added proof validation method

src/data-structures/tree/merkle-tree/MerkleTree.js

@@ -146,6 +146,57 @@ class MerkleTree {
         return result
     }
 
+    /**
+     * verify
+     * @desc verify a proof generated by getProof()
+     * @param {Proof} proof - proof object generated by getProof()
+     * {
+     *    node, index, path
+     * }
+     * @return {Boolean} - If true, the correct merkle root can be calculated through the path provided by input proof, false other wise.
+     *@example
+     * ```js
+     *const tree = new MerkleTree(['a', 'b', 'c', 'd', 'e']);
+     *const proof = tree.getProof('b'))  // {node: 'b', index: 1, path: [[3,0],[2,1],[1,1]]}
+     *console.log(tree.verify(proof)) //true
+     *```
+     */
+     verify(proof) {
+        const node = proof.node
+        const index = proof.index
+        const path = proof.path
+
+        if (node === undefined || node === null) return false
+        if (index >= this.originalArray.length ) return false
+        let hashed = this.hash(this.inputHash(node))
+        // If path is [] and index == 0 means the input array contains only one node. Just compare the hash of itself with root
+        if (path === []) {
+            if(index === 0) return hashed === this.root
+            return false
+        }
+
+        // Rebuild hashes bottem up by only calculating the necessary nodes, compare the final hash with root
+        while(path.length > 0) {
+            const current = path.shift()
+            const row = current[0]
+            const index = current[1]
+
+            try {
+                const sibling = this.fullPath[row][index]
+                // If the coordinate indicates the sibling is a left node, do H(sibling + current)
+                // H(current + sibling) otherwise*
+                if ((index%2) == 0) {
+                    hashed = this.hash(sibling + hashed)
+                } else {
+                    hashed = this.hash(hashed + sibling)
+                }
+            } catch (err) {
+                return false
+            }
+        }
+
+        return hashed === this.root
+    }
 
 }