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Commit 41855b0

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Merge pull request #328 from cheehwatang/add-1155-NumberOfDiceRollsWithTargetSum
Add 1155. Number of Dice Rolls With Target Sum (Dynamic Programming - Tabulation)
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‎README.md‎

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<th>Solution</th>
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<th>Topics</th>
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</tr>
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<tr>
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<td align="center">September 7th</td>
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<td>1155. <a href="https://leetcode.com/problems/number-of-dice-rolls-with-target-sum/">Number of Dice Rolls With Target Sum</a></td>
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<td align="center">$\text{\color{Dandelion}Medium}$</td>
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<td align="center">
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/1155.%20Number%20of%20Dice%20Rolls%20With%20Target%20Sum/NumberOfDiceRollsWithTargetSum_Tabulation.java">Dynamic Programming - Tabulation</a>
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</td>
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<td align="center">
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<a href="#dynamic-programming">Dynamic Programming</a>
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</td>
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</tr>
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<td align="center">September 6th</td>
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<td>1137. <a href="https://leetcode.com/problems/n-th-tribonacci-number/">N-th Tribonacci Number</a></td>
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<a href="#hash-table">Hash Table</a>
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<td align="center">September 2nd</td>
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<td>923. <a href="https://leetcode.com/problems/3sum-with-multiplicity/">3Sum With Multiplicity</a></td>
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<td align="center">$\text{\color{Dandelion}Medium}$</td>
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/923.%203Sum%20With%20Multiplicity/ThreeSumWithMultiplicity_Counting.java">Counting</a>
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<a href="#array">Array</a>,
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<a href="#counting">Counting</a>
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</td>
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</tr>
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</table>
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</br>
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</td>
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<td></td>
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<tr>
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<td align="center">1155</td>
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<td><a href="https://leetcode.com/problems/number-of-dice-rolls-with-target-sum/">Number of Dice Rolls With Target Sum</a></td>
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<td align="center">Java with Dynamic Programming using
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<a href="https://github.com/cheehwatang/leetcode-java/blob/main/solutions/1155.%20Number%20of%20Dice%20Rolls%20With%20Target%20Sum/NumberOfDiceRollsWithTargetSum_Tabulation.java">Tabulation</a>
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</td>
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<td align="center">$\text{\color{Dandelion}Medium}$</td>
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<td align="center">
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<a href="#dynamic-programming">Dynamic Programming</a>
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</td>
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<td></td>
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</tr>
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<td align="center">1578</td>
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<td><a href="https://leetcode.com/problems/minimum-time-to-make-rope-colorful/">Minimum Time to Make Rope Colorful</a></td>
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package com.cheehwatang.leetcode;
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// Time Complexity : O(n * k * target),
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// where 'n', 'k' and 'target' are the variables used by the method.
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// For each dice, 'n', we check each values of 'target' to add the number of faces 'k' that can sum to 'target',
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// in a 3 layer nested for-loops.
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//
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// Space Complexity : O(n * target),
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// where 'n' and 'target' are the variables used by the method.
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// We use a matrix of 'n' rows with 'target' columns for tabulation.
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public class NumberOfDiceRollsWithTargetSum_Tabulation {
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// Approach:
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// A dynamic programming problem where there are overlapping subproblem,
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// for which each roll has possible 1 to k number face-up.
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// Here, the iterative and tabulation method is used.
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// By reducing the target by the face-up number each roll (hence n - 1),
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// the successful sequence of rolls is achieved when n = 0 and target = 0, which forms the base case for the table.
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public int numRollsToTarget(int n, int k, int target) {
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// As the array is 0-indexed, we need + 1 length to accommodate 'n' and 'target' respectively.
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int[][] table = new int[n + 1][target + 1];
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// The seed/base case for successful sequence in the table.
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table[0][0] = 1;
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// Iterate through the table to get the result for all possibilities.
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int modulus = (int) (1e9 + 7);
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < target; j++) {
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// Skip if the position in the array is 0, meaning nothing to add to the j + 1 to k positions.
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if (table[i][j] == 0) continue;
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for (int face = 1; face <= k; face++) {
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if (face + j <= target) {
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table[i + 1][j + face] = (table[i + 1][j + face] + table[i][j]) % modulus;
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}
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}
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}
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}
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return table[n][target];
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}
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}

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