Add integer partition.

src/algorithms/math/integer-partition/integerPartition.js

@@ -0,0 +1,47 @@
+/**
+ * @param {Number} number
+ */
+export default function integerPartition(number) {
+  // Create partition matrix for solving this task using Dynamic Programming.
+  const partitionMatrix = Array(number + 1).fill(null).map(() => {
+    return Array(number + 1).fill(null);
+  });
+
+  // Fill partition matrix with initial values.
+
+  // Let's fill the first row that represents how many ways we would have
+  // to combine the numbers 1, 2, 3, ..., n with number 0. We would have zero
+  // ways obviously since with zero number we may form only zero.
+  for (let numberIndex = 1; numberIndex <= number; numberIndex += 1) {
+    partitionMatrix[0][numberIndex] = 0;
+  }
+
+  // Let's fill the first row. It represents the number of way of how we can form
+  // number zero out of numbers 0, 1, 2, ... Obviously there is only one way we could
+  // form number 0 and it is with number 0 itself.
+  for (let summandIndex = 0; summandIndex <= number; summandIndex += 1) {
+    partitionMatrix[summandIndex][0] = 1;
+  }
+
+  // Now let's go through other possible options of how we could form number m out of
+  // summands 0, 1, ..., m using Dynamic Programming approach.
+  for (let summandIndex = 1; summandIndex <= number; summandIndex += 1) {
+    for (let numberIndex = 1; numberIndex <= number; numberIndex += 1) {
+      if (summandIndex > numberIndex) {
+        // If summand number is bigger then current number itself then just it won't add
+        // any new ways of forming the number. Thus we may just copy the number from row above.
+        partitionMatrix[summandIndex][numberIndex] = partitionMatrix[summandIndex - 1][numberIndex];
+      } else {
+        // The number of combinations would equal to number of combinations of forming the same
+        // number but WITHOUT current summand number plus number of combinations of forming the
+        // previous number but WITH current summand.
+        const combosWithoutSummand = partitionMatrix[summandIndex - 1][numberIndex];
+        const combosWithSummand = partitionMatrix[summandIndex][numberIndex - summandIndex];
+
+        partitionMatrix[summandIndex][numberIndex] = combosWithoutSummand + combosWithSummand;
+      }
+    }
+  }
+
+  return partitionMatrix[number][number];
+}