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Lantern Pattern Paths

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At the Festival of Threads, architects illuminate a riverside maze with lantern arcs that shimmer above the tide. The design always begins with a single walkway, described by a short phrase that tells visitors when to pause and look up. Curators then announce how many mirrored corridors will wrap around that walkway. Each corridor has a signature name—such as "Azure Bridge" or "Golden Spine"—and ushers recite a predictable rhythm when guiding guests through the added layer.

The rhythm never changes. To surround an inner layout with a corridor named marker, ushers first say "Enter {marker}" while stepping into the new lights. They let guests experience the inner layout completely, then whisper "Mirror {marker}" to signal the balanced return, replay the inner layout again, and finally announce "Exit {marker}" to close the loop. When no corridors remain, the only phrase spoken is the base walkway description. Each layer therefore wraps the inner list of phrases with three new lines and a second pass through the inner path, creating a woven experience that still respects the original center.

You must list every phrase in the order the ushers speak them. The input provides base, the innermost walkway phrase, and markers, an array of corridor names ordered from the closest layer outward. Return an array of strings describing the full script. If markers is empty, return an array containing only base. Otherwise process the markers recursively: the first element wraps the base, the second wraps that result, and so on.

Examples

Example 1
Input
base = "Pause by the willow.", markers = []
Output
["Pause by the willow."]
Explanation

Example with input: base = "Pause by the willow.", markers = []

Example 2
Input
base = "Listen for distant bells.", markers = ["Golden Spine", "Silver Veil"]
Output
["Enter Golden Spine", "Enter Silver Veil", "Listen for distant bells.", "Mirror Silver Veil", "Listen for distant bells.", "Exit Silver Veil", "Mirror Golden Spine", "Enter Silver Veil", "Listen for distant bells.", "Mirror Silver Veil", "Listen for distant bells.", "Exit Silver Veil", "Exit Golden Spine"]
Explanation

Example with input: base = "Listen for distant bells.", markers = ["Go

Example 3
Input
base = "Pause by the willow.", markers = ["Azure Bridge"]
Output
["Enter Azure Bridge", "Pause by the willow.", "Mirror Azure Bridge", "Pause by the willow.", "Exit Azure Bridge"]
Explanation

Example with input: base = "Pause by the willow.", markers = ["Azure B

Algorithm Flow

Recommendation Algorithm Flow for Lantern Pattern Paths - Budibadu
Recommendation Algorithm Flow for Lantern Pattern Paths - Budibadu

Best Answers

java
class Solution {
    public int lantern_pattern_paths(int m, int n) {
        return (int) nCr(m + n - 2, m - 1);
    }
    private long nCr(int n, int r) {
        if (r > n) return 0;
        if (r == 0 || r == n) return 1;
        if (r > n / 2) r = n - r;
        long res = 1;
        for (int i = 1; i <= r; i++) {
            res = res * (n - i + 1) / i;
        }
        return res;
    }
}