Runtime beats 100.00%, Memory beats 80.00% [EXPLAINED]
Intuition\nThe problem requires dividing an array of integers into k subsets such that each subset contains unique elements, and the goal is to minimize the tot
# Intuition\nThe problem requires dividing an array of integers into k subsets such that each subset contains unique elements, and the goal is to minimize the total incompatibility, defined as the difference between the maximum and minimum values in each subset.\n\n# Approach\nUse bitmasking to represent subsets of numbers, check each subset for uniqueness, calculate incompatibility, and use dynamic programming to find the minimum total incompatibility for all possible groupings.\n\n# Complexity\n- Time complexity:\nO(k . 2n) because we explore all possible subsets and their combinations.\n\n- Space complexity:\nO(2n) for storing results of subsets in the dynamic programming table.\n\n# Code\n```typescript []\n/**\n * Function to calculate the minimum incompatibility of dividing the array into k subsets.\n * @param nums - An array of integers representing the input numbers.\n * @param k - The number of subsets to divide the array into.\n * @return The minimum possible sum of incompatibilities, or -1 if not possible.\n */\nfunction minimumIncompatibility(nums: number[], k: number): number {\n    const N = nums.length;\n\n    // Function to count the number of bits set in a number\n    function bits(x: number): number {\n        let ret = 0;\n        while (x) {\n            ret += (x & 1);\n            x = x >> 1;\n        }\n        return ret;\n    }\n\n    // Function to check if a subset represented by bitmask x is valid (no duplicates)\n    function check(x: number, nums: number[]): boolean {\n        const seen = Array(17).fill(false); // Adjust size according to max possible number\n        for (let i = 0; i < N; i++) {\n            if ((1 << i) & x) {\n                if (seen[nums[i]]) return false; // Duplicate found\n                seen[nums[i]] = true;\n            }\n        }\n        return true;\n    }\n\n    // Function to calculate the incompatibility of a subset represented by bitmask x\n    function calculate(x: number, nums: number[]): number {\n        let Max = -Infinity; // Start with the lowest possible value\n        let Min = Infinity;  // Start with the highest possible value\n        for (let i = 0; i < N; i++) {\n            if ((1 << i) & x) {\n                Max = Math.max(Max, nums[i]);\n                Min = Math.min(Min, nums[i]);\n            }\n        }\n        return Max - Min; // Return the incompatibility\n    }\n\n    // Dynamic programming array to store minimum incompatibilities\n    const dp = new Array(1 << N).fill(Number.MAX_SAFE_INTEGER);\n    const mp = new Map<number, number[]>(); // Map to store subsets by their sizes\n    const requiredSubsetSize = N / k;\n\n    if (requiredSubsetSize === 1) return 0; // If each subset can only have one element\n\n    // Generate valid subsets and group them by size\n    for (let i = 1; i < (1 << N); i++) {\n        const b = bits(i);\n        // Check if the number of bits is a multiple of the required subset size\n        if ((b % requiredSubsetSize) === 0 && (b !== requiredSubsetSize || check(i, nums))) {\n            if (!mp.has(b)) {\n                mp.set(b, []);\n            }\n            mp.get(b)!.push(i); // Store the valid subset\n        }\n    }\n\n    const subsetSizeValues = mp.get(requiredSubsetSize);\n    if (!subsetSizeValues) {\n        return -1; // No valid subsets of required size\n    }\n\n    // Initialize dp values for subsets of the required size\n    for (const x of subsetSizeValues) {\n        dp[x] = calculate(x, nums);\n    }\n\n    // Dynamic programming to calculate minimum incompatibility for all subsets\n    let cur = requiredSubsetSize;\n    while (cur < N) {\n        const currentValues = mp.get(cur);\n        if (currentValues) {\n            for (const x of currentValues) {\n                if (dp[x] === Number.MAX_SAFE_INTEGER) continue;\n                const subsetSizeValues = mp.get(requiredSubsetSize);\n                if (!subsetSizeValues) {\n                    continue; \n                }\n                for (const y of subsetSizeValues) {\n                    if ((x & y) === 0) { // Ensure subsets do not overlap\n                        dp[x | y] = Math.min(dp[x | y], dp[x] + dp[y]);\n                    }\n                }\n            }\n        }\n        cur += requiredSubsetSize; // Move to the next subset size\n    }\n\n    // Return result\n    return dp[(1 << N) - 1] === Number.MAX_SAFE_INTEGER ? -1 : dp[(1 << N) - 1];\n}\n\n```
['TypeScript']