at every cell of last row and return maximum of these sums. We can recursively compute these sums by recursively considering above two cells. Since there are overlapping subproblems, we use dynamic programming to find the maximum sum ending at particular cell of last row.
Below is the implementation of above idea.
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- Maximum path sum in a triangle.
- Maximum number of squares that can fit in a right angle isosceles triangle
- Maximum number of 2x2 squares that can be fit inside a right isosceles triangle
- Minimum Sum Path in a Triangle
- Minimum length of the shortest path of a triangle
- Path with maximum average value
- Maximum sum path in a matrix from top to bottom
- Maximum decimal value path in a binary matrix
- Maximum Perimeter Triangle from array
- Maximum path sum for each position with jumps under divisibility condition
- Maximum weight path ending at any element of last row in a matrix
- Maximum height when coins are arranged in a triangle
- Maximum area of triangle having different vertex colors
- Maximum path sum that starting with any cell of 0-th row and ending with any cell of (N-1)-th row
- Divide an isosceles triangle triangle in two part with ratio of area as n:m
Improved By : jit_t