diff --git a/Dynamic Programming/Integer Partition/code.js b/Dynamic Programming/Integer Partition/code.js
index 3618098c..da4d0380 100644
--- a/Dynamic Programming/Integer Partition/code.js
+++ b/Dynamic Programming/Integer Partition/code.js
@@ -8,48 +8,61 @@ const logger = new LogTracer();
Layout.setRoot(new VerticalLayout([tracer, logger]));
const integer = Randomize.Integer({ min: 5, max: 14 });
const D = [];
-const A = [];
+const A = "";
for (let i = 0; i <= integer; i++) {
D.push([]);
- D[0][i] = 1;
- D[i][1] = 1;
- for (let j = 0; j <= integer; j++) D[i][j] = 0;
+ D[i][0] = 1
+ for (let j = 1; j <= integer; j++) D[i][j] = 0;
}
tracer.set(D);
Tracer.delay();
// }
function partition(A, n, p) {
- // logger {
- if (n === 0) logger.println(`[${A.join(', ')}]`);
- // }
- else {
- let end = n;
- if (p !== 0 && A[p - 1] < n) end = A[p - 1];
- for (let i = end; i > 0; i--) {
- A[p] = i;
- partition(A, n - i, p + 1);
+ // logger {
+ if (p == 0) logger.println(`[${A.split('').join(', ')}]`);
+ // }
+ else {
+ if (n > 1) partition(A, n - 1, p);
+ if (n <= p) partition(n + A, n, p - n);
}
- }
}
function integerPartition(n) {
- // Calculate number of partitions for all numbers from 1 to n
- for (let i = 2; i <= n; i++) {
- // We are allowed to use numbers from 2 to i
- for (let j = 1; j <= i; j++) {
- // Number of partitions without j number + number of partitions with max j
- // visualize {
- tracer.select(i, j);
- Tracer.delay();
- // }
- D[i][j] = D[i][j - 1] + D[i - j][Math.max(j, i - j)];
- // visualize {
- tracer.patch(i, j, D[i][j]);
- Tracer.delay();
- tracer.depatch(i, j);
- tracer.deselect(i, j);
- // }
+
+ // cycle through each cell of matrix
+ for (let i = 1; i <= n; i++) {
+ for (let j = 1; j <= n; j++) {
+ if (i > j) {
+ // visualize {
+ tracer.select(i, j);
+ Tracer.delay();
+ // }
+ // set cell to cell above it
+ D[i][j] = D[i - 1][j];
+ // visualize {
+ tracer.patch(i, j, D[i][j]);
+ Tracer.delay();
+ tracer.depatch(i, j);
+ tracer.deselect(i, j);
+ // }
+ }
+ else {
+ // visualize {
+ tracer.select(i, j);
+ Tracer.delay();
+ // }
+ // grab above cell and add it to previous cell
+ const above = D[i - 1][j];
+ const left = D[i][j - i];
+ D[i][j] = above + left;
+ // visualize {
+ tracer.patch(i, j, D[i][j]);
+ Tracer.delay();
+ tracer.depatch(i, j);
+ tracer.deselect(i, j);
+ // }
+ }
}
}
return D[n][n];
@@ -58,7 +71,7 @@ function integerPartition(n) {
// logger {
logger.println(`Partitioning: ${integer}`);
// }
-partition(A, integer, 0);
+partition(A, integer, integer);
const part = integerPartition(integer);
// logger {
logger.println(part);
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