LeetCode 756: Pyramid Transition Matrix Solution

Master LeetCode problem 756 (Pyramid Transition Matrix), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

756. Pyramid Transition Matrix

Medium

Bit Manipulation Depth-First Search Breadth-First Search

Problem Explanation

Explanation:

To solve this problem, we can use a recursive backtracking approach. We can iterate through all possible combinations of pairs of characters in the current row, check if they form a valid triangular pattern according to the given rules, and then recursively build the next row. If we reach the top of the pyramid successfully, we return true, otherwise, we backtrack and try other combinations.

Algorithm:

Create a map to store the allowed patterns for quick lookup.
Define a recursive function that takes the current row and the row above it as parameters.
If the current row has only one block, check if it is the top block of an allowed pattern by checking with the row above it.
If the current row has more than one block, iterate through all possible pairs of adjacent blocks, check if they form a valid pattern, and recursively call the function with the next row.
If we reach the top of the pyramid, return true. If no valid pyramid can be built, return false.

Time Complexity:

The time complexity of this approach is O(2^n) where n is the length of the bottom row, as we are exploring all possible combinations recursively.

Space Complexity:

The space complexity is O(m) where m is the number of allowed patterns, as we store the patterns in a map.

Solution Code

class Solution {
    public boolean pyramidTransition(String bottom, List<String> allowed) {
        Map<String, Set<String>> map = new HashMap<>();
        for (String pattern : allowed) {
            String base = pattern.substring(0, 2);
            String top = pattern.substring(2);
            map.putIfAbsent(base, new HashSet<>());
            map.get(base).add(top);
        }
        return buildPyramid(bottom, "", map);
    }

    private boolean buildPyramid(String row, String above, Map<String, Set<String>> map) {
        if (row.length() == 1) {
            return true;
        }
        if (above.length() + 1 == row.length()) {
            return buildPyramid(row, "", map);
        }

        int pos = above.length();
        String base = row.substring(pos, pos + 2);
        if (!map.containsKey(base)) {
            return false;
        }

        for (String top : map.get(base)) {
            if (buildPyramid(row, above + top, map)) {
                return true;
            }
        }

        return false;
    }
}

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