The minimum number of remaining Quxes depends on the counts modulo 3

If all three counts have the same remainder when divided by 3, the minimum is the maximum of the three counts

Otherwise, the minimum is determined by the mathematical relationship between the remainders

Key insight: transformations preserve certain invariants related to the count differences

Code

[{"language":"C++","code":"class Solution {\npublic:\n    int minQuxes(vector<char>& quxes) {\n        if (quxes.empty()) return 0;\n        if (quxes.size() == 1) return 1;\n        \n        // Count each color\n        int r = 0, g = 0, b = 0;\n        for (char qux : quxes) {\n            if (qux == 'R') r++;\n            else if (qux == 'G') g++;\n            else b++;\n        }\n        \n        // Mathematical approach based on modular arithmetic\n        int r_mod = r % 3;\n        int g_mod = g % 3;\n        int b_mod = b % 3;\n        \n        // If all remainders are equal, minimum is max count\n        if (r_mod == g_mod && g_mod == b_mod) {\n            return max({r, g, b});\n        }\n        \n        // Calculate minimum based on the mathematical pattern\n        int total = r + g + b;\n        int min_count = (total + 2) / 3;\n        \n        // Special case: if total is divisible by 3 and counts are balanced\n        if (total % 3 == 0) {\n            int diff1 = abs(r - g);\n            int diff2 = abs(g - b);\n            int diff3 = abs(b - r);\n            int max_diff = max({diff1, diff2, diff3});\n            return max(1, max_diff);\n        }\n        \n        return min_count;\n    }\n};","lang":"cpp","html":"<pre class=\"shiki shiki-themes github-light github-dark\" style=\"background-color:#fff;--shiki-dark-bg:#24292e;color:#24292e;--shiki-dark:#e1e4e8\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">class</span><span style=\"color:#6F42C1;--shiki-dark:#B392F0\"> Solution</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\"> {</span></span>\n<span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">public:</span></span>\n<span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">    int</span><span style=\"color:#6F42C1;--shiki-dark:#B392F0\"> minQuxes</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">(</span><span style=\"color:#6F42C1;--shiki-dark:#B392F0\">vector</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">&#x3C;</span><span style=\"color:#D73A49;--shiki-dark:#F97583\">char</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">></span><span style=\"color:#D73A49;--shiki-dark:#F97583\">&#x26;</span><span style=\"color:#E36209;--shiki-dark:#FFAB70\"> quxes</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">) {</span></span>\n<span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">        if</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\"> (quxes.</span><span style=\"color:#6F42C1;--shiki-dark:#B392F0\">empty</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">()) </span><span style=\"color:#D73A49;--shiki-dark:#F97583\">return</span><span style=\"color:#005CC5;--shiki-dark:#79B8FF\"> 0</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">;</span></span>\n<span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">        if</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\"> (quxes.</span><span style=\"color:#6F42C1;--shiki-dark:#B392F0\">size</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">() </span><span style=\"color:#D73A49;--shiki-dark:#F97583\">==</span><span style=\"color:#005CC5;--shiki-dark:#79B8FF\"> 1</span>

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