From 69fbd69350d8da18f2721d86054ef3eb7588200d Mon Sep 17 00:00:00 2001
From: Soumya Pandey <43310171+100mya@users.noreply.github.com>
Date: Fri, 13 Oct 2023 16:09:46 +0530
Subject: [PATCH] Create all_possible_subsequences.js

---
 Backtracking/all_possible_subsequences.js | 40 +++++++++++++++++++++++
 1 file changed, 40 insertions(+)
 create mode 100644 Backtracking/all_possible_subsequences.js

diff --git a/Backtracking/all_possible_subsequences.js b/Backtracking/all_possible_subsequences.js
new file mode 100644
index 0000000000..36bb780530
--- /dev/null
+++ b/Backtracking/all_possible_subsequences.js
@@ -0,0 +1,40 @@
+/**
+ * Generates all possible subsequences of the given sequence using backtracking.
+ * Prints each subsequence as it is generated.
+ *
+ * @param {any[]} sequence - The input sequence for which subsequences are generated.
+ */
+function generateAllSubsequences(sequence) {
+    createStateSpaceTree(sequence, [], 0);
+}
+
+/**
+ * Recursively creates a state space tree to iterate through each branch using DFS.
+ * Each state has exactly two children.
+ * It terminates when it reaches the end of the sequence.
+ *
+ * @param {any[]} sequence - The input sequence.
+ * @param {any[]} currentSubsequence - The current subsequence being built.
+ * @param {number} index - The current index in the sequence.
+ */
+function createStateSpaceTree(sequence, currentSubsequence, index) {
+    if (index === sequence.length) {
+        console.log(currentSubsequence);
+        return;
+    }
+
+    // Explore two branches: one without the current element and one with the current element
+    createStateSpaceTree(sequence, currentSubsequence, index + 1);
+    currentSubsequence.push(sequence[index]);
+    createStateSpaceTree(sequence, currentSubsequence, index + 1);
+    currentSubsequence.pop();
+}
+
+// Example usage:
+const seq = [3, 1, 2, 4];
+console.log("Subsequences for [3, 1, 2, 4]:");
+generateAllSubsequences(seq);
+
+const seq2 = ["A", "B", "C"];
+console.log("Subsequences for ['A', 'B', 'C']:");
+generateAllSubsequences(seq2);