fixed test to correctly text relative URLs

doesnt add query param if source & target projects match

app/assets/javascripts/vue_merge_request_widget/components/mr_widget_header.vue

 <script>
 import tooltip from '~/vue_shared/directives/tooltip';
 import { n__ } from '~/locale';
-import { webIDEUrl } from '~/lib/utils/url_utility';
+import { mergeUrlParams, webIDEUrl } from '~/lib/utils/url_utility';
 import Icon from '~/vue_shared/components/icon.vue';
 import clipboardButton from '~/vue_shared/components/clipboard_button.vue';
 
@@ -43,11 +43,10 @@ export default {
       return this.isBranchTitleLong(this.mr.targetBranch);
     },
     webIdePath() {
-      return webIDEUrl(
-        `/${this.mr.sourceProjectFullPath}/merge_requests/${this.mr.iid}?target_project=${
-          this.mr.targetProjectFullPath
-        }`,
-      );
+      return mergeUrlParams({
+        target_project: this.mr.sourceProjectFullPath !== this.mr.targetProjectFullPath ?
+          this.mr.targetProjectFullPath : '',
+      }, webIDEUrl(`/${this.mr.sourceProjectFullPath}/merge_requests/${this.mr.iid}`));
     },
   },
   methods: {

spec/javascripts/vue_mr_widget/components/mr_widget_header_spec.js

@@ -150,19 +150,39 @@ describe('MRWidgetHeader', () => {
 
         expect(button.textContent.trim()).toEqual('Open in Web IDE');
         expect(button.getAttribute('href')).toEqual(
-          '/-/ide/project/root/gitlab-ce/merge_requests/1?target_project=gitlab-org/gitlab-ce',
+          '/-/ide/project/root/gitlab-ce/merge_requests/1?target_project=gitlab-org%2Fgitlab-ce',
         );
       });
 
-      it('renders web ide button with relative URL', () => {
+      it('renders web ide button with blank query string if target & source project branch', done => {
+        vm.mr.targetProjectFullPath = 'root/gitlab-ce';
+
+        vm.$nextTick(() => {
+          const button = vm.$el.querySelector('.js-web-ide');
+
+          expect(button.textContent.trim()).toEqual('Open in Web IDE');
+          expect(button.getAttribute('href')).toEqual(
+            '/-/ide/project/root/gitlab-ce/merge_requests/1?target_project=',
+          );
+
+          done();
+        });
+      });
+
+      it('renders web ide button with relative URL', done => {
         gon.relative_url_root = '/gitlab';
+        vm.mr.iid = 2;
 
-        const button = vm.$el.querySelector('.js-web-ide');
+        vm.$nextTick(() => {
+          const button = vm.$el.querySelector('.js-web-ide');
 
-        expect(button.textContent.trim()).toEqual('Open in Web IDE');
-        expect(button.getAttribute('href')).toEqual(
-          '/-/ide/project/root/gitlab-ce/merge_requests/1?target_project=gitlab-org/gitlab-ce',
-        );
+          expect(button.textContent.trim()).toEqual('Open in Web IDE');
+          expect(button.getAttribute('href')).toEqual(
+            '/gitlab/-/ide/project/root/gitlab-ce/merge_requests/2?target_project=gitlab-org%2Fgitlab-ce',
+          );
+
+          done();
+        });
       });
 
       it('renders download dropdown with links', () => {