Add Four-Color algorithm page
Introduce an interactive Four Color Theorem demo: add FourColorComponent (template, styles, standalone component) with canvas-based grid, region generation, adjacency detection and a backtracking solver; include models for nodes/regions and grid constants. Wire up route and RouterConstants/UrlConstants, add menu entry in AlgorithmsService, and add i18n entries for English and German. Also add global color styles in styles.scss and a few minor i18n text adjustments.
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@@ -526,6 +526,10 @@
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"TITLE": "Maze Generation",
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"DESCRIPTION": "Visualizing various maze generation algorithms."
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},
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"FOUR_COLOR": {
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"TITLE": "Four Color Theorem",
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"DESCRIPTION": "The four color theorem states that any map in a plane can be colored using at most four colors in such a way that regions sharing a common boundary (other than a single point) do not share the same color."
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},
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"FRACTAL": {
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"TITLE": "Fractals",
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"DESCRIPTION": "Visualisation of complex geometric patterns that resemble each other on increasingly smaller scales (self-similarity)."
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@@ -545,5 +549,35 @@
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"NOTE": "Note",
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"GRID_HEIGHT": "Height",
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"GRID_WIDTH": "Width"
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},
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"FOUR_COLOR": {
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"TITLE": "Four Color Theorem",
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"GENERATE": "Generate Map",
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"SOLVE": "Auto Solve",
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"CLEAR": "Clear Colors",
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"COLOR_1": "Color 1",
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"COLOR_2": "Color 2",
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"COLOR_3": "Color 3",
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"COLOR_4": "Color 4",
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"EXECUTION_TIME": "Execution Time",
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"STATUS": {
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"LABEL": "Status",
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"INCOMPLETE": "Map is not fully colored yet.",
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"SOLVED": "Congratulations! You solved the map correctly!",
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"CONFLICTS": "Warning: Adjacent regions have the same color!",
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"INVALID": "Map is fully colored, but contains conflicts."
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},
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"EXPLANATION": { "TITLE": "Four Color Theorem",
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"EXPLANATION": "The four color theorem states that any map in a plane can be colored using at most four colors in such a way that regions sharing a common boundary (other than a single point) do not share the same color.",
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"DISCLAIMER": "This algorithm uses backtracking to find a valid coloring for the generated regions.",
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"DISCLAIMER_1": "Map Generation: Regions are generated using a random seed growth algorithm (Voronoi-like) on a grid.",
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"DISCLAIMER_2": "Adjacency: Two regions are considered neighbors if they share at least one edge in the grid.",
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"DISCLAIMER_3": "Backtracking: The solver tries colors 1-4 for each region, backtracking when a conflict is found.",
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"DISCLAIMER_4": "Interactive: You can also click on regions to cycle through colors manually.",
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"DISCLAIMER_BOTTOM": "Click to color the region. Click again to change the color."
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},
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"ALERT": {
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"NO_SOLUTION": "No solution found (this should not happen for a planar map!)."
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}
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}
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}
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